Math Lit, and Pathways for Faculty

On my bookshelf, I have copies of two of the best math books available today:  Math Lit (Almy & Foes) and Math Literacy (Sobecki & Mercer).  Here are cover images:

Three years ago, this course was not offered anywhere.  As of this month, we have over 40 colleges offering the class with over 160 sections; Mathematical Literacy is an alternative to a beginning algebra course.  With the hard work of faculty, support from their colleges, and wisdom of publishing companies, the New Life Project continues to make a difference in our profession.

The work continues; the next course to be developed is Algebraic Literacy.  This alternative to an intermediate algebra course offers similar advantages; take a look at the “Missing Link” presentation (https://www.devmathrevival.net/?page_id=1807) from last fall’s National Summit on Developmental Mathematics.

I am seeing this progress as part of the pathway for us — a pathway for mathematics faculty.  We are moving from an accidental collection of relatively isolated topics with little benefit to students … to a deliberate design of courses containing mathematics to be proud of, with content designed to help all of our students.

In the process of moving from the old to the new, we are on a pathway ourselves.  We can become inspired by the design, gain skills in teaching mathematics, and experience a course that connects meaningfully to students.  Instead of being seen as “the last course to take, the one that stands in the way of graduating”, we can provide courses that show benefits to students earlier in their program.  Many students will find our new courses enjoyable; they will leave with a more positive view of what mathematics is.

We are on the path that leads to a mirror, a mirror which says “We do important work, and students benefit; be proud!”  I hope to see many of you on this trail.

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More Math Lit Materials Available

The second textbook for the Mathematical Literacy course is available.  Great news!!

The new book is by Brian Mercer and David Sobecki, published by McGraw Hill; the title is  Pathways to Math Literacy ( © 2014).  I had an opportunity to see some of the material prior to publication; you will find this text to be a good contrast with the other book currently available (some info below on that one).

This new book has a web site for instructors at http://successinhighered.com/pathways/   Take a look … they have information about the book that is actually helpful, and they have a resource page for faculty considering ‘pathways’ (whether you use their book or not).

Also available is the initial Math Lit book by Kathy Almy and Heather Foes, published by Pearson ( © 2013).  You can get information on that book at http://www.pearsonhighered.com/product?ISBN=0321818458  and at Kathy’s blog (http://almydoesmath.blogspot.com/ .  I noticed that a recent post on that blog is a recording of a webinar on implementing pathways; very helfpul.

As of this semester, we are up to about 170 sections of Mathematical Literacy across the country (this is not counting the Quantway™ sections).  Now that we have a second commercial textbook, even greater growth is possible!

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Math Lit/Applications for Living: Seeing the Power

Both the Math Literacy course and the Applications for Living course deal with two common models — linear and exponential.  I’m finding it interesting to watch how different and similar the experience is.

For both students, they have not seen exponential models in their college (developmental) courses; none of the current Applications for Living students had the Math Lit course previously.  (That will change as some Math Lit students take Applications for Living.)  In both cases, we explore models from numeric and symbolic forms; the Applications for Living course includes more variety, and also requires active graphing of exponential models.

In both courses, students have a difficult time leaving the linear world of adding and subtracting.  There is confusion about the role of slope in an adding world; during the exploring process, we take the time to show repeated adding as a multiplying, and identify the number as the slope.  When we work in exponential situations, the linear view seems to dominate.  During the exploring process, we show repeated multiplying as an exponent and learn about the role of the multiplier.  The performance learning outcomes are not what we would want; there are some differences between numeric and symbolic problems.

For example, the final exam in the Math Lit course had a doubling problem for which students needed to write the model.  Something like:

At the start, 25 people knew about the latest i-product; this number is going to double every day.  Write the exponential model for N (the number  who know) based on t (days since the start).

Another problem for the Math Lit final was a growth pattern from a numeric standpoint:

The cost of a machine is $400, and this is expected to grow by 10% per year.  Complete the following table of values.  [The table shows years 1 to 5, where the value for each year needs to be completed.]

In Applications for Living, the corresponding problems were this symbolic one:

The value of an investment is expected to grow by 6% per year.  Write the exponential model for the value in terms of the number of years.

And, this numeric one:

At 3pm, 20 mg of a drug were in the body.  At 4pm, 15 mg were in the body.  Complete the following table of values.  [The table shows hours 1 to 5, where the amount of drug needs to be completed.]

Almost half of the Applications for Living students treated the last problem as a linear one: They showed values of 10, 5, 0 and 0 (sometimes with a puzzled comment about having zero as the amount).  In class, we had done drugs in both half-life and percent decrease models; we had calculated the multiplier as well.  They did a little better on the symbolic form; part of this is the fact that this course also does work with finance formula, and one of those formulae is basically the answer for this problem.

The Math Lit students did well on the numeric problem; part of that success was the remediation we did earlier when most students had difficulty on all things exponential.  Few of the Math Lit students wrote a correct exponential model, which is noteworthy since the problem is a slight variation of a situation we used to introduce exponential models.  Most of the incorrect answers were variations on y =mx + b.

Clearly, this assessment feedback is indicating a need for an adjustment to the instructional cycles.

However, I also think that the results reflect a math curriculum that tends to treat topics in isolation.  How often do students need to deal with both linear and exponential models in one assessment?  Also, do we use the word “always” with students?  As in: “Compare the y-values; the difference always tells you what the slope is.”  Or, “If you can see how to get the next value in a table, you can always use this to complete a table.”  Or, “In a function, you can always get the next function value by adding or subtracting.”

During the instructional cycles in both courses, I can see the resistance to leaving the linear model.  It’s a bit like distributing, where students become fixated on one process.  I want students to see the power of understanding exponential models; students want the comfort of one model for all situations.

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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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