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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Math Literacy: Student Motivation

We’ve completed two weeks in our “Math Lab” format of the Math Literacy course.  [We’ve been teaching Math Lit for several years, but this is our first try at this format … the Math Lab format focuses on student learning and options, and much less on ‘teachers presenting’.]

One thing I have noticed is that students are working harder than they did in our beginning algebra course.  Math Literacy replaced beginning algebra (effective this year) so the students are similar in terms of background and goals.  Both courses emphasize the online homework system from the company, and the length of homework per section is very similar, especially in terms of number of problems.  The complexity of the homework is higher in Math Lit, as students need to do some reasoning (as well as calculating) right away.

I can measure the increased effort by both time on task and by sections completed.  By both measures, students are more ‘motivated’ in Math Literacy than the traditional course it replaced.

This increase came in spite of the fact that students are working primarily as individuals (they did not form small groups or pairs, in general).  The progress is almost totally based on what each student is doing.  We often use small groups as a way to build community and motivation; perhaps the motivation link is not as strong.

Although I have not interviewed students about this situation, I think there are a couple of basic reasons why they find the Math Literacy course more ‘innately motivating’:

  • They see the problems as more interesting, since the majority of problems are word problems of some kind — fewer problems are just procedural.  Perhaps they view them as having a ‘reason to solve’.
  • The content is different in a fundamental way from their K-12 math experience — the course is clearly not their Algebra I book with a different cover.  There may be an element of “appeal to adults to learn something” as opposed to fixing their math background.

Over the semester, I will get to know these students enough to understand the situation a bit better.  Right now, I’m happy just to be able to observe the effort they are investing in learning mathematics.

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Math Literacy … Focused on Students

After one week of our new “Math Lab” sections of Math Literacy (‘without a teacher at the center’), I am pretty darned pleased with the early results.

My institution replaced beginning algebra with Math Literacy this year, so we have dozens of sections for Math Lit.  Four of them are “Math Lab” classes, where students spend class time interacting with the textbook and material under instructor supervision but without any presentations.  I am teaching two of these four ‘Lab’ classes, so that is the basis for my comments.

The course work is highly structured.  The book work has been organized within each section/lesson so that students work a  couple of pages at a time (checking work against the solutions posted with each assignment); we have a video with guidance attached to each assignment.  A section/lesson has 3 or 4 of these assignments, along with a typical set of online practice problems at ‘the end’.

On the first day, I did a course orientation so students could see how this worked.  I strongly encouraged students to work together on that book work.  On the one hand, I am disappointed by the ‘together’ part — only a couple of students are working together in each class.

However, the students are getting in to the course work and the book work.  A high proportion are getting sections done (1 or 2 per day).  In the old algebra course, the progress was much slower … the change is evidence that the content & approach of Math Literacy has a higher innate motivation for our students.  Not only are students working and making progress, they are asking questions already (not all students, but more than the algebra course).  The material so far is basic numeracy (uses of percents, proportional reasoning, basic data summaries, etc) … the course transitions into algebra over the next weeks (though some algebra is present throughout).

The course design includes a Quiz (taking online) after the first 3 lessons.  That quiz is on the schedule for yesterday for one class; in that class, ten of the 14 students got to the quiz on time (with the lowest score being a 88%).  [The other class schedule is half a week behind.]  We’ve done quizzes in our Lab classes before, but I have never had even half the class take a quiz on time.

The early results are promising.  My conjecture is that some of the best learning occurs when we get out of the way, and configure the class so that students spend a lot of time interacting with mathematics.

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Math Literacy without a teacher at the center

We are trying something different this fall.  As we’ve eliminated our basic algebra class in favor of Math Lit, we are adding a student-directed format. I’m doing two of these classes as part of my teaching load this semester, and I hope to post commentary each week.

What’s different?  Well, the big difference is that students in this “Math Lab” (student directed) format work on the material without me standing in front of them.  The online homework system has videos in support of the workbook, which focuses on context and concepts; students will be following these detailed assignments for each section, and they are encouraged to work with other students.  [Of course, the students also face the usual assignment of problems to be done after this studying.]  The instructor is available to help when needed.  The goal is to get every student actively engaged with the mathematics (no sleeping in class 🙂 ).

I am testing a conjecture that students can learn significant mathematics (concepts and reasoning)  mostly ‘on their own’, even at this level.  Sometimes, I think we place too high a value on what we say or do.  In my view, all learning is essentially “on my own”.  Help is often needed, but is not always best prior to the learner recognizing that there is a need.  It’s not that one way is better for all students at all times; it’s that a different approach enables more students to succeed — and that this sometimes leads to students understanding the learning process a little better.

We’ll see how it goes!

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