Differentiation with Mathscapes Gr 6

I'm trying to make sure my high achievers are well served in my class. I'm considering rearranging my routine and class systems to open it up to allow for more differentiation. I've learned that I have to set goals at the start of each unit, and make materials available for all of my students, and demand less control moment to moment while the learning becomes more student led rather than teacher directed.

I'm teaching Whole to Parts, lesson 8 right now to my 6th graders. Anyone have any input on my differentiation efforts specifically relating to 6th grade Mathscapes?

Long division

Teaching long division "the Maggie way" was very rewarding. I just finished day two and most of my fourth graders can not only do it, but can explain the hows and whys of what they are doing. The minipulatives and the new language worked wonders. I am a believer.

On a completely different subject, according to the new MLRs fourth graders are supposed to be able to visualize a square meter, so that pvc square and cube I invested in for place value will now pay further dividends.

Increased Student Thinking

I am beginning to see students voluntarily verbalizing their thinking and finding their own way of doing things. It is VERY exciting! A recent example, the math program that we use teaches a strategy for adding 19 to a number. The suggested strategy is to add 20 and then subtract 1 from the sum. So, 25 + 19 would be 25+20=45, then we subtract 1 from that sum 45-1= 44. One of my 7th graders very quickly said, "Why would I need to do that? Why couldn't I just take one away from the 25 making it a 24? Then I put that 1 with the 19 to make it 20. My new problem is 24+20 which equals 44." YES! And his process made more sense to the others in the group, so we are now using Nick's method instead of the suggested book strategy. This particular student has always been very hesitant when it comes to math, but ever since he had that success, he is starting to take more risks and is always looking for his own way. I'm loving watching his thought processes!

Blind Student

Hello Everyone, 

I've been out of blog, couldn't log in, but FINALLY have been able to set up a new account. So, here goes...

One big dilemma that I am having in math instruction is dealing with how to get across math concepts to a blind child. Has anyone dealt with this in the past? I've been using a lot of manipulatives in class, but am having trouble with how do I modify this so that he can "see" what we are doing. 

National Math Advisory Panel's Report

I found some fascinating reading for you all over the holidays that comes from the National Math Advisory Panel, a group established by the Bush Administration in 2006 to pull together all the research that has been done in the field of teaching mathematics. This was in response to a study that showed that American students performed significantly below world-wide standards in math. The final report of this group was published in March of this year. You can find the report in its entirety at http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf To get to the nuts and bolts of the report, scroll to page xvi. There's lots of fodder for blogging if you need ideas! If you'd rather watch video, there are some overviews at
http://dww.ed.gov/topic/topic_landing.cfm?PA_ID=8&T_ID=20
I was especially interested in item 14 : "Experimental studies have demonstrated that changing children's beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes: When children believe their efforts to learn make them "smarter," they show greater persistence in mathematics learning....This is a critical point because much of the public's self-evident resignation about mathematics education...seems rooted in the erroneous idea that success is largely a matter of inherent talent or ability, not effort."
We've talked about the importance of having a positive attitude, but this goes a step beyond that. I think looking at a student's efforts sometimes happens in my own teaching, but not in a thoughtful, conscious way. That's something I can start to do right away.

the power of games

We have a school-wide initiative this year to use the Investigations curriculum. My new 3rd grade students have been struggling to comprehend and be able to apply the mathematical concepts that are based on already having the foundation of two to three years of Investigations under their belts, which they do not have. As usual, it has been a dance of one step forward, two (or more) steps back, because there is no point in continuing to try to move forward if the groundwork is not truly understood.
Investigations makes much use of games, and for the first time in my teaching of math, I am not limiting their time playing games to only a few trials (out of a need to "accomplish more.") We have been playing lots of games over and over again during classtime, and I am really amazed and pleased with the learning that has been going on during this time. It's a great way for kids to internalize the math concepts (in this case, place value, "trading up," and being able to see 120 as 12 tens, for example) while they are enjoying themselves! They are really learning concepts and beginning to be able to apply them in other mathematical settings.
Looking at the learning involved in playing games, and modifying for differentiation was the focus of the coach's training sessions, and Maggie also used games in both musters this past month, encouraging us to think how a game could be made easier/harder. I think this focus has helped me to realize how powerful games can be, and has given me permission to spend the time playing games in the classroom. And it's a lot more fun!

Suggestions Please

My students have been working on their place value and most of them can now work with small and large numbers in terms of standard, written, and expanded forms quite well. Very few of them may still need some work on one of those, but overall they are fine.

This past week, in iSucceed Math program, I began to work on their rounding numbers and they are fine up to the hundreds but for larger numbers they really get confused and just look at the number they need to round, rather than look at the number on the right, to determine whether they need to bump that number up or they should keep the number the same.

I have worked with each group on rounding numbers and they practiced, where they created their own 6 or 7 digit numbers and together they round the numbers. Their conversation was very interesting and I had to restrain myself from interjecting by trying to correct spelling words right in front of them. Most of them, occasionally, looked at me for some kind of signs, especially when they needed to argue. We checked them together and that was when they found out whether they were correct or not. I usually gave students practice sheets but thought that if they could create their own numbers it would be better. It went particularly well, I think because each of them contributed to this.

I have used the number lines and the number charts, but are there other tools or games to make it more interesting for them? Perhaps we can create games:):)

developing numeracy with the rekenrek (grades 1 and 2)

I have been searching for ways to develop numeracy among my sped students at about grade 1 and 2 and have had a lot of good results using the rekenrek. It's a small abacus with 20 beads that is divided up into fives (five red and five white beads on the top row and the same on the bottom row). I find it really helps my students to see how to make tens when adding numbers (such as seeing that 5+ 6 is actually 10 + 1 and 7 +7 is actually 10 +4) . Rather than just struggling to memorize those facts or always counting up to find the answer, they can begin to visualize pictures in their mind (by first seeing it on the rekenrek). If anyone is interested you can find a lot of information by looking up "www.rekenrek.com" on the internet. If anyone has other ideas about developing numeracy (especially with addition/subtracion facts) with this grade level I would love to hear your ideas.

WEBINAR K-3 Portland

The K-3 Webinar will be at Riverton School, Tuesday, Nov. 4. It will be in the Discovery Center. Enter the School, not the community center, turn right and head down the hall. The discovery center is on the left just before the library.

I need your help!

Do you have any information on color blindness and how it effects a child's spacial sense?
I'm using Investigations for the first time and the children have been building staircases using a set of connectiong cubes labeled 1-12 with partners. After building all the steps they were asked to put them in order. (This was done over time). All went well with counting the cubes and putting them in order by looking at the set of cubes labeled 1-12 but when asked what was added on to each number to get the the next and to transpose what they had built on to graph paper, one of my students could not tell or show me what he had done. He really couldn't see the staircase. I had him feel it and he acknowledged it was different but.....

Going back to mangoes.

This is the kind of post Maggie encouraged me to make on Saturday, so here it goes.
We have been working on factors and multiples. After working together to find all the factor pairs for 100, the students were asked to figure out the factor pairs for 200, 300 etc. What I knew from observing the kids was that some (a few) intuitively knew the factor pairs for 100 and, perhaps one or two of those few would know how to use what they knew about 100 to figure out the pairs for the next groups of 100. What was really bothering me was that I knew most of the students did not have nearly enough experience "playing" with materials to see, let alone, discover the relationships between the groups of 100. So, I stopped the paper and pencil work for two days and had the students build the factor pairs for the 200s, 300s. What happened was great - the kids started seeing the "groups of" that made up the multiples and discovered they could figure out all the factor pairs and consequently discovered the patterns involved in seeing the relationships among the multiples. This is really hard to explain without feeling that it sounds silly and simplistic, but it wasn't and I am a happy that I dropped where the program was sending me and took the time to serve some mangos.

Impact of Computer Games

Deb Smith and I got together to blog on our early release this afternoon. We began discussing play and how important it is for children. (We are strickly thinking of 5 and 6 year old children.) We read the article Piaget Development Statagies and I fould it fasinating how children move from stage to stage.
The following is the site if you would like to read it.

coe.sdsu.edu/eet/Articles/piaget/start.htm

Our world is changing and I wonder how video games, "the wee", computer games and the lack of playing games at home will effect children moving from the different stages. I have been amazed to hear from some kindergarteners this fall that on the weekends they play video games or are 4 wheeling.

I also wonder about Special Ed students (say Elementary) do they ever move from Preoperational Stage to Concrete Operational Stage or do they flip flop back and forth until they are in Middle or High School.

Pondering Play and Developmental Stages

I have been thinking all week about our Saturday morning’s MTM play session and watching my kindergarten students. Instinctively I understand the value of play, play that is not always incorporated into the lessons of many math programs (or at least not enough play). Or perhaps it is the time in a school day that does not allow for play. (For the purposes of this blog I am using the word play similarly to the way Maggie speaks of investigations.)

