Math pedagogy-Are we giving kids credit for what they can do?

Do we lock ourselves into a pedagogy that stymies our students. Do we sometimes actually slow up out students learning capabilities by our delivery methods. Check out this link and let's talk about this idea? Go to:

Tags: education, learning, math, pedagogy

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I'm going to read it but let me just say before I do that regardless of what it says the answer is yes, and it isn't just in math. Especially with our intelligent kids we are constantly slowing them down.

Great read, thank you for the link. It is this kind of transformative thinking that our education system needs. I am in California where for the last year I have heard countless (literally) teachers bemoaning our Governor's hope that all 8th grade students take Algebra. Hearing math teachers constantly say "many kids just can't do it" in response to that hope absolutely blew my mind. I'm afraid the gov will back away from the proposal given our budget mess now but it is a shame. Kids will do what we ask them to do and often so much more if we simply let them.

We teachers get so locked in to our routine that so often we refuse to see that our assumptions might be wrong entirely.
The answer to your question is absolutely YES. While reading the article, I remembered educational psychologist Jerome Bruner writing that students can learn any subject matter at any grade as long as the subject matter is presented in an appropriate way.

As a teacher I have found that often the most productive thing that I can do is prompt my students to start thinking about something and then step back. Too often teachers think that they must be at the center of the learning experience. When this occurs some students will be slowed down and others will be inappropriately quickened.
About a week ago, I was shocked to find that Wikipedia does not have an article on Early Algebra. I started an article, but it is still too short. Join the effort?
I added a couple of ideas based on the work of Carpenter and others at UW-Madison.
Great article. I couldn't agree more with the premise and agree that teachers need to open themselves up to possibilities. I'm struggling responding to this forum. I agree, we aren't using instructional strategies that are as effective as we would like. I work for a non-profit implementing research projects to help teachers change their instructional approaches, but it's difficult. I don't want to bash teachers because I believe that teachers really do want to do the best job they can, but am struggling with a system that doesn't set itself up for success (at least my version of success).

As I reread my response, I don't think I'm saying anything. So I'll change to this. I'm working on an RFA for IES to design a teacher development project to help teachers in middle school develop algebraic reasoning in their classrooms more effectively (to change the focus away from solving equations to understanding that algebra is about relationships between variables and quantifying that relationship). I would love to set up a conversation about what to include in that project or how to design the activities. Anyone interested?

Thanks for sharing this article Mark!
Roland, I am interested in talking with you about your project. I have started a mind map about algebra, for the purpose of initiating conversations with teachers and parents on what algebra is. It's a "wiki map" - try playing with it:

You are facing two opposite challenges working with teachers. First, you need to connect to their existing experience and realities. Second, you have to show something that is "new enough" (or even "radically new enough") that people feel the need, first, to even pay attention, and second, to accommodate the new ideas.
I noticed that you were working an an algebra mindmap. I thought that you might find interest in seeing a student's concept map for algebra. THIS LINK will take you to the base map for my son's algebra map. He began the map in 7th grade and has added to it over time as his understanding has been growing. It is a student map, so you may see areas that are as of yet imcomplete and areas where his maps have some errors, but I figured seeing a student's mind at work would be worth sharing.

Navigating the map:
The link takes you in on the base map for the subject of algebra. It is simple because he wanted to keep it focused on what he was seeing as the core. From the base map though, you can link to the may submaps from the little icons at the bottoms of the nodes.

You may find his arithemetic map of interest too. He has been working on that one since 5th grade, so it has a fine level of completeness. HERE is the LINK.
Tammy, these are incredibly cool maps. I think I am going to start using ongoing concept maps with my long-time students. Thank you very much for sharing. Why did you son decide to work with concept maps like this?

I use "the rule of three" all the time and I did not know it was "the Harvard rule of three." My version is a bit different, though:

Whenever you use a concept, you need at least three examples and at least three representations.

So, if we are doing a positional number system, we look at three bases at least (I like binary, base three and base ten). Bonus points for qualitative examples, when possible - say, "love is not a commutative relationship." This goes well with another principle - students creating instances of every entity we work with...
Cmap is a software I would highly recommend. It is free and has either a server version which your school can set up so the kids can post their public maps school-wide or individual computer version which can be set up to keep the maps merely on that computer or the kids can post it to one of the free university sponsored Cmap public servers which would make their maps available to them beyond high school. We opted for the university public server because I want my kids to see their maps as a part of life-long learning. They can continue to add to them for as long as they live (or the software/server disappears).

Why did he use concepts maps? I guess it is just a natural extension of the way we do things. For instance, instead of studying biology from one text, filling in the blanks for practice, and taking an exam, we have been e-notebooking for years. The kids research and build their own notebooks (a cross between a scrapbook, web-page, and portfolio) that shows what they learned and did. Concept maps were something I required them to create the maps and place a link to the appropriate portion in their e-notebooks to show how their studies fit into the big picture and how their studies narrow down to fine detail. Learners often get lost in an ocean of disconnected parts. I wanted to emphasis that the fit was as important as the pieces. I have found that when they take the time to learn as much about the fit as they do about the piece, they do a much better job of retaining the information. I think the math e-notebooking and concept mapping has done a lot of good for him. He scored in the 96th percentile on the last standardized math test that he took.
I wanted to know if your son only did the map by himself, or if it was a part of some bigger project. It looks like you have a wealth of experience using maps with many classes and people. Thank you for sharing.

Hosting on a server seems great. I would like to see a tool that inserts pictures into maps, and also allows online sharing and collaborative maps (wikimaps). MindMeister does the sharing part, but I don't like their "tree-only" structure not allowing loops.
Cmaps can do images within the nodes or in backgrounds. The math Cmaps don't have much need for images, so you probably didn't stumble across any with them in it.

Take a look at THIS collaborative Cmap for our online biology class. You can use the nodes at the bottom of the screen to view many maps that my kids have made individually, as a family, and in our online classes from many subject areas. Feel free to wander through.

Yes, Cmaps can be made collaboratively. You merely set the folder permissions with the usernames of the students that may edit on that map. If two are signed in simultaneously, Cmap automatically opens up a text chat window. Students working at different times on the same map have many other tools as well such as notes (it looks like a yellow sticky note on the page) and you can connect the map up to a larger forum tool.

Besides collaboration, another option is to plant a seed map with some basics and have them access that seed map to make their own changes to. As soon as they make a change they are flagged that they do not have permission to alter the original map but that they can makes changes to create their own based on the original map. You can give them nodes, for instance, and ask them to provide linking terms to show that they understand inter-linking relationships.
Thank you for the great overview-in-context, Tammy. I will drop you a line when we have something interesting happen with Cmaps. You have great ideas!



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