Comparing Texts for Mathematical Literacy

The “Mathematical Literacy” course has been taught at colleges for about 5 years now, with hundreds of colleges involved.  For this post, I will look at the alternative textbooks for Math Lit with some quick comparisons.

First, I’ve got to point out that some books are being marketed for “Pathways” with very little change in content.  Math Literacy is not just a name for a modified old course; Math Literacy is the first new course in developmental mathematics with content drawn from modern standards, with an emphasis on reasoning and communication.  This comment applies to books from most major publishers; in particular, Cengage and Hawkes do not have a Math Lit textbook (though they do have books for pathways).

I recognize 3 textbooks available which faithfully implement the Math Literacy learning outcomes (whether as Math Lit, Quantway™, or Foundations of Mathematical Reasoning).  Quantway courses run differently from the others in the sense that colleges join the collaborative, and use shared materials & online system; colleges not in the collaborative do not have access to those same materials.  However, the Quantway materials were the basis for the Foundations of Mathematical Reasoning (FMR) from the Dana Center.

• Foundations of Mathematical Reasoning (FMR); Pearson
  https://www.pearsonhighered.com/product/Dana-Center-Student-In-Class-Notebook-for-Foundations-of-Mathematical-Reasoning/9780134467481.html
• Math Lit (Almy/Foes); Pearson
  https://www.pearsonhighered.com/product/Almy-Math-Lit/9780321818454.html
• Pathways to Math Literacy (Sobecki/Mercer); McGraw Hill
  http://www.mheducation.com/highered/product/1259278751.html

If you want the ‘most different’ materials, you’d choose the FMR materials.  There is not really a ‘textbook’ with FMR; the lessons are a series of contexts and problems with the mathematics tied in to those situations.  The core of FMR is the classroom work (highly group based).  The lessons are presented in ’25-minute’ pieces, and the instructor has a set of supportive materials including suggestions for processes.  A number of colleges (mostly in Texas) are using the FMR materials as part of a larger project; other colleges adopt them as they would any textbook.  (Again, the Quantway materials are very similar to FMR but  only used ‘in the network’.)

The Almy/Foes Math Lit shares some of those properties.  The lessons are highly group based, focused on contexts and problems; instructors have support materials.  The  Almy/Foes structure is not as finely grained as FMR, which I think fits what most faculty prefer (though I have been known to be wrong … on occasion!).  This was the “original” math literacy text, written before most of us thought about offering the course.  Unlike the FMR materials, the Almy/Foes text is definitely geared towards the non-STEM pathway.  If you are pretty sure that you can support a discreet path for non-STEM, this text is a good alternative.

The Sobecki/Mercer “Pathways to Math Literacy” combines some of those properties within a slightly more traditional structure.  The lessons employ significant group work, but also significant whole-class work.  This book includes slightly more mathematical content, and a little less divergent lesson work (where students might create 4 different methods to ‘solve’ a problem).  Instead, the Sobecki/Mercer text tends to keep a goal or outcome in mind.  If your dev math program is highly adjunct-based (as mine is), this text probably is a good choice.  As does FMR, the text does not assume that all students are non-STEM — though the contexts are generally non-STEM.

Each of these sets of materials has advantages, and they all deliver the core learning outcomes of Math Literacy.  All 3 are doing well in the market, from what I can tell.

If you have specific questions about a specific set of materials, I can try to help get an answer.

 
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Why We Will Stop Doing Pathways in Mathematics

Currently, and for the past few years, “pathways” has been a big thing in community college mathematics education.  For students not needing calculus or similar courses, alternate paths have been established — with a focus on courses such as Statway™, Mathematical Literacy, and Foundations of Mathematical Reasoning.  The fact that all three of those courses are very similar in content is not an accident, and the fact that the three organizations involved collaborated is a key reason for their success.

The reasoning behind the creation of pathways is essentially “give them what they need, not what they don’t need”.  Students with a pre-calculus target are still placed into the old-fashioned developmental math courses, and students with other targets are placed into a ‘pathway’.  All students are generally required to meet some arithmetic criteria before starting at the Math Literacy level or beginning algebra.

My own work has certainly played a role in this creation of pathways.  However, that was not the intent of the efforts beginning this work.  Neither do pathways have a good prognosis for long-term survival.

Let’s go through some of the reasons why “pathways” are not a long-term strategy.

Reason 1: Pathways are a dis-service to “STEM” (calculus-bound) students!
The original design of the major pathways courses (Quantway™, Math Literacy and Foundations of Mathematical Reasoning) was based on identifying what all students needed in college-level mathematics — statistics, quantitative reasoning, AND pre-calculus.  These outcomes were then categorized in two clusters … those needed by ALL students became the core of the Math Literacy course, and those primarily needed by pre-calculus students became the core of Algebraic Literacy.  [Algebraic Literacy also includes some outcomes needed for technical programs.]