Basically, what I have been thinking is how easy it is to forget how children/students build their understanding of mathematical concepts ( through real world play or investigations). One of my favorite theorists on cognitive development is Jean Piaget. Here is a website Gay and I found on googling one day that discusses age/stage theory in relationship to cognitive development, specifically mathematical development:
http://coe.sdsu.edu/eet/Articles/piaget/index.htm

Added thoughts to Sat. 10/18 classGeoboards

We began with this question: How many ways are there to make a square on a 5x5 geoboard? The we asked:
Is there a numerical pattern or formula that can be used to determine the number of squares contained in any geoboard square?
Deb & Gene

Clarity of Purpose

It was helpful to me to hear Maggie (and others) declare that we are trying to learn to teach conceptually rather than procedurally. These words helped me to clarify my efforts

Ethnomathematics at Bates

Hi Everybody,

For those who went to the Ethnomathematics talks at Bates, could you share what was discussed please? I was not able to attend but am curious about what went on there.

Thank you so much!!
Ina

Learning Environment

I think that I have mentioned in an earlier post that I find the articles in Teaching Children Mathematics (NCTM) very valuable. They are very relevant to learning in elementary mathematics classrooms.

The most recent issue arrived today and the focus is "Learning Environments That Support Mathematical Understanding" - sound familiar!

I've only had time to read one of the articles, Learning to Think and Thinking to Learn. I seem to always set the goal to leave more lesson time for discussion and continue to fail to make the time. I will say that using the new Investigations program has helped me immensely because it is built into each session - yippee!

This article provides classroom examples for using incorrect solutions to facilitate discussions, encouraging students to question each other's solutions, and allowing time to develop understandings. The author also talks about extroverts and introverts and providing for both types of thinkers. There is nothing earth shattering in the article but it reinforces strategies I have used and has given me some ideas for tweaking what I do so I can be more effective. If you have a learning community/study group with a mathematics focus at your school this article has a reflect and discuss page that is a good way to guide the process of self-observation and self-reflection.

Have you used incorrect solutions to facilitate discussions in your classroom? Do you have the students share (as in the article) or do you share the errors anonymously?

Dates Please

Maggie, could you post some specifics about our upcoming Webinars?  We are wondering about locations and if we need to bring anything.

My principal today was asking about the October Coach Training, Administrative Support and Muster, so we will be looking for details about those events as well.

Thanks!

Accelerated students

I would be interested to know what other districts do to provide math instruction for accelerated students. Our teachers have developed a variety of activities, extensions, etc for kids who welcome and can handle more expanded math experiences beyond the curriculum, but what about the extraordinarily motivated and accomplished rare student who masters the curriculum, standards, extensions, etc? We currently have 2 such students in our elementary school, and with no GT program or other support, per se, have accelerated them to the next grade level in math, and both are at the top of their math classes. Was that the best solution for them? What have other districts done?
Thanks,
Debbie

Speaking of Master Teachers...

Our very own Debbie Butterworth has been recognized with an award by the Parents Foundation of Cape Elizabeth for her work in the K-2 Math-Lab!  

Debbie, perhaps you would take a few minutes when we next meet to share with the rest of the group so we can better understand your work there.

Congratulations... we are proud of you!

Ethnomathematics Talk at Bates

Hi everyone... a reminder that Ubiritan D'Ambrosio (Bonnie introduced us to his work in ethnomathematics this summer) will be a guest speaker at Bates on Thursday.  There will be a lecture at 4:30 and a public talk at 7:30.  Copy paste the following link into your browser address bar for specifics:  www.bates.edu/x182781.xml 

I will be driving down for the event - hope to see you there!

Maggie

Ethnomatematics and time

The additional article from Bonnie that highlights an interview regarding Ethnomathematics is quite weighty, a lot to think about. After reading it I decided to begin thinking about one small part of the article as it relates to my classroom. An earlier area of exploration in our blogs encompassed creating a math climate. On page 99 of the last from Bonnie article Milton speaks of “a broader view of mathematics, which embraces ideas, processes, methods, and practices that are related to different cultural environments.” When I read this comment the word embraces rang in my head. The math climate or, for that matter overall classroom climate is optimal when the students thinking, ideas, processes are embraced. When we meet student where they are with prior knowledge we create a culture, yes, a community of learning in which children feel valued, therefore safe to take risks and share their thinking.
We, all at some point in our teaching careers, struggle with the demands of insuring that the curriculum benchmarks (MLR’s) are met, and that we expose our students to the concept strands of our math programs. After reading this article and reflecting on my various experiences teaching, includes those experiences with ELL’s, I found myself thinking about time and how it can be used to enhance a math lesson (any lesson). There was another comment in the article by Ubi that I found myself thinking about. “It is natural, in the view of many educators, that by making children happy and at the same time building a recognition and respect for other cultures, there is a concern for losing ‘precious’ instructional time, which could be used [for] teaching mechanical techniques.” I wish I had some profound insight to share about the use of time and building an embracing community that supports a positive learning climate for all areas of learning including math. What I can say is that creating an embracing environment is one of the professional growth areas to which I feel strongly committed at this point in my life as a teacher. Sylvia Ashton-Warner said it best, “But I must do what I believe in or nothing at all. Life’ so short.”
There are several books that guide my thinking and planning in my classroom, and support me on my journey:

TEACHING CHILDREN TO CARE Management in the Responsive classroom
By Ruth Charney

SERIOUS PLAY IN THE PRIMARY CLASSROOM Empowering Children
Through Active Learning Experiences
By Selma Wasserman

MORAL CLASSROOMS, MORAL CHILDREN Creating a Constructivist
Atmosphere in Early Education
By Rheta DeVries & Betty Zan

DEVELOPING CROSS-CULTURAL COMPETENCE A Guide for Working
With Young Children and Their Families
By Eleanor W. Lynch & Marci J. Hanson

THE MIDDLE OF EVERYWHERE Helping Refugees Enter The American
Community
By Mary Pipher
TONGUE-TIED The Lives of Multilingual Children in Public Education
Edited By Otto Santa Ana

It is a juggling act for sure balancing time with the diverse needs of our students. How do you approach diversity in your classroom as it relates to math and beyond?

Document Camera Possibilities

I was searching for ways to use document cameras on the web and came across an interesting application for them:  this particular teacher uses it to document student work as they move through investigations.  She created a digital folder for each student and when a project was finished, the students used the documentation to help explain to their parents what the project was about and how they were thinking.  At the end of the year, she burned each folder to a CD and added it to their portfolio.  She recommends going to Reggio Emilia sites for more information about the power of documentation.  Here is a link for you to start with:

http://en.wikipedia.org/wiki/Reggio_Emilia_approach

Reggio Emilia is a small place in Italy  - you can read how the approach was birthed there.  One thing that stood right out is, although they are saying it in a different way, it's all about eating mangoes!!

The explanation made me think of so many things you could do with this... what about using a bulletin board to post photo series taken as pairs or groups of students worked on an investigation, and getting others to imagine what each pair/group was thinking and all the ways that thinking might be recorded.  

For RTI... imagine the applications!  What a wonderful reference for them to return to - reminding them of their thinking path... could create a small album with chapters (concepts) and, again, have them think of ways to record their thinking path.  It seems the possibilities are endless.  

Happy reading! 

Posing or asking the right questions can be crucial to learning, esp. for the challenged students.

When we are teaching new concepts, the way that we ask a question can create clear or murky understanding. Posing a quiding question that is open is essential, so that there is room for inquiry and student exploration into the answer. Students
need to search out the answer by creating connections, adding vocabulary, and collecting their own data. Using the data and discussing their understanding will lead them forward. But it is up to us, as educators to create the "right" questions, questions that leave room for student thinking and lead into the concept that is to be discovered.
There is a text titled, "Good Questions for Math Teaching" by Peter Sullivan and Pat Lilburn.
I think that if we want students to investigate and learn the what and why of math before we introduce the symbols, than we need to be very careful of our language and the questions we ask in math. Students need to gain confidence in inquiry and dare to make mistakes along the way to be stronger thinkers and problem solvers, "math thinkers", who can take the challenge as we teach new concepts throughout the year.

Teaching Math to Students with Disabilities- Reading Room

The following article from TEC (Teaching Exceptional Children), is titled "Teaching Math to Students with Disabilities". The whole article is worth reading but I particularly enjoyed an excerpt on creative problem-solving activities, which I have included a piece of.

"Brian Bottge, professor at the University of Wisconsin, Madison, developed a unique way to bypass reading difficulties and get students enthused about math word problems. He presents word problems on video. Students can hit the remote to get the information they need to solve the problem, and video makes it easier for students to visualize the problem. The second and equally important aspect of video problem solving is that the problems posed are intriguing: building skateboard ramps and hovercrafts. These types of real-life problems embed numerous skills, skills that suddenly become imperative to learn. Students realize they need to know how to add fractions to see if the lumber they are cutting will be the right size."

