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?
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I also wondered whether there would be different results at lower grade levels, especially k-4 where bringing experiences to our learning and learning through experiences seems to occur daily. Questioning is second nature as we want to entice children to think but at some point this technique dissipates and we as educators focus on the equation and the answer rather than the "how did we get here?" Having used the KWL chart often for language arts lessons and finding this to be a powerful tool, I was fascinated by the KWC chart for mathematics. Bringing cognitive strategies to mathematics - I love it! I visualize the braid created as having a much stronger ability to hold together than a single strand, just as decoding is not the only strand in the reading process. I have acquired more true math comprehension this week than in my years of "formal" education.
At our school I think that the teachers of grade 4 and 5 are mostly concerned about the MEA results and are very concerned about covering everything in math before it is time to administer the test. I recently did a survey to find out what manipulatives are needed at specific grade levels in order to implement the new Investigations program. It was not surprising for me to find out that our primary teachers have many materials for math instruction while most of our grade 4 and 5 classrooms have very little. My prediction would match your prediction of decreasing use of active questioning as students progress through school. I must say that I do not feel pressure to "get through everything" but I know that teachers in grades 3-5 do feel some urgency.
The article, "Mathematics and Cognition," makes a great deal of sense. I have always felt that there is an advantage to teaching in elementary classrooms because we have our students all day and it is easy to relate strategies across the curriculum. When I am teaching math I think about the skills we have been practicing in reading, writing, science, etc. We apply them during math and math becomes integrated into reading class and other areas throughout the day.
There is a Cantor video course offered through UNE that emphasizes the five key cognitive processes identified by NCTM (and mentioned in the article). At our school we used our staff development time during the first semester of last year to study these processes and then we worked with our grade level teams to develop lessons that focus on one or more of the processes. The course and subsequent staff development were very helpful to me in improving instruction and learning.
Pat Grade 2 teacher
I also like the idea of KWC. It's a way of organizing information and also it gives us the ability to try to assess students' thinking and understanding. We as teachers must model and teach kids to "infuse language and thought into mathematics".
Building connections is also important especially to the middle school student who thinks he or she will "never use this in real life". Meaningful work for all should be our goal.
Pat, You have a brought up a valid concern for 3-5 teachers who have a March MEA to consider. I believe we can teach math in an investigative, experiential, dialogue-rich way even with this factor. Bridging best cognitive practices from reading is one way to maximize and connect the learning for kids so that we can prepare kids to show what they really know and understand by March.
I would love to talk more about this MEA factor so we can get past it being the impediment to using best teaching practices in math but instead into just another reason why we use them. I think if we really looked at the MEA - conceptual math teaching does help with 80 percent of the test; the other 20 percent is test taking strategies - I don't mean teach to the test but strategies that help you to think out a reasonable answer. And these strategies only work if kids can think math not just do math.
The Mathematics and Cognition article was great. It is about time that research has related learning math concepts to strategies that work for other areas of learning and cognition. It is essential that we begin to engage in the K-W-C process during mathematics. This process will help to facilitate necessary meaningful connections and awareness of patterns for students. It will give math teachers a structure to help facilitate teaching that is best practice. I hope I too can begin to do a better job of teaching mathematics that helps to foster a life long love and understanding of math in my children.
Deb S. kinergarten
The idea of "braiding reading and math cognition" reminded me of scaffolding used for teaching any academic content to English language learners. The academic content goals are paired with lanuguage goals. Reading and writing strategies are viewed as an integral to learning in all content areas such as math. When I think about my students and reflect on exploring math concepts the general classrroom setting, I realize that a good many of the times we have struggled with a concept there has been a connection to language (ineffective or misleading use of) and termonology imbedded in the lesson or activity. Similar to reading and writing, children are trying to find a meaningful connection with any given math concept. This article and Maggie's emphasis on language have really got me thinking about how to integrate lliteracy strategies with math investigations and the language I use to facilitate students during a math lesson. I too am intrigued by the KWC chart.
This article certainly gives me food for thought. I've been chewing over various pieces of it all evening. Capitalizing on student connections and building conceptual understanding should be at the heart of everything we do as teachers. How did we, as a country, stray so far from the mark with math, turning it into a series of formulas to follow?
One sentence stood out to me, especially: "Meaning making and comprehension in mathematics requires deep conceptual understanding of abstract ideas (Hyde, 2006)." In our haste to 'move 'em on," we are robbing kids of the chance to build to that level of comprehension. I, for one, will be rethinking how I'll structure my math lessons this year.
I also really likes the idea of braiding together different methods and using an interdisciplinary approach to teaching math. Time is definately a factor when we are supposed to reach a certain chapter by the end of the year!! All of these ideas relate to critical thinking skills, and I believe that right across the curriculum we must do a better job of helping students with this.
I especially liked what Deb said, about realizing that students' misconceptions or uncertainties about how to approach a mathematical problem may very well be due to ambiguous language. Maggie's repeated modeling has hammered it home to me that what we communicate to our students must clearly match what we expect them to do. Using the KWC chart is another way to simplify or make clear the essential elements of the mathematical challenge. I am looking forward to trying it with my new 3rd graders.
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