In Mathematics instruction, the mental processes that are taking place in students’ minds are often as (or more) important than the output that they produce. But, instructions to “show your work” aside, it can often be difficult to evaluate whether a student has fully grasped a concept like a slope-intercept formula, long division, or place value. One way to gain a better understanding of the mental models that students approach problems with is to record or observe students as they attempt to solve (relatively) open ended problems. According to Goldsmith and Seago (2013), this system for gaining insight involves three steps:
- Select representations for particular purposes – find out which representations will support your students’ access to the content
- Recognize the math involved in a particular representation – for example, students need to know that there are 100 cents in a dollar in order understand how to use 100s blocks to solve coin problems
- Link representations to underlying ideas and other representations – for example, students learn to skip count because they have been asked to memorize the multiples of certain numbers. So, often, students don’t know that skip counting is a form of multiplication
The analysis below examines this video using the three steps listed above. (Note: this exercise was carried out for EDUC7520.01 – Math and Technology in Teaching – at Boston College)