Link:

http://www.cec.sped.org/AM/Template.cfm?Section=Search&template=/CM/HTMLDisplay.cfm&ContentID=7015

Prior Knowledge

Most educators agree about the value of assessing a student's prior knowledge to determine how best to proceed with instruction.  There are several strategies we might use to do that; for the purpose of this post, let's think about good questions that have potential to make student thinking visible.  

Suppose you wanted to assess a student's prior knowledge/understanding of addition/subtraction.  You have invited her to tell you something she knows about adding.  Her response is "5+5=10".

What will you say next?

On Teaching Thinking: Art Costa

There is a short article from ASCD that is worth reading:

On Teaching Thinking: A Conversation With Art Costa

Although it isn't specific to mathematics, the content is certainly applicable to mathematics.  As you read it, try to see it through a math lens.  What questions does it bring to mind?

Here is the link:

https://www.ascd.org/ASCD/pdf/journals/ed_lead/el_198804_brandt2.pdf

Math Climate

Two books I am reading this fall to help with a positive climate - both from Responsive Classroom

The Power of Our Words by Paula Denton

In Our School, building community in elementary schools by Karen L. Casto and Jennifer Audley

I have just got them and plan to start reading shortly. Will comment after I have read them. And would appreciate feedback from anyone who has already read one or both of these books.

Susan has a question

Please go to the list of labels at the left and click on 'Logistics'.  Susan has posted a question about time that each and every one of us struggles with. (I'm trying to stay out of it until a few comments have been posted.) 

New Article on Ethnomathematics

Bonnie has sent us another article on Ethnomathematics.  The more I read about this topic the more fascinated I become with this common-sense approach to building mathematical capacity in our schools and society.  It is more the norm than not, these days, to have significant numbers of culturally diverse populations in our communities and schools.  (Portland is a wonderful example of this, with over 80 different languages spoken in the homes of their students.)  That is not to say that the study of Ethnomathematics is a panacea for our current dilemma in mathematics, but it offers valuable insight as we strive to meet the needs of all of our students, not only for their own benefit but for that of society's as well.  After all, let's face it... we have a lot of catching up to do and cannot afford to waste one ounce of mathematical potential!

The other thing that pokes me in the eye as I read more, is how similar we are all over the planet (in many ways, but here I am addressing mathematics specifically); we all address the same ideas regardless of how those ideas are represented (symbols) or the procedures we use to manipulate them.  Reason gives us the logical sequel... the mark (symbol) is not the math - the real math is the IDEA represented by that mark.  Teaching IDEAS rather than MARKS seems the only reasonable choice.  

New Article on Ethno-Mathematics from Bonnie

Bonnie has sent us another article on Ethno-Mathematics.  The more I read about this topic the more fascinated I become with this common-sense approach to building mathematical capacity in our schools and society.  It is more the norm than not these days to have significant numbers of culturally diverse populations in our communities and schools.  (Portland is a wonderful example of this, with over 80 different languages spoken in the homes of their students).  The study of Ethno-Mathematics is not a panacea for our mathematics dilemma, but it offers valuable insight as we strive to meet the needs of all of our students, not only for their own benefit but for that of society's as well.  After all, let's face it... we have a lot of catching up to do and cannot afford to waste one ounce of mathematical potential!  

The other thing that  continues to poke me in the eye as I read, is how similar we are all over the planet (in many ways, but here I am addressing mathematics specifically); we all address the same ideas regardless of how those ideas are represented (symbols) or the procedures we use to manipulate them.  Reason gives us the logical sequel... the mark (symbol) is not the math - the real math is the idea represented by that mark.  Teaching ideas rather than marks seems the only reasonable choice.  

Happy Reading!

Maggie

Practice for struggling students

Maggie's comment:
Pat, Can you elaborate a bit on what 'extra practice' means for your struggling students please? I am curious as to what that looks like.

I think it might be helpful to have a place to post ways that people provide extra practice so I am starting another post.

I will give examples from our second grade classroom.
During the past year we had a boy in our class who struggled across the board academically. He had a great deal of difficulty with all math concepts. As Margaret posted earlier we invite our families in for an entry conference prior to school and last August started doing a brief math numeracy assessment. Using the data collected from that assessment and individual assessments throughout the year I was able to identify specific skills that this student and a few others were missing. At our school we are lucky to have some excellent classroom volunteers. One of ours is my mother who is a retired teacher with strengths in the area of math. She sat with this particular boy on a regular basis throughout the year and helped him with skills that I shared with her. He could build 2-digit numbers in only one way so she used materials to help him think more flexibly about the way numbers could be built. He couldn't read three digit numbers so they practiced together. He had a great deal of difficulty learning the doubles addition facts. With the extra practice he was able to master each skill and use it throughout the year in our math lessons. Now the question is: will he remember everything this year? Other volunteers worked with students who needed less extra practice and probably saw them a few times during the year.

Margaret Slocumb and I team teach so we are often able to have flexible groupings. I might work with a large group of students who are successful in math while Margaret provides many additional practices for the students who are "not getting it yet." Within that group she often identifies a very small group that needs even more practice and she works with them. Having two of us responsible for the class (usually 32-40 students) allows for more flexibility.

When I have parents who want to be helpful with math at home I try to be very specific about what they can do to help. I give them just one or two things to work on at a time. I also stress the need to make it fun - not endless drill!

A side note: Yesterday during an entry conference I was goal setting with a girl and her father. She said that she needed some work in spelling and the father said, "Oh, that will always be trouble for you because I am not good at spelling." My response, "Now, just because you are not good at spelling does not mean that _____ can't learn to spell." Then I assured the girl that she was going to do just fine at spelling this year. I must remember to say something similar when a parent brings up their own math difficulties.

Articles-postive climate

Maggie asked that I repost this reference to articles in a post labeled "Reading Room" so here it is:

I have recently read two articles that I think will be helpful as I meet my students where they are and encourage them to move forward in their learning. I think that you can probably get the articles through Marvel. I belong to NCTM and ASCD so I receive the journals and find them very helpful.
The articles are:"Identifying Opportunities to Connect Parents, Students, and Mathematics," Teaching Children Mathematics, August 2008. The author shares her experience with family math nights. Margaret and I have held a family math night during each of the last two school years. I am sure that we will do it again (with Sheila) but I am wanting to rethink some of our activities.
"The Power of Our Words," Educational Leadership, September 2008. This article is useful across all curriculum and refers to the Responsive Classroom approach.
Both articles are quite brief and I think that they will help me to set a positive climate for my students and their families.

Good Climate for Learning

Creating a positive learning environment is not exclusive to mathematics. Creating a student-centered classroom where academic choice, respect for individual learning styles and the safety to take risks are the accepted norm is part of my classroom management goal each year. MTM math academy served as a reminder of how important it is to provide an environment where students are encouraged to explore materials to understand concepts, free to make mistakes while they are building their understanding.
One thing I will do differently this year is give students more time to construct understanding and not feel pressured to get "everything in". I believe this will set a new tone - giving all students the freedom to spend the time they need to "get it".

I have at least two professional books I plan to read this year regarding building positive climate in my classroom. The first I am reading is The Power of Our Words by Paula Denton (same author as the Ed Leadership article Pat mentioned in her post) and the next book I will read is Our School (Building Community in Elementary Schools) by Karen Castro and Jennifer Audley (both books can be purchased from the Responsive Classroom Resource site). I believe building a positive climate for learning coupled with the philosophy that we are embracing in MTM regarding the building of understanding of math concepts will only have a positive impact on student mathematical learning.

A question I have......How did we (schools) get so caught up in following programs such as Everyday Math, Investigations etc. and forget the need students have to construct their own knowledge?

Organizing Posts

Hello All...

I will be sorting through all posts/comments today and rearranging some groupings to make it easier (quicker) for you to access main ideas.  If you find things in different spots, you will know why.  Once these are sorted out, we can keep it tidy by following a few basic 'rules':

1. Make sure your title reflects the content of your post. We should be able to look at the title and know if it is something we are interested in pursuing. that, of course, doesn't mean a long title... simply a meaningful one.
   
2. Be sure to label each post (bottom right on the composition box). If you click on the blue link there it will show you all labels that have been created thus far. You just need to click on the appropriate one to make your post part of that group (label). If, however, you do not see a label there that is appropriate for your post, simply type a new one in the label box before you post. When you go back to the post list, you will see your new label in with the others. You will notice that I am creating a new label with this message, called 'Heads Up'.
3. If you have resources to share (Links to sites, suggested books or articles), please take the time to add those in a separate post and attach the label 'Reading Room'. To date, most of the references to articles, etc. are buried within a post or comment, therefore scattered throughout the blog. It would be good to have them in one place. So, do include them in your post if you like, but follow up with a separate post that cites the resource (and where to find it) and a sentence or two so we can know whether or not it is what we are looking for. If we all do this, we can build a significant Reading Room in little time. Additionally, for those of you who are citing material you intend to read, please remember to keep us up to date by way of a quick review once you have read them. It goes a long way.

