Implementing Better Math Courses, Part III: Connecting All the Dots

The traditional developmental math sequence focuses on school mathematics, biased by an algebra fixation … narrowly defined to be algebraic procedures.  Although some have the perception that this sequence serves ‘STEM students’ well, professional standards and research indicates that the sequence does not serve them well.  In this post, I will focus on truly connecting all the dots — to STEM math and most college mathematics&nbsp. #NewLifeMath #AlgebraicLiteracy

The prior posts on implementing better math courses focused on the beginning algebra level.  The Level I implementation (Pathways) described a side-by-side model; the Level II implementation (Medium) provided a total replacement of beginning algebra as well as all courses prior to that.  The next level (III) involves replacing intermediate algebra with Algebraic Literacy (AMATYC New Life project).

Here is an image of this implementation model:

Algebraic Literacy provides a modern course connecting students to STEM and related college mathematics.  I’ve posted information on the course and research for Algebraic Literacy at https://www.devmathrevival.net/?page_id=2312; here, I will focus on the implementation aspects.

One benefit of this ‘high’ implementation is that we can minimize remedial enrollments while providing intentional preparation.  Because Algebraic Literacy focuses on communication and reasoning, we provide an accessible course with higher expectations — more students can start in the 2nd course, and they will be better prepared for what follows.  For example, if intermediate algebra required a 77 on a placement test, algebraic literacy can succeed with a cutoff of 60 to 65; if an ACT Math 19 is required for intermediate algebra, algebraic literacy can manage with a 17.  These numbers are very generic, and are simply meant to illustrate the increased access.

The preparation is also improved in this model.  The cumulative message of the college math standards is:

Focus on learning core ideas in mathematics to a high level. (AMATYC; MAA – CRAFTY and CUPM)

Even if students flow from Algebraic Literacy to a traditional college algebra course, they will have more capabilities.

However, the curriculum at the college algebra level (and above) is in desperate need of modernization.  Those courses are almost all modifications of either a 19th century college algebra course in college algebra or slight variations of calculus from the mid-20th century.  We live in a golden age of mathematical sciences, but our students still take courses on dead (aka obsolete) mathematics.  Having the Algebraic Literacy course in place will provide both the motivation and safety needed for our departments to begin updating the STEM math courses.

This “High” implementation results in a total replacement of obsolete dev math courses and the beginning of renewal in the courses which follow.  The New Life Project dev math courses share much with the work of the Carnegie Foundation (Pathways) and the Dana Center (New Mathways).    The Carnegie work builds an option after the pathways courses (Statway or Quantway) to enable the student to take college algebra; the Dana Center work provides a different replacement model, where the STEM path (pre-calculus) begins right after a Math Literacy-type course.

Many in our profession would like to teach Algebraic Literacy instead of intermediate algebra; Algebraic Literacy is better mathematics and is consistent with modern teaching methods.  The main barrier to progress right now is ‘textbooks’, since there are no commercial materials available (Pearson; McGraw Hill; Cengage; Hawkes; etc).   The path out of this ‘chicken-egg’ dilemma is YOU … talk to the publisher representatives at every opportunity about the books you want to see.

A primary goal of this “High” implementation is a combination of improved preparation and the minimizing of the remedial math enrollment function.  I believe that we can achieve a situation where the mode of remedial math enrollments is 0 and 1, with a mean between those values.  We don’t need to eliminate remedial math courses … we need to modernize them to better serve our students.

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New Life Project presentation at National Math Summit (March 2016)

The New Life session (at the 2nd National Math Summit) involves these materials.

• Presentation slides:  AMATYC New Life Project NADE Math Summit March 2016
• References:  References NewLife NMS 2016
• Implementation Maps and curriculum:  Implementation Maps AMATYC New Life Project 2016
• Math Literacy Learning Outcomes:  MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2
• Algebraic Literacy Learning Outcomes: Algebraic Literacy Goals and Outcomes Oct2013 cross referenced 2 by 2

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Intermediate Algebra Must Die!!

