Math Literacy: What do Students Struggle With? (part I)

In our “Math Lab” sections of Math Literacy, all tests are given individually … and graded while the student watches.  This is done by having 3 alternate forms of each of the 6 tests, with an answer sheet.

The process results in deeper knowledge of what students struggle with as well as what is going well.  For example, the little bit of algebra on the first test went well for all students.

On the other hand, two ‘estimating’ problems are struggle zones.  One question involves angle sizes:


The choices are provided to make this less stressful for students.  Quite a few students select sizes that are obviously too big for the image (choice A or B in this case). Very few select a ‘too small’ option (C).

The other estimating looks like this:


Our answer key allows about 10% leeway around the expected answer (390 miles for this one).  Again, students who miss this usually estimate too high (sometimes way too high).  A rare student went low in their estimate.

The issues seem different in each problem.  Estimating angles seems to be a perceptual challenge, where the eyes look at the distance between the rays instead of the opening size (or ratio of distances).  The map problem appears to be a simpler challenge — not using the measuring device provided (the scale at the bottom).

This test has a third estimating problem:


Students are missing this one for an odd reason:  instead of writing “-82”, they write “82”.  They knew that they were on the left side (it’s not like they said ’78’) but did not connect the sign with the estimate (even though it’s on the graph).  I don’t look at this as a struggle as much as ‘attention to detail’ … an issue for many of our students at all levels.

All of theses problems have similar exercises in the homework.  [We also have a Practice Test in the online system, which also has the problems.]  For most topics, those exercises are sufficient.  The first two listed above ‘not so much’.  These fit in the category “learning how to learn” … noticing a problem, seeking help, reasoning about it, practicing, etc.

Overall, the Math Lab method is working well for this course.  We will see other ‘struggle points’ for other topics as we go through the material.

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