Watch for a few changes over the next few days... if you have questions, you can email me at anytime.

Cheers! 
Maggie

Interesting Articles You Might Want to Read

How will I establish a "good math climate" in my second grade classroom?

I definitely agree that my own attitude toward math sets the tone for my students and their families. I love teaching math and try to make clear to my students what the focus will be for a lesson and help them to see why it is important to learn. Margaret (from our MTM course) and I team teach so we both teach math - sometimes whole class and sometimes by skill needs. This gives us the opportunity to brainstorm ways to help our struggling math students. During the past year we had a small number of students who had difficulty with math. The good news is that they didn't realize it. One of them even said that he is great in math. By using volunteers and peers we were able to give these students extra practice with some very basic skills that they were missing. They could feel successful and better able to participate in lessons with the rest of the class.

Our week spent with Maggie, Peg, and Shawn will help me to be clearer about the math that students need as prerequisite skills to what I am teaching in second grade. I have always found it frustrating that literacy instruction is looked at on a continuum and we start our students from the point that they enter our classrooms; while in math we often just jump in where the program begins. I hope that working with colleagues will help me to be clear about where my students need the most help to be successful or the most challenge to remain interested.

Our school will be using a math program for the first time in many many years. Our staff will be learning together as we implement the Investigations program. I think that this program will encourage students and parents to share mathematical thinking.

I have recently read two articles that I think will be helpful as I meet my students where they are and encourage them to move forward in their learning. I think that you can probably get the articles through Marvel. I belong to NCTM and ASCD so I receive the journals and find them very helpful. The articles are:
"Identifying Opportunities to Connect Parents, Students, and Mathematics," Teaching Children Mathematics, August 2008. The author shares her experience with family math nights. Margaret and I have held a family math night during each of the last two school years. I am sure that we will do it again (with Sheila) but I am wanting to rethink some of our activities.

"The Power of Our Words," Educational Leadership, September 2008. This article is useful across all curriculum and refers to the Responsive Classroom approach.

Both articles are quite brief and I think that they will help me to set a positive climate for my students and their families.

Creating and integrating a Math Climate in READ 180 and iSucceed Math computer programs.

I has always been my belief that teaching literacy has a lot to do with teaching mathematics, so I have put numbers and math vocabulary on the wall opposite the literacy references for reading and/or writing strategies in my Read 180 room. Let me put it this way, mathematics is found/interwoven in literacy (e.g. word problems), science (e.g. measurement and medicine), and social studies (e.g. census, cartography, history, and, I can safely say, cooking). Well, these are what I can think of at the moment.

What I heard/learned at the Summer Academy about the similarity in the delivery of teaching math and literacy was a confirmation that make me delve more into this notion!! In the past, because I don't always follow directions, I have sneaked in some Math lessons (you know, those teachable moments) during the Read 180 sessions. After all, we have number sentences in Math and similarly we have sentences in literacy. My English Language Learners (ELLs), some still in contained ESL classrooms while some have been mainstreamed, need to learn how to correctly spell single and/or multiple digit numbers in words. These students don't have a minute to waste since they are already running after a moving target! They can perform well when computing problems represented by numbers, however, when they are faced with word problems they have difficulties due to the language proficiency. That does not necessarily mean that they don't have mathematical abilities. It is my own experience when I moved here from Indonesia, because I was accustomed to use the metric system and I had to switch to the American system of pounds, gallons, and miles.

So far, this is what I have come up with when I compare math to literacy:

Basically, in literacy we have the letters from a-z while in math we have the numbers from 0-9 and we need to know them and read them. We can read letters and numbres. We can arrange letters into words that we can read and we certainly can read numbers. We have one letter and multiple letter words just as we have numbers, which stand alone and we have multiple numbers too.

A sentence has three parts: subject, predicate, and object. Can I, possibly/correctly think that it is similar to our place value, where we have the ones, tens, and hundreds, going on and on.......separated by commas, just like the complex sentences with the commas and conjunctions? I always tell my students that they have to read all the symbols in math, including the commas. If they see one comma then it will be in the thousand for a four digit number, if they see two commas then it will be in the million for a seven digit number and so on.......What do you think?

What about the parts of speech? Where are they in comparison to math? Is there any connections here?

I have a quadrant, on a poster board, of additions, subtractions, multiplications, and divisions (with examples and vocabulary) on the wall, but I don't have it for the parts of speech. So perhaps, next week I can create a quadrant of nouns, verbs, adjectives, and adverbs (with examples) and put that up on the wall with the reading and/or writing strategies. How are they similar and how are they different? I am tired and am going to bed now........good night!!

Have a great weekend you all!!

Math Attitudes

"Perhaps one of the most important ways that families can reinforce mathematics achievement is simply by having a positive attitude that children can master challenging math. Too often, we undermine our children's interest in math by using statements such as "math is hard" or "I didn't like math either." ( Richard W. Riley, former Secretary of Education)

I think that this applies to teachers, as well, especially early elementary teacher

Positive Attitude and Math Climate

"Perhaps one of the most important ways that families can reinforce mathematics achievement is simply by having a positive attitude that children can master challenging math. Too often, we undermine our children's interest in math by using statements such as 'math is hard' or ' I didn't like math either'." ( Richard W. Riley, former Secretary of Education)

I think that this idea of a positive attitude is also crucial in creating a good math climate in schools. I have seen firsthand how much this can impact a child's response to math. In the past I have worked with first and second graders in the resource room. Sadly, some of them came with beliefs already that "math is hard" and "I hate math." For those kids it was imperative that an attitude adjustment needed to occur. The best way that I found to reverse their thoughts was to let them witness my genuine enthusiasm, laced with phrases like "This is going to be fun," and "You'll be able to do this, too." At least for young kids, it is amazing how they can become believers that they, too, can be good math thinkers.

This year I am in a slightly different position and will be working with math strugglers in the general ed. population. I know that in addition to creating a positive "can do" climate, I must also have a good plan for taking kids where they are mathematically and moving them forward at an appropriate pace. I'll be working on creating lessons laced with fewer periods and more question marks this year. I have little contact with parents, but if it presents itself, I will also convey to parents how important their attitudes affect their children's attitudes in math.

Has anyone else noticed how important crafting a positive attitude is when you teach math?

Math Climate and Use of the Environment

How will I set up my classroom space, create inviting small group spaces and effective traffic patterns that encourage exploration on the part of my students? This is a question that surfaces each year as I prepare for the school year. As a kindergarten teacher I believe in using the physical space as a partner (though quite silent) in the learning process. In addition to well-placed environmental print of any kind, where shelves, tables, desks, investigation centers, the meeting area, etc. are placed affects how the students use the room.

This year I am starting out with 19 students in my AM class (13 in my PM). I am now asking myself where I want to begin investigating math. At the same time I also want to build an effective pathway for my students to develop self-management tools to allow me to move between small groupings of children in the midst investigating. These are not new questions but I find that the number of students changes our inquiry process.

Here is what I have come up with thus far. As teachers, we all encounter them these questions. What struck me during our week long academy adventure was how easily teaching patterns can develop into status quo and how important it is for teachers to be challenged to rethink how and what we do, and most importantly why we do what we do. For me it is vital to look at the environment because it is my habit to use the space as a "partner" in teaching. What worked for me last year may or may not work this year.

Ironically, when I have taught at the college level I have also experimented with the space as part of an enhancement to learning. I found that we were more excited about what we were doing when I was very intentional in how the space was set up and used. Call it Fung Shua, but I am now rethinking how the room environment can enhance the climate for investigating and learning.

So does it matter how you set up and use your classroom space? How do you use your classroom? How can you use the environment to its best advantage for creating a math climate or a learning climate in general?

Setting the tone

Good Morning Master Teachers...

After our brief post-Academy hiatus, it's time to get blogging again!  The momentum gained during that first week surpassed my expectations and I have been 'singing' your praises all over town.  As the year unfolds it will be fun to watch that sharing habit grow.  We will all be the richer for it.

In thinking about strategies to manage the posts / comments in a way that won't overload you but will still be significant, I have settled on the suggestion made during our Academy week (rotating groups A,B,C,D: with a slight modification).  We'll try it for a while to see how that works out.  Feedback is always welcomed and appreciated.  

This week's posts will be done by groups A and B.  Groups C, D will comment.  Remember that this is the minimum.  Additional posts and comments are strongly encouraged.  If sharing is to become a habit it has to ultimately become something we are motivated to do because we find it valuable (not simply a requirement).  At some point in our year, as evidence of a sharing habit is clearly seen, I would like to phase out the assigned groupings and simply offer articles/topic suggestions/etc.  as starters and let the sharing continue on its own.  Sounds good in theory... let's see how it goes!

