Thread 5 : Let’s get to the real problem.

Posted on September 20, 2018

5


Part 1   Part 2   Part3    Part 4  Part 5   Part 6

 

This is part 5 of a summary of research and articles about  remedial/developmental math in colleges and adult education.

What would I like to see happen?   What would I be willing to invest my time and energy and knowledge in?

Remember this?

In particular, we are interested in exploring the hypothesis that these students who have failed to learn mathematics in a deep and lasting way up to this point might be able to do so if we can convince them, first, that mathematics makes sense, and then provide them with the tools and opportunities to think and reason.

Stigler, J.W., Karen B. Givvin, and Belinda J. Thompson (2010) What community college developmental mathematics students understand about mathematics. MathAMATYC Educ. 10, 4–16

Yes, this has been tried!

Cox R. “You’ve Got to Learn the Rules”: A Classroom-Level Look at Low Pass Rates in Developmental Math. Community College Review [serial online]. July 2015;43(3):264-286.

This author observed math classrooms at two schools.  Each was making major efforts to improve student outcomes for developmental math. Both schools provided lots of support and advising, and dedicated enthusiastic instructors.

One school kept the traditional textbook and “remedial pedagogy” with structured procedural practice.  The other brought in instructors who focused on students’ developing meaning and making connections between their intuitions and the mathematics.

The second school had much better results.

Yes, small sample size… but both schools were Trying New Things They Believed In and, yes, student attitudes shifted in positive directions.

The teaching was fundamentally different though, with the “conceptual” schools making lots of “real life” connections and building from cognitive models the students already had.   So, for integer lessons, the “rules” classroom had clear explanations and practice with rules and patterns… the “concepts” class started with temperature data from different cities.

And… ponder this from the conclusion — I could only get access to “full text HTML” unformatted text so I’ve added white space:

From this perspective, the two classrooms at College X serve as a profound existence proof: There is an alternative to the default “remedial” pedagogy that dominates developmental math classrooms,…

The fundamental differences between “remedial” pedagogy and an instructional approach that reflects math educators’ formal recommendations for developing mathematical proficiency are not necessarily glaringly obvious when the vantage point is located outside of the classroom.

… adding resources to or amending the structure of a developmental math course does not, by itself, affect the nature of instructional practice enacted within the course.

Given the persistent dominance of the default “remedial” pedagogy across developmental math classrooms, tinkering at the margins of instructional practice holds little promise.

In the absence of sustained attention to what actually unfolds inside developmental math classrooms, such efforts at reform may perpetuate similarly dismal outcomes to pre-reform levels.

As Hinds (2011) aptly notes, “Rather than addressing the instructional methods that dominate remedial math classrooms and the cultural and systemic factors that keep those methods in place, . . . the most popular reform efforts actually sidestep the critical issue of teaching practice” (p. 23).


So…. given that, what do we need to change?   What should we be teaching?

From

 Ginsburg L. What’s an Adult Numeracy Teacher to Teach? Negotiating the Complexity of Adult Numeracy Instruction. Journal Of Research & Practice For Adult Literacy, Secondary & Basic Education [serial online]. Spring2017 2017;6(1):57.

This is about the assorted courses to prepare students for High School Equivalency (HSE) tests.

“Some educators choose to prepare learners for the HSE test by spending hours practicing sample questions from test prep books. While familiarity with the types of test questions can be helpful, learners do not come away with much understanding of the mathematical content and thus are less likely to be successful on the HSE assessment or any additional assessments used for entry or placement purposes for certification programs or further education. Better preparation for the HSE might be to delve deeply into the mathematical concepts and procedures, particularly addressing algebra. “

And from another article in that issue featuring numeracy

Curry D. Where to Focus so Students Become College and Career Ready. Journal Of Research & Practice For Adult Literacy, Secondary & Basic Education [serial online]. Spring2017 2017;6(1):62.

Unfortunately, too many teachers feel like they don’t have the time to give students the foundation that would allow their students to actually understand what is being taught. They may teach students procedures and tricks, hoping that they will retain those procedures long enough to at least pass the test.

However, without foundational understanding, students rarely remember those procedures…As a result, teachers reteach the same procedures over and over again, rarely successfully getting their students to understand when to use those procedures. According to Givvin, Stigler, and Thompson (2011):

Without conceptual supports and without a strong rote memory, the rules, procedures, and notations they had been taught started to degrade and get buggy over time. The process was exacerbated by an ever-increasing collection of disconnected facts to remember.

This has been your erstwhile blogger’s experience in K-12 education:  as students went from year to year, they’d start at arithmetic because the students didn’t really understand it and… move faster and faster through the procedures because there was so much to catch up to and it is *EVER SO IMPORTANT* to say they are “doing grade level work.”   If they’re memorizing to survive, that’s not really that grade level work.


I’m going to make this its own “part” because it deserves a big drum rolll… so posting this much now…

Part 1   Part 2   Part3    Part 4  Part 5   Part 6

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