As I read the Early Childhood article on algebra I am gently reminded that teachers need to do more than patterning in the early grades. I see lots of repeating and growing patterns in primary classrooms, but does the algebraic thinking stop here? Young students need to have many experiences representing and analyzing mathematical situations and structures. As a fourth grade teacher, I see students who don't truly understand the concept of equality, the idea that the equal sign means balance and not "the answer comes next."
They also need experiences in quantitative relationships. The other day I gave my students a problem: There are some kids and some dogs on the playground. There are 22 heads and 68 legs. How many kids are there? How many dogs are there? More than half of my students had no idea how to think about this problem. I don't remember much of my algebra learning and I know there is probably a way to solve this problem using algebra, but I want my students to be able to make sense of what they are doing, not use someone else's rule........so we muck around a lot with manips, tables, pictures and it starts to make sense.
So as I think about my kiddos all being ready to take algebra in 8th grade, I think not. Some may be ready before then, some later, but I am hoping with lots of early experiences in the primary and intermediate grades, they will all meet success.
Sunday, February 8, 2009
Friday, February 6, 2009
Book Reviews
If you are thinking of buying a book online to add to your mathematics library, but are unsure of the contents, you can post your query on the blog and ask if anyone has it and what they think. If no-one has it, I'll order it and write a review for the whole group. That may help to ensure your money is well spent. Just a suggestion. I am ordering Family Math Night by Jennifer Taylor-Cox as Linda has expressed interest in it. When it arrives, I'll post the review for all.
Tuesday, February 3, 2009
How the Brain Learns Mathematics by David Sousa
This book is published by Corwin Press- ISBN 978-1-4129-5305-4 - Sousa takes the reader through how the brain develops number sense to how teachers can recognize and address mathematics difficulties. Each chapter ends with a section called "Reflections" which helps the reader process the information. A fascinating read!
Link to Rita's algebra article
Here is the link to the article Rita introduced us to on algebra in the early years. Copy and paste the following into your browser to access it.
http://journal.naeyc.org/bti/200301/
Monday, February 2, 2009
Teaching Math and the Brain
I thought I would try to get into this conversation, although I am not too sure how to BLOG, so I will just muddle through. I have read a good book, How the Brain Learns Mathematics, by David Sousa. He explains how the brain has a special area called a number module - where number symbols are hardwired - this is located in the parietal lobe.
Now, the language module is in a different place in the brain and it is where the words are stored, including all our "math" words - I wonder if how we teach these two concepts help link these two parts of our brains - Now, I am just writing this because I think it is really interesting. I hope to join in other conversations with you.
Marcy Emberger
Basic Facts - A Compromise
Coaches... I can't paste the contents of the email I sent here (about a solution for sharing the basic facts presentation) without retyping all of it. So I would ask you to simply refer to that email and post your comments here. Thanks!
I have heard from Karen and David so far.
Basic Facts Reaction to Maggie e-mail
Providing us with a video allows us to concentrate on remembering the content, and delivering the message in a compelling way.
I am not sure I can get 3 hours (3, hopefully consecutive) with the other math teachers at my school.
I am not sure I can get 3 hours (3, hopefully consecutive) with the other math teachers at my school.
Presentation Tips
For your upcoming MATH MOMENTS session, you were emailed a document called 'Presentation Tips' for you to consider as you prepare to deliver this first session. You have put a lot of effort and thought into developing this session and my hat goes off to each of you. Please let us know, by comments to this post, how your plans are coming along, what logistic issues you may be having, brainwaves to share, what worked and what didn't etc. This team is gelling nicely and each of you has a lot to share. I can't wait to hear!
Sunday, February 1, 2009
Algebra from the Primary Perspective
Okay? You want me to comment on Algebra?, was my first reaction to our assignment. Before I muddle forward with any discussion regarding the subject of Algebra let me layout some background information. My "eighth grade experience" with Algebra was in the 10th grade and it was 40 years ago. Having taught either preschool or primary grades, mostly kindergarten, in the last 30 years, my contemplation of Algebra has been limited to thinking about my own children and their various experiences with Algebra. Out of 4 of our children the youngest who is now 24 took Algebra in the 8th grade. A comment he once made during his eighth grade year has stuck with me and echoes in my mind whenever I work with students and the idea of equations. My son said,
"Teachers should really use blocks to help kids understand Algebra." Incidentally, my son enjoyed math a great deal, tried it as a major in college, and finally settled in the geosciences.