Suggested Blogging Topic For the Week:  Creating a Math Climate:  Posting by Groups A, B

As you wind up for your new year, the Summer Academy fresh in your mind, what thinking have you done about establishing a 'good math climate' in your classroom?  What specific strategies will you try (or have you tried) to make your math class a place that all of your students look forward to?  Please finish your post with a good question that will invite comments from your colleagues.  Remember that asking brings at least as much learning as telling.  

When you are finished composing your post, please remember to 'label' it.  There is a white box at the bottom where you need to type the label: Math Climate.  That way, our posts can be grouped by topic (label) and easy to find.  Also, BE SURE to title your post in a way that gives us a clue about the content - again, for easier searching.  Thanks.

We are all looking forward to what you have to say.

Cheers! 

Maggie

Professional Resources from Maine

Hi everyone!

The Department of Education has a new math page which they are collecting resources on for teachers. This is the URL......lots of links on the left hand side are handy!
http://www.maine.gov/education/lres/math/index.html

BE SURE TO SIGN UP TO BE ON THE --- MAINE MATH LIST-SERV ----the link can be found on the DOE website. It is a great way to keep up with mathematics activity in the state and beyond. Lots of great opportunities are posted here.


Also, don't forget to get yourself and your friends to the 2008 ATMNE (Association of Teachers of Math in New England) Conference to be held at the Holiday Inn By the Bay on November 6-7. Registration and information for the conference can be found at: http://atomim.net
The link is in a big green box on the right.


ATOMIM (Association of Teachers of Mathematics in Maine) is our state mathematics professional organization. If you are not a member yet, you should definitely consider joining! We publish a newsletter 4 times a year which is a great resource for what is going on in Maine in mathematics.

Have fun!
~Shawn

Stages of Concern

The listing of the Stages of Concern struck a chord within me. Our school is two years old. One third of our staff was transferred in from one school, while most of the remaining two thirds of our staff came in from many other places within our district. (We also hired a few teachers who were absolutely new to Portland.)

Prior to the opening of the school, many of the stages of concern were addressed with that one third of the staff who were already part of a community. East End was billed as a place where school would be "done differently," and our leadership realized that preparatory work needed to be accomplished to ready the staff for the challenge. 

When the rest of the staff joined the community at our new school, some effort was expended to help the new (whole) community achieve the attitude necessary to tackle the transformational changes we faced.

As we enter our third year, I see us still in the 5th and 6th stages. We are not yet wholly unified as a collaborative staff, however we are making progress. I wish the entire staff could have experienced the attention paid to the first four stages of concern. Two thirds of us jumped in at the point when stage five was the focus. I think this created a schism... one that will take a bit more time to resolve.

I realize it's an economic issue... and Portland can probably never afford such a luxury... but I believe that a better way to prepare for the opening of a new school would be to have an advance planning team. This team would be charged with the responsibility of preparing for the formation of the new community and for all the many details involved. This team could use the stages of concern as a guide in their early work, then onward to the opening, and afterward too, as the staff became unified in vision, purpose, and commitment.

For the process of change we are in at our school, I see my role as that of a pioneer. My personal quest is to influence and support the increased success of our students. I know we can improve our practices... our students deserve this.... we will all gain from the effort.... as a community.

I am hopeful that this post makes some sense... I just watched the torch lighting... very awesome!... and I am exhausted.

Principal's influence

Like other posters I found the clarity around roles people play in the change process to be very interesting. They are similar to other documents I have read but use different language.

I especially related to the column on the influence of the principal. It is frustrating when the principal is not a trailblazer. Many years ago we had a principal who was a trailblazer but some central office staff may have considered him to be a saboteur at times. Now that I look at the descriptors for other roles I realize why some staff (trailblazers and pioneers) loved working with him while others were glad to see him retire.
I would describe our next principal as stay-at-home or a settler. It was discouraging that those of us who had momentum to continue projects had little, or no, support. The next principal was a slow trailblazer in some areas and a settler in others.
Now we have a principal that is a trailblazer in a few areas, mostly math - Yippee! The reaction by staff has been interesting to watch. Now that I have read these clear discriptors I believe that the staff who are struggling with her style may be stay-at-homes or even saboteurs. As a person who has some staff development responsibilities how do I meet the needs of all? The article says that it is "probably not wise to spend too much energy trying to convince the stay-at-homes that they too need to move to the frontier." The problem I have is if these stay-at-homes never move what happens to their students?
If central office provides administrators with staff development that can lead to developing skills that promote quality teaching but no one supervises the implementation of those strategies, how can principals improve their skills?

On The Frontier of School Reform

I've read this article or other work by Phillip Schlechty and, like anyone who has been on a committee that represents change in a school district, can identify with the roles he outlines in this article.
I'm wondering, however, what Schkechty would identify as true school reform or what he would think of the trend of the past 5-10 years of schools clamoring for Reading First grants that mandate the use of one of three (two?) "scientifically proven" reading programs or for the adoption of rigid, lock-step math programs such as Everyday Math that leave little room for creative thinking and design on the part of the person who knows the students best - the educator. I've been discouraged lately when I see and have been part of districts that consider reform to be an adoption of a specific program to fix a problem, the "problem" usually manifested in low test scores, rather than make the investment of time, effort and resources to examine classroom practices and student work. I can not see the role of trailblazer being attached to an individual or committee who pushes for an adoption of a program when it is not paired with thoughtful staff development designed to examine teacher practice and pedagogy. I believe teacher and especially administrative participation in staff development opportunities such as TMT will lead to true reform and hopefully return us to the practice of examining student learning and not test scores as we look at ways to improve our classroom practices.

Frontier of School Reform Article

Last year my building implemented the RTI initiative so I related quite well to the article "On the Frontier of School Reform with Trailblazers, Pioneers, and Settlers" by Phillip C. Schlechty. As I read this piece, I had a rather fun time mentally assigning roles to some of the members of our building staff! It was actually reassuring to know that our staff reaction was normal - some climbed on board willingly, some sought more information and assurances, and others cemented their feet firmly to the ground.

That was on a small scale compared to, for instance, the reformation of our schools' math pedagogy by promoting a BIG change in our thinking about the way of we teach math . We will all have to determine our roles in this venture. Thank goodness Trailblazer Maggie will be here for us all year to forge the way, keep us on the right path, and encourage us to stay the course. I'm up for the challenge. Anyone else?

How much time in the day?

We spend a lot of classroom time on reading and writing, the literacy part of the day. Math is given about an hour. In order to change math into a more cognitive learning experience, you need more than an hour. Where do we get the extra time?

Problem Solving

Great article.... and the others in this issue look interesting as well. 

As an undergrad, I worked as a math tutor at USM. Invariably, I had more customers during the time when the  "Word Problems" chapters were being covered than at any other time of the semester. I did not use a KWL chart with my students, however I did develop the habit of probing their thinking with questions. The difference between Hyde's technique and mine is that I urged students to read the entire word problem several times before beginning to work things out. I wanted them to recognize the importance of understanding the problem and the task before doing any of the ciphering. 

The questions we used were similar to Hyde's: What are you being asked to find? What do you know from reading the problem? What do you think you should try (operation, diagram, table, acting out, etc.)? 

I had students first identify the purpose, because, as they then identified the givens in a problem, they could begin to make a plan of how to use the information. Maybe it was because the texts often would start the problem with the task for the student, then follow with the information useful (and not useful) for finding the solution that this worked well. Probably, also, it worked because my students were all at least 18 years old... and had some prior knowledge about solving problems. Anyway, that was the technique I used with college students.

In my fourth and fifth grade classrooms, I have continued using the questioning techniques, (modified a bit, of course) and though this practice has been somewhat successful, I am now anxious to see if there would be any difference for my students if I incorporated the slower introduction of the sentences of the problem until they built that habit into their own repertoire.

There is always a great deal of dialogue in my math classes, however, I can see where having students take more time to make connections, explore all the language in a problem, and share their insights/experiences about certain words or concepts, would have a positive effect. I am expecting we'll see some additional side benefits too, such as developing a stronger sense of community and trust, expanding vocabulary, and practicing reading and thinking skills.

I can't wait to try this.

Think Reading, Teach Math

Between Oprah's special report today on how poorly our schools are performing compared to other nations, and the study cited in this article, I'm feeling a little pressure... :-))) I liked this article a great deal, and I can see how effective it can be to use those key reading strategies to teach math. The study mentioned in the beginning of the article quotes that effective teachers "not only assigned their students challenging mathematics problems, but also used active questiong and dialogue to help students see and understand the connections among math concepts as they solved problems." I've always struggled with the reasong part of math, especially explaining my reasoning. Because this is a weakness, I see it as a weakness in my teaching as well. This week in our class the instructors have done a great job of eliciting reasoning and explanations from the students, and it has helped me as a learner! Great role modeling... thanks Sean, Maggie, and Peg!! It really rings clear how vital it is to discuss concepts with groups of students, and they WILL come up with some good reasoning if given the right opportunity and the right questions. I am certainly adding this as another goal to work at!

