Summary and Comparison of the Pathways, New Life, and Mathways

Three emerging models of developmental mathematics — AMATYC New Life, Carnegie Pathways, and Dana Center Mathways — have enough similarities that people can mistake one for another.  The basic genetic codes of these models does look very similar.  I’d like to provide some comments of comparison in order to highlight the differences; most of these differences are operational or matters of implementation.  You might want to read this Summary:  Summary of Three Emerging Models for Developmental Mathematics

One difference between the models is that the Pathways are always targeted towards specific groups of students — namely, students who only need an introductory statistics course (Statway) or only need a quantitative reasoning course (Quantway).  The New Life model can be implemented this way, which is what my own college is doing; however, the New Life model describes a curriculum that can completely replace a traditional developmental mathematics program.  Although still under development, the Dana Center Mathways is likely to be flexible in the same ways as the New Life model with some differences within the design.

All three models incorporate student success design factors.  The Pathways materials have both imbedded and supplemental work on issues such as productive struggle, deliberate practice, productive persistence, and growth mind-set.  The New Life model, because it is a professional framework, does not prescribe how these factors are incorporated in the local implementation; some instructional materials for the New Life model embed the design and others are strictly supplemental.  In the case of the Dana Center Mathways, the model includes a required student success course as a co-requisite; the details are still being developed.

Placement is handled differently in the models.  The Pathways (statway & quantway) are two-semester packages; the design assumes that all students begin in the first semester and continue into the second semester.  The New Life model could be implemented this way; however, the basic design suggests a normal process where some students could begin at the second-semester level without taking the first semester.  The preliminary descriptions of the Dana Center Mathways suggests that they will also provide flexibility concerning where students begin.

None of the models assume a change in the actual placement tests at this time.  In all three cases, the first course uses ‘placement into beginning algebra’ as the benchmark; local colleges adapt this guideline to their environment.  Since all three models focus on concepts of mathematical literacy, they collectively suggest that our placement tests need to have a measure of basic quantitative reasoning at a pre-college level.

The largest difference in implementation is in the domain of ‘institutional committment’.  The Pathways model presumes (and requires at this time) that the institution will sign a multi-year agreement to develop, implement, and participate in the activities of a shared network; individual faculty can not ‘join’ statway or quantway.  [However, the instructional materials will be publicly available later this month for open-use as version 1.0 (first classroom version) under a license like Creative Commons.]  The New Life model allows for individual faculty to pursue incremental changes at their institution, as well as allowing for institutions to make a committment for a larger change.  My current interpretation of the Dana Center Mathways model is that they will seek some level of institutional committment to a change, though the change might not be total reform of the curriculum.

Mathematically, the models differ in how they address the old intermediate algebra course. The Pathways model does not address this course in any way, since the student populations are selected to avoid intermediate algebra — the Pathways include mathematical literacy and the ‘terminal’ math course only.  The New Life model provides a replacement course (currently called “Transitions”) that can be used instead of intermediate algebra; the outcomes for Transitions include a fair amount of the topics of intermediate algebra — the approach is more balanced between symbolic and numeric work, and the content is not limited by tradition (exponential change is consider a basic skill in Transitions).  Although still being developed, I anticipate that the Dana Center Mathways model will also provide a replacement for intermediate algebra; this will provide the profession with two strong alternatives to the old ‘non-functional’ intermediate algebra.  [‘non-functional’ has two meanings — does not work well, and does not integrate function work]

I have been fortunate to have (1) led the New Life project, (2) been deeply involved with Pathways, and (3) involved with Dana Center Mathways [with the hope of doing more].  My statements above do not represent an official narrative from the 3 sources; rather, this is my professional evaluation offering a comparison.  To the extent that I have information or knowledge, I would be glad to answer questions about how the 3 models are similar or different.

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