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[Future Text] Math Cache

a/k/a Great Moments in Digital Networked Math Curricula

You Should Check Out

Math Caching and Immediately Useful Teaching Data from Evan Weinberg.

What It Is

Evan has his students working on some practice exercises. As they complete their exercises, they use their Macbooks to submit a) an answer (which is nothing new in a world driven by quantitative machine-graded data) but also b) a photo of their work.

The images are titled with their answers and then start populating a folder on Evan's computer.


Why It's Important

Mistakes are valuable. Student work is valuable. This collects both quickly.

Mistakes are valuable for starting conversations, for prompting to students to construct and justify arguments, for asking students, "What different question does this work correctly answer?"

Most machine-graded systems hold back students with wrong answers and let them advance once they've corrected their errors. But this essentially sweeps clear the brambly trail that led to that correct answer when there's so much value in the brambles. Those systems don't tell you why the student had those incorrect answers. They don't allow the teacher to sequence and select incorrect student work for productive discussions later. Math Cache does.

Here's Evan:

I didn’t need to throw out the tragically predictable ‘who wants to share their work’ to a class of students that don’t tend to want to share for all sorts of valid reasons. I didn’t have to cold call a student to reluctantly show what he or she did for the problem. I had their work and could hand pick what I wanted to share with the class while maintaining their anonymity. We could quickly look at multiple students’ work and talk about the positive aspects of each one, while highlighting ways to make it even better.

Somewhat Related:

Nicora Placa:

A main assumption that I work with when doing these [student] interviews is that children do what makes sense to them even if it seems like nonsense to me. My job is to figure out what makes sense to them and why.

2013 Oct 2. Pearson's research blog picks up this post and argues that I'm too pessimistic about machine-graded data.

4 Responses to “[Future Text] Math Cache”

  1. on 02 Oct 2013 at 9:20 amMegan

    I love this idea!! Not only is it good for the teachers and a better way to get information for the students, I think is it also a more fun way for students to interact and engage in the lesson. It encourages the students to complete the problem so they can take a picture of it and turn in it, love it!

  2. […] Dan Meyer posted today an example of a technology that allows students to submit an answer and a photo of their work that teachers can then use as prompts for discussion. I completely agree that examining this student work is essentially for getting at their understandings and misunderstandings. We need to make student work products, even when done on technology, available to teachers. He also writes that “most machine-graded systems hold back students with wrong answers.” This is a problem with the system design, not machine-grading. We can create machine learning systems to identify misconceptions. What happens next depends totally on what we tell the system to do. Do we want the student to move on? Do we want to alert the teacher? Do we want them to go to a different set of exercises? This decision is part of building an “instructional model” on which a technology system should be based. […]

  3. on 03 Oct 2013 at 3:16 amCathy Yenca

    Nearpod is another great tool for generating, analyzing, and sharing student work… in real time! Authentic, anonymous error-analysis has become a regular part of my practice thanks to this handy app.

    Not only is student work instantly available for analysis, anonymous student work can be “launched” by the teacher to all students’ iPad screens for discussion. Work samples are also accessible by the teacher as a series of image files for further analysis after class is over.

    See here:

    or here:

  4. […] took machine-graded learning to task earlier this week for obscuring interesting student misconceptions. Kristen DiCerbo at Pearson's Research and […]

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