So did anyone else see Oprah's report???? Are you as frightened for our future as Oprah and Bill Gates ???

Math and Cognition

Marianne

Grade 2

Mathematics and Cognition

Comparing the process of problem solving to the process of reading makes so much sense to me. (an aha moment for me) Making connections, making predictions, asking what is important, visualizing, and synthesizing the information in a math problem defines step needed to internalize and finally solve math problems. I can't wait to break down problems for my class this way. It will make the process much easier to understand, because the language and thought process are already so familiar. 

This  article also forces me to realize that mathematics is as a complicated and complex a cognitive process as reading (maybe even more so). As teachers, we need to break up the steps into small bits of knowledge starting from the conceptual begin just like we do in reading. We would never expect a student to read chapter books before knowing the sounds and combinations of sounds. So going back to the question asked today in class about how far do we back up if a student has missed a concept... We go back to the beginning to build on the basic concepts just like we do in reading.

Oprah's School Report

When I got home from class today I flipped on the tube and happened upon Oprah's special report, in conjunction with Bill Gates, on just how bad off our schools are compared to other countries, even poor countries!! (Did anyone else see this?) Then I read tonight's article. I feel a little pressure?? :-)))) I thought the article brought up many great points! I can see how using these key "reading" strategies would be very effective in teaching math. I always had (and still have) difficulty explaining my reasoning. I sympathize with my kiddos who have the same difficulty, and my nurturing instinct tends to kick in and "help" them out a bit too much. One of the things I'm getting out of this class is some great role modeling from the instructors (Maggie, Sean, and Peg) on just how to do this. That is, how to elicit students' answers with reasoning. I can hear Sean or Maggie saying, "Really? How do you know? Prove it! Who can say this another way? Cut the language down. Are you sure? .... etc." That "active questioning and dialogue " is critical, and I'm motivated to do more of it!

Spinners

I am adding a post for math materials and resources that we can share via our blog.
The following url has the arrow cards (not exactly the same) that were shared today as well as printable spinner bases. The site looks like it has many useful ideas and materials so check it out!

Arrow cards and spinners:
http://www.kentuckymathematics.org/resources/tools.asp

Arrow cards:
http://www.firstschoolyears.com/numeracy/placevalue/resources/Arrow%20Cards%20(thousands).pdf

Connections in Math

This article reminded me of our word problem exercise this morning, as we were sorting the word problem strips, the categories my group seemed to be using centered around what do we know about the problem and what do we want to find out...that leading to the question HOW do we find out?
Students are very accustomed to predicting the outcomes of stories based on prior knowledge, but has that strategy every been methodically applied to math? I need to remind myself to do that, not only when guiding students in taking apart word problems, but with any challenging math concept they attempt.
I also could see some of Maggie's philosophy in the statement that problem solving has been considered as a way to apply what students have been taught, leading them to believe that the problem WAS the math, and as we have learned this week, that is not the case. The problem is a vehicle for understanding the math. I understand the difference now.

Math Instruction and the Exceptional Child

The ideas posed in tonight's article got me thinking more about the importance of language in math and ways in which we can reach our students with language-based learning disibilities and/or struggling readers. The following strategy was posed in an article from Teaching Exceptional Children and seems valuable:

Brian Bottge, professor at the University of Wisconsin, Madison, developed a unique way to bypass reading difficulties and get students enthused about math word problems. He presents word problems on video. Students can hit the remote to get the information they need to solve the problem, and video makes it easier for students to visualize the problem. The second and equally important aspect of video problem solving is that the problems posed are intriguing: building skateboard ramps and hovercrafts. These types of real-life problems embed numerous skills, skills that suddenly become imperative to learn. Students realize they need to know how to add fractions to see if the lumber they are cutting will be the right size.

Authentic problem solving puts a lot of responsibility on the teacher, says Bottge. "The teachers have to know their kids well and know when to stop and do more in-depth teaching," he says.

Bottge adds that careful planning is also essential in developing video and authentic problem solving. "You have to figure out what the problem is and the math concepts embedded in the problem. You have to keep math as the focus."

For more information, see TEC, Sept./Oct. 2001 or contact the Cognition and Technology Group at Vanderbilt for math videos

Braiding Reading and Math Cognition

As I read this article I began to wonder if the results might have been different in the US if the Math and Science study had been if the study had been done in than one grade level (8)? Would the results be different if the study had been, for example, in Grades 1,4, and 8? It might show us that we use alot of active questionning and dialogue in grade 2, less in grade 5, and then none in grade 8. Why is this happening anyway? Are we putting too much emphasis on getting the right answers instead of making sure kids really have the rich experiences they need to be able to come up with the way to find the answer themselves. Several times this week I have heard teachers talk about time-not having enough!

I am intrigued by the idea of braiding cognitive strategies used in reading (such as those found in Mosaic of Thought) to cognitive strategies in math. I have been thinking a lot this week about how Mathmatics is a language all its own. We need to make sure that kids have enough experiences to build knowledge in math before we expect them to read and write and understand math. We don't expect students to read and write before they are ready, yet we often jump right into symbols and numbers in math long before we should. I think I've often been guilty of that myself, but hope to do better in the future by incoprporating these reading strategies into math. The References included a book published by Heinemann, Comprehending Math: Adapting reading strategies to teach mathmatics, K-6. Has anyone read this, and if so, what do you think of it?

Mathematics and Cognition

Wow! This article is right up my alley as my background is in literacy not math (as any of you who have had the misfortune of working with me this week can attest!) The concept of using these reading strategies: making connections, asking questions, visualizing, inferring and predicting, determining importance, synthesizing and metacognitive monitoring to help students gain a greater understanding of math makes perfect sense. As I will be assisting students in math for the first time this fall, it's comforting for me to know that I can use the same strategies I'm already using in reading. The author's statement that "the quality of most student's work, especially their explanations of the concepts, improved dramatically during the school year"spoke to me as well. If we can help children to verbalize their thinking we've accomplished at lot!

Drill V Practice

Practice & Drill

I agree that practice is necessary, but practice can take the form of activities that vary and include "real life" use for the skill or concept. Practice teaches persistance, too. Treat practice as a challenge and keep it positive.
Maddy R 4/5

To Drill or Not to Drill?

Should both practice and drill be used in the classroom or at home? It depends... what is the purpose for the strategy? If I want students to solidify a concept, process, etc. then I would have them practice the concepts in many differenct ways until they can demonstrate they understand the concept. So, in general, practice is the strategy to use to have your students "eat mangoes." However, drill does have a place in learning basic facts. Once students can demonstrate the concepts behind the 4 operations, it is important for them to obtain automaticity in their facts because if they don't have this automaticity, then later down the math highway they mostly likely will have car trouble. The car trouble is that those students without automaticity will have an additional cognitive task with any math that requires computation.

DRILL vs PRACTICE

Since my primary area of focus is in Language Arts, I, of course, started by looking up the definitions of these words. Dictionary.com defines DRILL as any strict, methodical, repetitive, or mechanical training, instruction or exercise. PRACTICE is defined as the repeated performance or systematic exercise for the purpose of acquiring skill or proficiency. 

In my mind the word drill brings about a negative connotation. It makes me think of a military drill sergeant. It makes me think of being under a time pressure. It makes me think of the moans and groans that usually come from my students when they hear the word drill. When we do timed multiplication (or other skills) drills, students are asked to repetitively perform the same action, often with no true understanding of what they are doing. It is based on rote memorization. 

On the other hand, practice has a far gentler feel to it and does not bring about such negative emotions.  "Practice Makes Perfect" comes to mind. When we are providing the kids with activities for practice, we are giving them a way to become "perfect" at that skill, a way to play with the concept until they can truly understand it for themselves. To use Maggie's terms--we are feeding them mangoes!

Practice Vs Drill

Sorry...had trouble getting my post to stick! Third time was a charm! Ignore these first two!

Practice Vs Drill

Drill vs. Practice?

http://olc.spsd.sk.ca/DE/PD/instr/strats/drill/index.html

What is Drill & Practice?
As an instructional strategy, drill & practice is familiar to all educators. It "promotes the acquisition of knowledge or skill through repetitive practice." It refers to small tasks such as the memorization of spelling or vocabulary words, or the practicing of arithmetic facts and may also be found in more sophisticated learning tasks or physical education games and sports. Drill-and-practice, like memorization, involves repetition of specific skills, such as addition and subtraction, or spelling. To be meaningful to learners, the skills built through drill-and-practice should become the building blocks for more meaningful learning.

I think the most important part (the last sentence) should read- to be meaningful to learners, the skills built through drills should become the building blocks by practicing and applying them for more meaningful learning.

memory strategies - practice or drill?