“Intermediate Algebra Must Die!” … I said this at two recent meetings (first at a conference, then at my college).  The need for this demise is ‘over-determined’, to use a social science phrase:  several factors, each of which would be sufficient, are present to create a conclusion with multiple rationales from different perspectives.  #IntermediateAlgebra #AlgebraicLiteracy  #NewLifeProject

The first rationale for the necessary demise of Intermediate Algebra comes from data concerning preparation for ‘college math’ (most often college algebra or pre-calculus).  The CCRC and ACT both have discontinuity regression research showing that intermediate algebra does not prepare students.  [See the first part of my presentation on Algebraic Literacy at https://www.devmathrevival.net/?p=2331.]  The most optimistic results show a 2% to 5% gain in pass rates after an intermediate algebra course compared to students with similar backgrounds; of the 4 data sets, 1 had this very small positive result … 2 have ‘null’ (no gain), and 1 has ‘negative’ (students do worse after intermediate algebra, compared to similar students who did not).

The second rationale for the necessary demise of Intermediate Algebra comes from the policies about degree requirements at our institutions.  At hundreds of institutions, students can meet a general education requirement for a degree by using the remedial math course called ‘Intermediate Algebra’.  This policy makes two horrible statements at once:  first, that we don’t think it is important for students to learn additional mathematics; second, that we don’t think students have sufficient abilities to learn additional mathematics.  We are not just accommodating negative perceptions about learning mathematics, we are reinforcing them.

The third rationale for the necessary demise of Intermediate Algebra comes from its origins:  Intermediate Algebra was copied from the high school curriculum during a period when procedure and repetition were emphasized (in reaction to the original ‘new math’) in a design based on low standards for teacher credentials (the thought was ‘make it teacher-proof’).  This origin of the course is clearly related to the data referenced above; however, this rationale is based on the contradictory nature of the course compared to any set of modern curricular standards (as in Common Core, or even the original NCTM standards).  Intermediate Algebra is a professional embarrassment.

The last rationale for the necessary demise of Intermediate Algebra comes from the politicization of developmental mathematics:  as long as we are teaching ‘high school courses’, policy makers are going to attack our curriculum in colleges.  These stakeholders do not see why they should pay a second time for the same treatment, and many do not see any appropriate benefit from the course.  This rationale, like the third, suggests that all traditional developmental mathematics be removed ASAP and replaced (to the extent needed) by modern courses designed for college use (such as the New Life Project courses, Mathematical Literacy and Algebraic Literacy).  A course being “pre-college” does not mean “high school”.

We need to ‘own our problem’; for too long, we have continued our weak copies of weak high school courses to stand in the way of actually preparing students.  We have taken the easy road, sometimes creating a significant revenue source for our colleges, when we should have focused on our students’ needs in college.  We have reinforced the “I can’t do math” belief, and sold our profession short.  We have placed our entire curriculum at risk by requiring many students to take high school courses in college.

Intermediate algebra must die!

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Algebraic Literacy: A Bridge to Somewhere (AMATYC 2015)

Here are the materials being used for the session at the AMATYC conference (November 21, 2015).

1. References, and the New Life Project curricular vision
References Bridge to Somewhere AMATYC 2015 final

2. Algebraic Literacy Goals and Learning Outcomes
Algebraic Literacy Goals and Outcomes 2015 cross referenced

3. Sample Lesson: Trigonometry
Algebraic Literacy Sample Lesson Trig Functions Basics 2015

4. Sample Lesson: Rational Exponents
Algebraic Literacy Sample Lesson Rational Exponents 2015

5. Sample Lesson: Rates of Change, Exponential
Algebraic Literacy Sample Lesson Rate of Change Exponential 2015

The sample lessons are licensed under a Creative Commons agreement … ‘by attribute’; the content can be used or modified, with attribution.

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