In effect, “pathways” is preventing STEM (calculus-bound) students from getting the learning they need for success.  We have accumulated data showing the the traditional developmental algebra courses do not add significant vale for these students when they take pre-calculus.  In addition, we also know that the traditional courses were not designed for this purpose — they were designed to replicate the 9th to 11th grade content of a 1970’s high school.

Pathways create a better experience for non-STEM students, at the price of harming (relatively) those bound for pre-calculus.

Reason 2: Curricular complexity costs too much
One of the extreme cases I have seen is a college with SIX different courses at the Math Literacy level.  Clearly, half of these are quite specialized for students in particular occupational programs.  However, half were general in nature — a Math Literacy course, and two basic algebra courses.

Curricular complexity raises the cost of support functions at an institution, advising in particular.  Few colleges can support this extra work in the long-term, even when the initial launch of those efforts is strongly supported by the then-current administration & governing board.  As time goes on, the focus on advising slips … mistakes are made … and a later administration will question why things are so complicated.

This curricular complexity also raises costs within the mathematics department.  More courses at the same level means more difficult scheduling, less predictable enrollments in each course, and a host of faculty coordination issues.  Unless an institution has excess resources not needed for other situations, the mathematics department will realize in a few years that they can not support the complex curriculum.

Reason 3: Pathways allow the continuation of arithmetic courses at colleges
The presence of arithmetic courses at a college involves several problems and costs; the fact that our profession has not accepted these are overwhelming rationales for discontinuing arithmetic courses is a failure with moral and economic dimensions.

First of all, these extra courses at the developmental level are primarily taken by students of poverty and minorities.  This is the moral dimension for us:  these are the students coming to college to get out of poverty, who are then required to take one or more courses prior to the course that is a prerequisite to their required course.  No possible benefit from learning arithmetic can justify this process; in fact, there is no evidence of any significant benefit for taking such arithmetic courses in college.

Secondly, arithmetic courses in a college create costs for the mathematics department. We often have a fairly discreet set of faculty (heavily adjunct), and these faculty are seldom qualified to teach a college mathematics course.  In many colleges, the arithmetic courses are administered in a separate department.  As faculty, we should want to design a curriculum that does not depend on a course at the arithmetic level.

Thirdly, the presence of arithmetic courses at a college will tend to perpetuate the outdated focus on procedures and answers.  This conflicts with the design of Math Literacy, and impedes development of basic reasoning needed even in a traditional basic algebra course.

Reason 4: External Forces Will Continue to Push Us To Change
So far, the evaluation of ‘pathways’ has focused exclusively on the impact for students taking Math Literacy (or companion course) as preparation for statistics or quantitative reasoning courses — specifically, students who enroll in stat or QR after passing Math Literacy.

Curricular complexity means that there will be a less successful experience for students needing pre-calculus … by definition, because those students need two courses (beginning algebra, intermediate algebra) compared to the one & done of Math Lit.  There are also operational causes for other ‘bad’ data to show up — students taking Math Literacy instead of the course they were supposed to take, for example.

In addition, we can predict that these change agents will critique our developmental math courses compared to modern standards (whether Common Core, or NCTM standards).  We are not ready for this critique, and have no response for the results that are bound to come from such a critique — that developmental mathematics operates as if the year is still 1975, ignorant of the fundamental changes in our students’ experiences in K-12 mathematics.

In a way, I am reminded of something I learned at a conference session on graph theory and traffic design.  Our intuition might say that it is better to have more options in street designs, where there are several north-south options and several east-west options.  The traffic design results were the opposite … that the best throughput for a traffic system is the fewest possible streets.

A pathways curricular design presumes the presence of at least two courses at the same level in a sequence.  This design is not particularly stable, as a system.  In the long term, I think the system will collapse down to one of the options.

We need to be prepared for the demise of pathways so that we can maintain the improvements from those efforts.  The danger is in assuming that both Math Literacy AND the old courses will ‘always’ be there.  Within a few years, one of them will be gone.  Which type of course do YOU want to survive?

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Math Literacy: Placement, Prereqs, and Access

In response to a recent post on placement tests, a colleague made this comment:

In my experience, many of the people who struggle with arithmetic really aren’t ready for Math Literacy. [S. Jones]

This colleague teaches at one of the premier colleges in the “Math Literacy Movement”, with experience and wisdom.  I think this is one of the most important issues we face in community colleges.

The intended curriculum in a Math Literacy course has very limited prerequisites.  Among these are basic number sense (place value and order), and some understanding of basic operations within contextual situations.