I did some research on that websight "www.mathforum.com and there were some interesting lists of strategies to help with memorization. Some of the strategies seemed to me to be more like "practice". These included: explaining the math concept to someone else, solving the math problem both backwards and forwards, using mneumonics, using visual associations or making associations to real life situations. They also talked about "repeated review" which to me seemed more like math drill.

Practice v. Drill

Interesting question for todays discussion

When I think of the terms "drill" and/or "practice" as strategies for reinforcing math concepts I start to sweat and shake. My personal experience in elementary school was similar to what Maggie shared today. Both terms when used with certain activities (eg. memorizing multiplication facts)are lower order thinking skills. They would be used to help build understanding of concepts. When teamed with critical thinking activities and creative background foundations they could boost some of our students confidences to explore more math.

Lisa
Falmouth ELL

When Does Practice Become Drill?

Oh dear, the word drill makes me think of an unhappy time at the dentist. Luckily, in Second Grade we teach and practice strategies for number operations. We frequently practice our facts with card games, dice games, using the calendar and even student made flash cards. Doesn't that seem like fun?

There is a difference

Off the top of my head,a mathematical drill is an activity where students are given an algorithm or a skill and do it repeatedly, like memorize math facts. Practice is when they investigate a concept, play with it and then practice applying it to other mathematical situations. Perhaps practice is applying symbols to a concept and/or practicing it with paper and pencil.

Janine, Falmouth, 7th grade resource room

practice vs drill

I am still a bit foggy on the difference and am having difficulty finding a resource that clearly defines the difference but my sense is that drill and practice are, indeed, different. I am thinking along the same line as J :-). An example: drill might be for memorizing math facts (such as multiplication) where a student is using repetitive activities/behaviors to increase automaticity with calling out the answer for each fact. This would not include a reference to or exploration of patterns and strategies within those facts. Practice would include a child reviewing his math facts (9s in multiplication) by reviewing patterns or strategies learned in an attempt to both better understand relationships within the facts as well as increase automaticity with facts. Yes? No?
KarenD F sped 3-4

not the assigned post topic, but..

I wanted to share 2 interactive games that help kids navigate the number grid.
This one is a completed grid that I use as a Guess my Number game. Kids make educated guesses about the number you are thinking of and when they tap or click on that number a paint splat appears on it. They use their understanding of greater than and less than as I announce if my number is greater or less than their guessed # .
www.oswego.org/ocsd-web/games/SplatSquares/splatsq100.html

This one is a blank # grid and a number is displayed on the corner. Students use their knowledge of the # grid to locate the #, if they tap or click on the correct #, a dog bone comes flying out. If they tap the wrong #, that number is displayed so they can use that to navigate to the correct one.
www.oswego.org/ocsd-web/games/DogBone/gamebone.html

Practice VS Drill

Practice and drill are not the same in my book.
According to Dictionary.com:
Drill is any strict, methodical, repetitive training, instruction or exercise.
Practice is repeated performance or systematic exercise for the purpose of acquiring skill or proficiency.
This sums up the differences pretty clearly for me. Drill means doing something over and over regardless of one's understanding of the task while practice indicates applying one's knowledge multiple times to become proficient at the task. Copying Chinese letter formations would be drill for me since I have no understanding of the concepts for which they stand. I could be successful completing the drill. However, I could not practice these same forms without learning their meanings. Given that, the drill would become practice and thus a valuable task to further my knowledge.

Same Face, New Name

In accordance with Maggie's request, LKJ is now Linda Fal K-2.

I am in???!

Another Myth?

I wonder what everyone thinks about the following: "Math has never been one of my best subjects in school either. I think that makes me a better math teacher because I can relate to my struggling students."

Sound familiar?

I cannot believe how often I have heard this over the years. I personally think it is a load of garbage. The best teacher for a struggling student is one with thorough understanding that can approach problems from several different angles.

On the flip side, I have never heard a teacher say that they were never a very good reader, and that makes them a good reading teacher since they can relate to struggling readers. Sounds odd, doesn't it?

I'd like to hear your opinion on this.

Parents/HW Strategies

I am fortunate that my students are well supported by parents and generally complete about a half hour of math homework M-Th (6th grade). There are times that I specifically instruct students to not seek help from parents-when teaching decimal multiplication for example. I want them to develop the concept before their parents tell them to "move" the decimal.

One strategy that helps students avoid frustration is homework isn't graded. I don't believe it is fair to grade work while students are still acquiring the concept. I keep track of whether it is completed or not. Any question not completed must have two questions written down that the student would have asked me if I had been there. This requires the student to give the question some thought, and goes beyond, "I didn't get it."

Although we thoroughly go over most questions orally, I would be interested in strategies others use to track homework completion and quality.

Parents and Homework

As a middle school teacher I often hear from parents that they can not help their child do homework because they don't know how to do it. The purpose of homework should be to reinforce skills learned in class. It should be something the student should be able to do independently.
The parents' role should be one of supervision. They should provide a place to study and oversee the process to assure completion. Parents sometimes sign homework policy guidelines so they are aware of requirements. Parents should check in with their child to see what they are
studying and ask questions in order for the learner to demonstrate their knowledge.

Seating

I have got to mention that it is very uncomfortable and bad for people's backs to be sitting on cafeteria benches for the entire day. It would be good if we could all move to the library or povide seats with backs for everyone. Even folding chairs if that is all that is available should be provided as an option. Thanks!

Parents and Homework

I teach newcomer ELL students at the middle school. I do not have my parents formally involved with the homework process. However, when they ask during a conference or it comes up in conversation, I ask them to help their child with math flash cards (I give to the student or they make in class) or take them to the library to get a library card and check out books. I recommend picture books, books on tape/CD and educational/family videos. I encourage the parent to listen to their child read, even if they don’t understand the language, and partake in the books and such brought home from the library. I also discuss that their child can and should read to a younger sibling or ask that they encourage siblings to work together and study spelling words and math facts. I also let them know that I do assign homework every night so they should ask to check to make sure it is getting done.

The other big idea I talk to parents about is that their child should be reading every night. I talk about making sure the home language is used and practiced at home. If my student can read in their language I encourage this above all else. We had our first annual multilingual parent night last fall and if I remember correctly, much of this was addressed then, and I will make sure it is again this year.

Just to add, I view homework at this proficiency level as a way for students to become accustomed to school culture and norms, as well as to practice school-related responsibilities. The hw I assign is not such that needs parental support beyond monitoring and inquiring what their child is learning.

parental involvement and HW

In the beginning of the year in the elementary grades I think that it is important for parents to assist their child, if they need it. As the year develops, the child should be getting more independent with their hw and shouldn't be needing as much help. Having a parent around for a sounding board is also helpful, for the child that still may just need a way to get started. I also think that a parent could be there to make a last check on the hw, if they are there to do so, just to see that the child put the effort they should into it. The older the child gets, the more independent they should become with the hw. I believe that the teacher should spell out to parents what the expectations are for them as parents, at the begtinning of the year. Many parents do not know how much or how little to intervene.

Homework and Parents

My response to parental involvement with student homework is mixed. On the one hand, it is great to have a parent want to be involved in their child's education, spend time with their child and be supportive. On the other, it can be a nightmare to all; child, parent and teacher. In order to make this a positive experience, we need to ask ourselves some questions. Do the parent(s) have the necessary background knowledge to answer questions and provide direction to the child? Do the parent and child have a good working relationship? Are the parents able to recognize their role so they are giving support and not doing the homework? Is the homework being assigned reasonable in length, have clear purpose and directions and have the students been given all the tools to complete this with minimal support? Does the home have resources available when homework questions are confusing such as a MATH ON CALL book, dictionary, thesaurus? Will the parent know when to say "I don't know?" and suggest ways or ask pertinent questions as how to find out? Will the parent leave it to the student to talk to the teacher when he/she does not understand or is unable to do their homework?
So here's the nightmare: I have experienced parents doing their child's homework for them (but not admitting to it), getting frustrated with their child for not knowing how to do the assignment, making negative comments about the homework perhaps because they don't see the big picture, and creating an overall negative experience/relationship with their child and possibly his/her teachers.
My personal opinion is that parents provide a suitable study environment for their child; quiet, good lighting, appropriate tools and resources. There should be a set time when homework starts and ends. Parents should check in periodically without being a nuisance to make sure their child is on task and whether they need help. Parents should check their child's assignment notebook and backpacks to confirm 1. that he/she has their assignments written down, 2. that he/she has the materials for the assignment 3. that he/she understands the assignment. Upon completion, the parent should have the child show that they attempted or finished each assignment by showing the actual work and having the parent sign off or check this off in their assignment notebook. These will hopefully alleviate to some degree the "Well, he worked for 2 hours and I know he had it done" conversations. These to me, are more supportive then sitting down and trying to help with the actual homework.
And again, the homework should be a practice of skills that have been taught and reviewed in school, not an assignment of unfamiliar skills to see if the child(or parent) can figure it out. It has been documented (I'll look for the article later) that it takes longer to unlearn something that has been learned incorrectly and practiced, than if it was learned correctly the first time. SO do we want parents delving into homework? Not without some specific parameters. COMMENTS ANYONE?

