Mathematical Literacy: How Did it Go?

In our Math Lit class, we are taking the Final Exam today. Seems natural to talk about how the first semester went.

As you would expect, the first time through presents some challenges; we already know of several things to change for next time. In general, the high use of small groups did what we wanted and got students directly involved with the material. Naturally, this process uses quite a bit of class time. My major change for next time will be an adjustment to the balance between group work and whole-class work. When we are developing new concepts, I will keep the focus on group work; when we are more into rules and procedures, I will blend more whole-class work. This is mostly an issue of practicality, as we ran out of time on most class days.

The Math Lit course is more about understanding than a traditional course, and this is a good thing for our students. However, students have a harder time judging ‘did I get that’ when the focus is more on understanding. To help them, I will be doing more daily assessments. Obviously, this takes class time — which was a problem already.

One specific observation that I did not expect to see — students needed a symbolic rule for slope. They generally understood that we were looking at a rate of change, but the concepts (rise and run) did not communicate what comparison to make; the ‘(y2-y1)/(x2-x1)’ statement cleared up problems they were having with two things — which values go on top, and keeping the order consistent.

Related to that is another problem — since we saw both linear and exponential models (which both involve two parameters), there remains a bit of confusion about how to write each model. We still emphasize linear more than exponential, but I can see students mis-match the parameters between and within models.

The single biggest problem? Getting students to do online homework! When I could see that students were not doing any homework in the first two weeks, I started checking homework everyday. The assignment in the book was generally done (though not always including a comparison with the answer key). The online homework had a rate less than 10% for the class of being done — and this is with one of the better online systems. In talking to students, internet access was the single biggest problem (though this perhaps was a polite excuse, better than ‘I did not want to do it’); they reported that they could not get online at home, and the usual work/school schedule made it difficult to get to a library or computer lab. I can not solve the access problem; however, I will apply some additional motivation for them to keep up with the homework.

One of the pleasant surprises is how well ‘dimensional analysis’ went. The first two times students ran into this, they really did not get it (in small groups, and whole class discussion the same day). After a quiz and another whole class discussion, most students understood enough to do 3 to 5 step conversions in this style, with work that looks reasonably good.

Overall, the Math Lit class is off to a good start. The focus on understanding and the use of small groups resulted in a good attitude about learning for most students. With some adjustments to class procedures and more assessments, the class will work well next time. [Yes, the outcomes this time were not that good; partially, this is due to a system error in registration which allowed some non-qualified students to be enrolled.] I am making some changes to the daily schedule, along with the group/whole class shifts and more assessments.

Math Lit is a productive approach for students learning mathematics with understanding. I am hoping that you will look into developing such a course at your college.

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Mathematical Literacy Course | Jack Rotman | May 9, 2013 9:23 am

8 Comments

By schremmer, May 9, 2013 @ 11:13 am

Re. “students needed a symbolic rule for slope” Never noticed that. But then I let them plot two points, draw the segment of line and then the oriented rise and run arrows.

Re. ” Getting students to do [ ] homework!” Yes, that’s a problem with students with two jobs and a family and what not. I have no idea what to do about it.

Regards
–schremmer
By schremmer, May 9, 2013 @ 11:29 am

Re. “One of the pleasant surprises is how well ‘dimensional analysis’ went.” Not a surprise to me but then I never use ‘naked numbers’ but only ‘numerator,denominator’ pairs as in 3 apples and then 3 apples • 5 cents/apple, cancel the apples and get 15 cents.

In other words, cents per apple is a dual denominator. Think “dual vector space”. And, in fact, there is really no need to stay in dimension 1 and not deal with ‘baskets’ and ‘price lists’. See <17. Fruit Salad and Linear Algebra>

Regards
–schremmer

Regards
–schremmer
By Sue Jones, May 9, 2013 @ 1:00 pm

My experience here in the tutoring lab was that students felt like the online part took ***forever***. For some of them, it was over their heads — which meant the inevitable Assessment bounced them back down and they had to do Even MOre Exercises… but many of them also acknowledged that the serious immersion had made them a whole lot better at doing the stuff of math. Sometimes it transferred over to the classroom stuff and sometimes it didn’t.
By Jack Rotman, May 9, 2013 @ 1:56 pm

Thanks. Good point about struggling students getting ‘recycled’ through again.
By Sam, May 13, 2014 @ 12:09 am

Having just finished a semester of this, with two college classes, the students were frustrated at the sequencing, the confusing wording in the book, and the tedious assignments. One student quit the class in large part because of the Excel piece. They also noted that there were not clear math explanations, nor were there any explicit formulas, nor anyplace to look up any information. I have never treated students like children by giving them ‘participation grades’ nor have I ever made them do tedious repetitive writing assignments as the portfolio asks them to do.
One of the authors arrogantly started out his presentation at our college by saying ‘it is said that math progress is made on the backs of resignations’. . .this is most definitely not progress, but insulting to students’ intelligence and a dumbing down of dev ed classes.
By Jack Rotman, May 14, 2014 @ 11:02 am

Sam:
Sounds like your department might consider some adjustments to the learning environment. My own intent in promoting a new curriculum is to strengthen the mathematics that students learn by focusing on good and important mathematics from the beginning. Support for student success is an integral part of this vision, which led to inclusion of writing assignments. For some faculty, this also meant an emphasis on context along with discovery learning — both of which have sound research if implemented correctly. I would encourage you to avoid discouragement; I would not expect the course to work well in the first year. [My own first semester in a Math Lit class was “not pretty”.] Faculty will need to adapt materials for these courses, as we have for other courses; you will find a way to make the components work. You might look at some reduction of some components, but it’d be more important to look at supplementing — posting explanations and summaries, making the math (‘formulas’) explicit.
We need to support and encourage each other in this process. These courses are still in the early stages, which we might call first approximations in a numerical process. We will have errors, and we have the wisdom to identify corrective steps.
By Sue Jones, May 14, 2014 @ 12:33 pm

I heard some similar issues from students here, including the (anticipated) expression that “the teachers don’t teach us anything! we’re just supposed to figure it out!”
Many students came down to our Center For Academic Success for help with that, and I had to wonder if many of our successes were because we have lots of support, myself included. I wondered about teachers using the same approaches for students who didn’t have access to support.
Our teachers trimmed some of the Excel demands this time through, which I appreciated. This year was the first “non-pilot” and it was also interesting to see how some of the faculty adapted things to their own style, with varying degrees of buy-in.
The mathematical demands of these courses *is* less than what our students would have been required, as far as level of abstract manipulation of symbols goes. For an awful lot of them, though, this course was a chance for math to be something much more meaningful than the old, rather strange ritual of code manipulation.
By Jack Rotman, May 14, 2014 @ 12:41 pm

Good points, Sue. We need to share and collaborate to make basic changes. The bumps may be frustrating, but the potential gains for our students is real. In terms of details, my view is that the use of Excel is not that important; people sometimes see use of Excel as helping occupations where spreadsheets are used. Might be true — but the learning curve for Excel is steeper than most work on a calculator.
As some might say … “Keep the faith!”

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