If a student struggles with these items, yes … they are likely to be ‘not ready’ for Math Literacy:

• Add 24.1 + 1.3     [know place value ‘across’ the decimal]
• Which of these is smallest?   0.23, 0.201, or 0.1065?  [order of numbers]
• A set of bleachers has 6 rows, and 10 people can sit in each row.  How many people can sit on the bleachers?  [operations in context]
• A recipe calls for 24 ounces of diced dried fruit.  The packages I’m buying contains 3.5 ounces; how many packages will I need for that recipe?  [operations in context]

On the other hand, struggles with these items are far less related to readiness for Math Literacy:

• Add 3/4 + 5/6 and write as a mixed number if necessary
• Which of these is smallest:   3/13, 5/14, or 2/7?
• Divide (without a calculator):  19.3 ÷ 2.56
• If the area of a rectangle is 56 square feet, find the width if the length is 6 feet.

To understand what the prerequisites are for a course like Math Literacy, we need to think about the end point of that course.  The goal of Math Literacy is to build readiness for the next math course (quantitative reasoning, statistics, or Algebraic Literacy).  This goal drives the content of Math Literacy, which is outlined in four areas in the document mlcs-goals-and-outcomes-oct2013-cross-referenced

This goal, as operationalized in the content, seeks to have students meet the necessary and sufficient conditions for readiness in the next math course … any of those next math courses.  None of these courses are arithmetic in nature, though all of them depend upon numeracy skills to some extent.

The problem with our conceptualization of arithmetic in a college setting is that we attribute “here is what we would like students to know” to that content.  Of course, we’d like people to be able to perform fraction operations and decimal operations without depending upon a calculator.  Of course we would like students to know some basic geometric relationships.  In fact, most implementations of Math Literacy will assist students in those areas, but not as a core goal of the course nor as a prerequisite.

The truth is … that arithmetic was never a prerequisite for algebra, based on content structure.  Sure, some parts of arithmetic had a role.  In fact, we might call those parts ‘numeracy’ just like we do in the conversations about Math Literacy.  However, competency in arithmetic procedures is (and has been) unrelated to readiness for a subsequent math course.

Too often, we create artificial barriers to students reaching their goals.  One of the largest barriers in a college environment is the “arithmetic placement test”.  We have a situation where:

1. A content analysis does not support the treatment of arithmetic as a prerequisite to a math course.   AND
2. No data exists to suggest that there is any practical connection between competence in general arithmetic and readiness for a math course.

My college is currently using an arithmetic placement test merely for the purpose of sorting students relative to our two Math Literacy courses … the Math Literacy with Review course has a lower cutoff than the Math Literacy without review.  We no longer offer any math course ‘before’ Math Literacy.  Eventually, we might be able to make the determination about which Math Literacy course from other measures.

Think about this aspect of the situation: Most of the students who might take an arithmetic test have experienced 12 years of mathematics with over half of this time focused on arithmetic.  Do we expect to ‘fix’ most of their problems in arithmetic within a few months?  Also, what do the students look like who get lower scores on placement tests (especially arithmetic)?  The polite phrase is “this group is very diverse”.  The fact is that tests on arithmetic impact certain minority groups (race, poverty) more than others.  Unless we can show a very strong connection between ‘arithmetic’ and success (in a specific math course, or in general), we have a moral obligation to NOT impose an arithmetic barrier.

Using an arithmetic placement test to identify students required to take an additional math course is a fundamental access issue.  Such courses are obsolete relics of a different era, and lack connections to both school mathematics in this century and to other math courses in colleges.  We can help thousands of students by following one simple plan.

Just stop it!!

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Looking for new Textbooks? Be an Author!

Are you looking for a math literacy book that is different from those available now?  Are you looking for any algebraic literacy textbook?

These books get written by people who want to teach the courses.  We understand the goals of the courses, the type of content that should be present, and how to present this material so that students can succeed.

Perhaps you are somebody who might be interested in writing either a Math Literacy or an Algebraic Literacy text … either by yourself or as part of a writing team.   If so, you can certainly approach any publishing company to start the process.

In particular, Pat McKeague of XYZ Textbooks is willing to work with potential authors of textbooks for our new courses.  He is excited about developing more textbook choices for us, while providing materials to students at a lower cost.  When XYZ publishes a textbook, they do some of the wrap-around work (such as videos).

I appreciate Pat’s support of our work and his willingness to work with authors.  If you are interested in learning more, contact Pat at pat@mckeague.com

The textbooks should be a close approximation to the course goals & outcomes:

• mlcs-goals-and-outcomes-oct2016-cross-referenced
• algebraic-literacy-goals-and-outcomes-oct2016-cross-referenced

Clearly, the intent is that any textbook focus on understanding and reasoning.  The level of “context” and “small group work” can vary (though always being a part of the package); some of this could be left up to the instructor using the materials.

If you have questions, feel free to contact me!

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