Homework and Parental Involvement

I'm sure that all of my fellow Falmouth teachers have been diligently reading The Art and Science of Teaching by Robert J. Marzano. It's our assigned summer reading - not exactly a beach book! Anyway, studies on homework are discussed on pp.65-71 and one section concerns parental involvement in that area. It states, "Based on a series of studies designed to identify the conditions under which parental involvement enhances homework, Epstein and her colleagues (Epstein, 1988, 1991,2001; Epstein and Becker, 1982; Van Voorhis, 2003) promote the notion of interactive homework. Following are some general features of interactive homework:

• Parents are provided with clear guidelines as to their role.
  
• Parents are not expected to act as experts regarding content.
• Parents ask clarifying questions and questions that help students summarize what they have learned.
  

Comments?

Unpacking Geometry

I found the "Big Ideas" in fractions clarified by grade level to be very helpful today. The activities to explore concepts without recording will be very helpful in my second grade classroom. I am familiar with the van Hiele Levels of Geometric Thought and wonder if we might "unpack" the "Big Ideas" for geometry according to these levels of visualization, analysis, informal deduction, deduction, and rigor (Levels 0-4). Might we unpack levels 0-2 during one of the K-3 webinars? I had never thought about what Maggie said today - geometry skills are entirely based upon your experiences. That statement certainly justifies providing many geometry experiences for our students. I love it!
During the past two years I have been involved in math course work and a wonderful opportunity to work with a small math study group at my grade level. I am well aware of the need to take more time to discuss/process activities to get to a clearer understanding of where my students are in their thinking and to help them to communicate their ideas more clearly. It is sometimes challenging to remind myself that I can take the time and not to worry about getting to everything. I love working with a team because they provide support for the steady, deeper approach to math instruction. Lucky me.

Homework Dilemmas

Our school uses Everyday Math. I teach 1st grade and the children get homework (except weekends) as a support of our day's lesson. Parents receive a letter at the beginning of each unit that explains concepts and supplies homework answers (I'm always surprised when parents tell me how relieved they are to get them!). Parents are advised to help since the children can't read the directions as yet. However, it's also a window into their child's day, which I feel is important to home/school communication. It lets them know if their child is struggling with certain concepts which helps if a conference is necessary. 10 minutes at night is usually sufficient to complete it. In our district, some parents want more. This can be a struggle since I try to impart that their child does so much in school already and other than reading, they need to relax and play. Does anyone else have a different way to address this or feel as I do?

On another note, vacation homework. Specifically vacations outside the scheduled school vacations. We are advised not to give any, but some parents try anyway. Personally, I'm relieved not to have to create all the extra work, but professionally I dread how much they will miss and catching them up if I don't. How do other districts handle this?

Patty Papers!

I thought those patty papers we used today in Shawn's activity were incredibly versatile, and something I had never seen-- found them for sale on Amazon. If this link doesn't work, you can just Google patty papers--Lots of choices--
http://www.amazon.com/s/?ie=UTF8&keywords=patty+paper&tag=googhydr-20&index=aps&hvadid=1102693901&ref=pd_sl_7h6pvxc2fx_b

Homework-Simple and Predictable

Yes to homework----but keep it simple and predictable so the students, parents, and you can deal with it.  I have a self-contained third or fourth grade classroom so my idea may not work for all. I assign homework on Mondays.  The categories are: Word Study-Mon.-Thurs. (Parents have a list of how to practice with their child every night), Math-( simple worksheet to practice{simple for parents to understand}), Reading-45 minutes a week, Long Term (has to do with science or social studies (simple as collecting 5 different types of leaves), and Free Choice (choose from a list of 76 items such as help an adult make dinner or one of which is other). 

      The assignments are all listed on a half sheet of paper and there is room for a parent's signature and heart check.  The heart check is simply a heart with a check inside that the parent makes to show that they think their child has put their 'heart' into their work.  I collect the homework from their purple folders on Friday and give them a sticker on the chart inside their folder if the work is done.  Five weeks of complete homework (with parent signature) gets them a free pass for No Free Choice Homework for one week--anytime they want to use it.  

     Parents like this way of doing homework since they can fit it into their busy schedules.  Soccer or basketball or dance class, etc, count as other.  There's lots of learning outside the classroom that goes on that I learn about, which I then can use as examples in the classroom.  I also can talk to my students about the other things going on in their life.  

parents & homework

Students should understand material well enough to do homework independently.  Homework should not be an assessment of a parents knowledge.

comment to reading

I agree with the idea of helping students to learn the idea of what is behind the symbol...when they figure it out for themselves it makes sense to them forever. We as teachers need to make more time for the process of figuring our the concepts, and not worry so much about covering so much in our specific programs. This is the difficult part when we are supposed to be covering a certain amount!

Symbols / = balance in Algebra / math is a language

If you were to do Algebra without a clear understanding about the balance of the equation then work would just be mud to the students thinking. Showing balance with a scale, seesaw, and equality with sets of items can give students the prior knowledge needed. Clarity is the goal for higher achievement and long term learning. Also, always return to a concept doing a quick problem or activity. This tells the student that the learning concept is important and gives them another chance to do it successfully.
Students need to know the reason a symbol is being used and have a clear understanding of what it means. MATH IS A LANGUAGE.

Web site --balanced equations

I thought of this great interactive website when reading the article. It shows a pan balance and students increase or decrease the number on one side to = the other side.

You also have many options like comparing numbers and number models. I use it frequently on a Smartboard, but it could be used for small group instruction or as a center as well. I use it after using manipulatives.

http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/850/calcbalance.3swf

Everyday Math Program

Many of the things we've been discussing in class, and the ideas set forth in the article are inherent aspects of the Everyday Math Program. Falmouth adopted the program about five years ago and it really changed the way I taught math. It allows the students to use multiple strategies for solving problems and it provides many opportunities for students to understand a concept, not just memorize answers. I'm wondering how many people in this class use the Everyday Math Program.

"Un-used" things

Thanks to Dave Santoro and his online resources, I was successful in retrieving my "un-used" METRICS:):) When I immigrated to Bath, Maine, from Indonesia in 1974, I switched from METRICS to the POUNDS, GALLONS, and FEET/MILES. That was challenging, to say the least because they are not based on tens!! When I put my metric "away" in my "basement" for the last 32 years, they became "mouldy" and "rusty" so naturally when I tried to think of/switching to metric today, I was confused!! Math is just like language you know, if you don't use it enough, you may not remember accurately. Revisiting was easier though and my mother's metric teachings, that's right, not my teachers', came back. The reason is plain and simple, my mother helped me "see" things. She made me create a stairway to help me remember the metric system!!
My job as the Literacy intervention educator (using READ 180 program on the computer) has become more interesting when I began the implementating a Math intervention, called iSucceed Math, also a computer program. I was able to intergrate Literacy AND Math simultaneously, giving students more support in Literacy to help them better understand Math concepts. I am so glad that Maggie wants us to "CALL NUMBERS BY THEIR REAL NAMES/VALUES," instead of digits. "KYE" is an interesting system. I wonder though, will it work with four or more digit subtractions? Or does it work for three digit subtractions only?
Speaking of homework, was I suppose to just read the article "3 Is Not Three?" Or am I supposed to do something else?? Perhaps I was not listening to Maggie when she assigned that to us:):):) Am I in trouble now?????

Kudos!

Our room was filled with the buzz of activity today.  As you well know, nothing feels quite as good to a teacher as the sweet sound of learning when it echos back from your pillow at night (which is exactly where I will be in about 5 minutes).  My hat goes off to all of you.  Your enthusiasm and thoughtful reflections are first class.  See you all bright and early tomorrow!

I've been teaching math for thirty-nine years and have experimented with multiple ways for kids to grasp the subject. I absolutely agree with focusing on concept development (hands-on, pictorial, then abstract) as probably everyone in the room did today. My "insightful" question is this: If this is the best way to teach math, and research apparently shows that it is, wouldn't it benefit everyone (children and teachers alike) to have a "national curriculum" focusing on thorough concept development and its common language along with collegiate training of future math teachers in the best practices for delivering this type of curriculum?  

Family issues

When teaching children in 1st grade the concept of the "fact family", where the numbers 10, 8 and 2 are a family, I have found that the addition facts can be generated, but when they have to create the subtraction facts they don't always use the greatest number first, which is the "rule"! After doing the exercise today with 3x4=4x3 I have been trying to think of a way to visually demonstrate this concept and to use better language, (is there a better term for subtraction, take-away or minus?) I am new at this and the answer may be blatantly obvious... but that's ok.