Blocks! What do they have to do with the article "Recalculating The 8th Grade Algebra Rush? Before I contemplate that question I want to focus on a small quote from the article that struck me as the heart of article and is also very connected to my thinking about blocks. The last paragraph states,
"It would be better to think of Algebra as we do swimming: something everyone should learn, most importantly learn well. Get everyone into the pool as soon as possible. But let's not mark them as having passed the course until we are sure they can swim several lengths without drowning"
I am also a swimmer and past teacher of swimming. Of swimming I can say: not everyone learns swimming at the same rate, over the same length of time, through the same methods of teaching, or with the same amount of practice. H-m-m-m, that sounds familiar; Teaching Methods 101, differentiating instruction.
This quote illustrates a developmental perspective in that any given skill, in this case swimming or Algebra, each need time to develop, have an individual component for each learner, and in the case of either, to be useful to the learner they have to be firmly connected to prior knowledge (learned well). From the perspective of a primary level teacher where student thinking is very concrete and connected to real objects that may eventually be represented by equations, blocks and other math manipulatives become an integral mode of teaching. Blocks are a concrete medium through which students can develop theories, test their thinking and make conclusions. Unit Blocks, the large, blonde colored blocks that need their own shelf in most kindergarten rooms, can be used to build equations: block size A = 2 of block size B or A = 2B. Similarly, Cuisinare Rods also give rise to exploring equivalent relationships. From my experience, concrete exploration with materials that can be manipulated and assist in evolving mathematical thinking is a key developmental component that lays ground work for Algebraic understanding. The reason why my son's comment has stuck with me is that it illustrates how the cultivation of well-based new learning has a connection to prior knowledge and experience. In his case to all the years he played with blocks and legos. Starting with block and other manipulatives, a concrete model to bridge mathematical knowledge to the abstract world of Algebra can be built.
So what do all my ramblings have to do with "the 8th grade rush?" I believe learning is developmental and experiential, not everyone will be ready in the 8th grade for Algebra. Whether any given student is developmentally ready for abstract thinking (Piaget- formal operations) and to learn Algebra will vary from individual to individual. Experientially I wonder what role the primary teacher plays in providing concrete investigative experiences on which bridges can later be built for learning Algebra and learning it well. Thinking of "getting everyone into the pool as soon as possible, what do you think our role, if any, as primary teachers is regarding the development of mathematical thinking that leads to learning Algebra well whether it be in the 8th grade or later?
"Teachers should really use blocks to help kids understand Algebra." Incidentally, my son enjoyed math a great deal, tried it as a major in college, and finally settled in the geosciences.
Blocks! What do they have to do with the article "Recalculating The 8th Grade Algebra Rush? Before I contemplate that question I want to focus on a small quote from the article that struck me as the heart of article and is also very connected to my thinking about blocks. The last paragraph states,
"It would be better to think of Algebra as we do swimming: something everyone should learn, most importantly learn well. Get everyone into the pool as soon as possible. But let's not mark them as having passed the course until we are sure they can swim several lengths without drowning"
I am also a swimmer and past teacher of swimming. Of swimming I can say: not everyone learns swimming at the same rate, over the same length of time, through the same methods of teaching, or with the same amount of practice. H-m-m-m, that sounds familiar; Teaching Methods 101, differentiating instruction.
This quote illustrates a developmental perspective in that any given skill, in this case swimming or Algebra, each need time to develop, have an individual component for each learner, and in the case of either, to be useful to the learner they have to be firmly connected to prior knowledge (learned well). From the perspective of a primary level teacher where student thinking is very concrete and connected to real objects that may eventually be represented by equations, blocks and other math manipulatives become an integral mode of teaching. Blocks are a concrete medium through which students can develop theories, test their thinking and make conclusions. Unit Blocks, the large, blonde colored blocks that need their own shelf in most kindergarten rooms, can be used to build equations: block size A = 2 of block size B or A = 2B. Similarly, Cuisinare Rods also give rise to exploring equivalent relationships. From my experience, concrete exploration with materials that can be manipulated and assist in evolving mathematical thinking is a key developmental component that lays ground work for Algebraic understanding. The reason why my son's comment has stuck with me is that it illustrates how the cultivation of well-based new learning has a connection to prior knowledge and experience. In his case to all the years he played with blocks and legos. Starting with block and other manipulatives, a concrete model to bridge mathematical knowledge to the abstract world of Algebra can be built.
So what do all my ramblings have to do with "the 8th grade rush?" I believe learning is developmental and experiential, not everyone will be ready in the 8th grade for Algebra. Whether any given student is developmentally ready for abstract thinking (Piaget- formal operations) and to learn Algebra will vary from individual to individual. Experientially I wonder what role the primary teacher plays in providing concrete investigative experiences on which bridges can later be built for learning Algebra and learning it well. Thinking of "getting everyone into the pool as soon as possible, what do you think our role, if any, as primary teachers is regarding the development of mathematical thinking that leads to learning Algebra well whether it be in the 8th grade or later?
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