New “Instant Presentations” on the New Life Model

The Instant Presentations page (https://www.devmathrevival.net/?page_id=116) now has a set of new presentations on the New Life model.

New presentations include:

1. Reform — the Big Picture
2. Reform — the New Life Model
3. The Mathematical Literacy Course overview
4. The Algebraic Literacy Course overview
5. New Life at your Institution

Instead of a redesign, or just flipping a classroom, look at ways to provide better mathematics to your students.  We can create shorter paths through math and enable students to learn sound mathematics that means something.

If you have ideas for other quick presentations, let me know!

 
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Everything I Needed to Know About Math … Learned in 8th Grade?

Various organizations have been issuing reports critical of developmental education, and developmental mathematics in particular.  Those ‘studies’ tend to be repeated and quoted and cited … until everybody assumes that the conclusions are true.

Well, a similar thing happens with the content.  We had an ‘algebra II for everybody’ flurry, and we are starting to see the ‘algebra II for a lot less’ movement.  One recent report is being used to say that the math that students need in life is generally taught in 8th grade — fractions, rates, proportions, and simple equations http://chronicle.com/article/High-Schools-Set-Up/139105/ ).  Of course, if we read the original source for this article (see http://www.ncee.org/wp-content/uploads/2013/05/NCEE_MathReport_May20131.pdf ) the conclusions are much more subtle; the source actually says that students need conceptually understanding in general, and list ‘functions’ as a needed topic — and mentions complex measurement ideas and geometric visualizations.

In many ways, the actual source (at the National Center on Education and the Economy) is very consistent with what we found in the New Life project.  The ingredients of Math Lit (MLCS) are based on a very similar list of quantitative needs in occupations and client disciplines at the basic level.  I encourage you to read their math report (link given above at NCEE).

The worry, however, is that people will remember the articles talking about the study; that people will see that story line repeated enough that we begin to believe that it has to be true.

We need to keep our voices in the public conversation so that policy makers hear a more informed point of view, one based on professional expertise and information about what students really need in college for mathematics.

No, Virginia, students do not just need 8th grade math in life.  Many college programs will involve courses which depend on other quantitative abilities, and many occupations involve more than just 8th grade math.

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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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Getting to Know the New Life Model

We started our work on the New Life Model in 2009.  When I started this blog in 2011, I created some short presentations about different aspects.  Since then, the New Life Model has become used in more colleges … which means that we understand more about the issues.

I am started an updated series of presentations on the “Instant Presentations” page https://www.devmathrevival.net/?page_id=116

Two of the new videos in this series are now available — “Reform, the Big Picture” and “Reform: The New Life Model”.  I hope you and your colleagues find these videos helpful!  If you have suggestions for other presentations, pass them along.  The planned videos at this point include: the Math Lit course, the Algebraic Lit course, and Implementing New Life at your institution.

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