{"id":1,"date":"2014-04-14T07:08:47","date_gmt":"2014-04-14T11:08:47","guid":{"rendered":"http:\/\/www.coast2coast.me\/carl\/?p=1"},"modified":"2014-04-30T08:00:24","modified_gmt":"2014-04-30T12:00:24","slug":"hello-world","status":"publish","type":"post","link":"https:\/\/www.coast2coast.me\/carl\/2014\/04\/14\/hello-world\/","title":{"rendered":"Carl’s NCTM Experience: Hyman Bass And Theory Building"},"content":{"rendered":"

2014 NCTM Annual Meeting and Exposition<\/em><\/p>\n

This year\u2019s annual meeting took place one short drunken stumble away from Bourbon Street at the New Orleans conference center. \u00a0The entire space was used by the NCTM conference, and they still had sessions hidden away in deep recesses of the center as well as in the Hilton which was a onerous 5 minute walk down the street. Selecting talks at this event was a constant struggle between dozens of excellent speakers. \u00a0The best algorithm that I found to choose which talks to go to was to attend the talks that people smarter than you recommended. Using this method, and a little \u2018phonebook\u2019-style searching, I ended up attending and learning from the following talks. After three action packed days I came away with a lot of ideas, and a lot of notes, but nothing really concrete.\u00a0 So in order to squeeze every little bit of learning out of the experience I am going to write up as many talks as I can remember here on the blog.<\/p>\n

The Mathematical Practices of Finding Structure and Making Connections<\/b><\/a><\/h3>\n

Hyman Bass – Slides<\/a><\/h4>\n

This talk had a number of situations that push students to think deeply about solving problems and making connections between the ways you can solve problems. \u00a0For example, slide 2 shows a problem that students can understand as a visual problem or as a problem that can be dealt with by adding the pattern of odd numbers. \u00a0He went on to show how a generalization of this problem could be expanded to larger squares, (but the slides shared on the NCTM website don\u2019t seem to have all of the things that he talked about). \u00a0The connection between a geometric representation of something that can be expressed with an equation was the big concept and slides 3 and 4 show two geometry problems that can have similar math connections and produced genuine \u201cAha\u2019s\u201d from the crowd of math educators.<\/span><\/p>\n

<\/p>\n

Following the 3 problems, Bass went into a talk about how to make students into \u201cProblem solvers and Theory Builders\u201d which wasn\u2019t really reflected in the slides. \u00a0My notes show that when people look to create more rigorous or deeper learning situations that they can to place students in, there is a huge thrust to push students into applied situations, where mathematics is used to solve specific problems in a specific way. \u00a0This focus on calculation only lets students participate in a small part of what it means to be a mathematician. \u00a0Mathematicians were thought of as thought leaders through history, as they also used their brains to examine evidence, analyze patterns, and create theories about numbers. \u00a0While all of the math that children study in school has been examined and studied to an exhaustive degree, students need to come out of math class with this theory building skill set. \u00a0<\/span><\/p>\n

 <\/p>\n

Math teachers have to create new problems that put situations to build their Problem Solving\/Theory Building skills. \u00a0Bass boiled it down to a few steps that were important in helping them build theories off of patterns by doing the following with a given pattern in order of which shows the most understanding:<\/span><\/p>\n

 <\/p>\n

    \n
  1. \n

    Repeat the given patterns or duplicate the pattern (Ex. \u2018star star circle\u2019)<\/span><\/p>\n<\/li>\n

  2. \n

    Extend or continue a sequence of the pattern (Ex. \u2018star star circle star star circle\u2019)<\/span><\/p>\n<\/li>\n

  3. \n

    Reproduce the pattern with new materials (Ex. \u00a0given new shapes: \u2018diamond diamond triangle\u2019)<\/span><\/p>\n<\/li>\n

  4. \n

    Explain why the reproduced pattern is has the same pattern as the original (Ex. \u201cSame, Same, Different, Same, Same Different\u201d<\/span><\/p>\n<\/li>\n<\/ol>\n

     <\/p>\n

    To expand this to more advanced math he showed a problems set that had students look through 4 different example of combinatorics problems which are shown on the 5th slide. \u00a0These problems are all interesting in their own right, but when put in a set, it gives students the opportunity to think about how these problems should be solved and perhaps talk about how the structure of these problems. \u00a0Once students see the similarities in the problems, teachers could look to ask students to apply the thinking to new problems, create their own situation when given a different context, and explain all the similarities between the mathematical thinking required to finish all of the tasks.<\/span><\/p>\n

     <\/p>\n

    One quote that stood out was while he was talking about making problem sets to get students to think differently. \u00a0Bass said, \u201cGive kids problems that force them to fail enough to where they see the benefits of the kind of thinking that would be useful.\u201d This means having a bunch of the same kinds of problems that have simple procedures is going to be harmful for their development since they won\u2019t get a chance to learn from their mistakes. \u00a0<\/span><\/p>\n

     <\/p>\n

    Next, Bass started talking about the Tea and Wine problems, which I saw detailed in this article <\/span>Theory Building in the Mathematics Curriculum?<\/span><\/a>. \u00a0This article also includes a proof of the situations in slides 6 and 7. \u00a0These problems are part of Common Structure Problem Sets (CSPS). \u00a0My notes at this part of the talk were not very useful as I was also texting my school to see how everything was going while I was gone (it all was fine). \u00a0<\/span><\/p>\n

     <\/p>\n

    The talk ended before I was able to get more an understanding for these kinds of problem sets, and google isn\u2019t too much help either, but I think the pattern of repeated problem solving strategies is definitely something I am going to employ the next time I want to explicitly teach mathematical thinking.<\/span><\/p>\n

    \n
    \"\"<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    2014 NCTM Annual Meeting and Exposition This year\u2019s annual meeting took place one short drunken stumble away from Bourbon Street at the New Orleans conference center. \u00a0The entire space was used by the NCTM conference, and they still had sessions hidden away in deep recesses of the center as well as in the Hilton which […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[2,1],"tags":[],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4xz6U-1","_links":{"self":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/1"}],"collection":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/comments?post=1"}],"version-history":[{"count":5,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/1\/revisions"}],"predecessor-version":[{"id":80,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/1\/revisions\/80"}],"wp:attachment":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/media?parent=1"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/categories?post=1"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/tags?post=1"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}