What is Homework?

Do your students do homework?  Do they know how to get help on homework?  Most likely … no to both questions.  After trying other steps over the years, I am trying an invasive tool this semester:  Every student must take homework to a source of help on campus during the first week of the semester; they get a faculty member signature on a quick little form, and get 10 points for completing this.

Some interesting problems arose very quickly.  Several students asked “What is the homework?”  This might seem like an odd question, until you think about it from their point of view.  Most math books have reading, examples, section problems, chapter problems, review problems and more … some texts have ‘margin’ problems (or equivalent).  In my beginning algebra class, students were having a difficult time discriminating among these components — and a difficult time generalizing these in to a category called ‘homework’.  My students were thinking that ‘homework’ meant the written steps they did for a set of problems on one page (similar to the section problems); I was thinking of homework as being any and all of these components.

“Getting help” holds some mysteries for our students.  Without direction from faculty, students may not not see the sources of help as being a resource for them to use; one of my students reported that she is repeating the course because she waited until the last two weeks of the semester to get help.  We might think that “I am not passing” would be a strong enough message to go get some help, but this does not work out for many students.  For whatever reasons, there seems to be a large social gap between students and the sources of help that will get them through their course.

If you are curious, my experiment with requiring students to get help in the first week is working well.  Some of the students are getting comfortable with the process of getting help as a result.  For others, this process also helps uncover misunderstandings about what ‘homework’ means.    The number of points (10 for the assignment, out of 1000 for the course) is high compared to the effort, which makes the assignment more tolerable for students.   The sources of help available include my office hours (not during class time), our campus tutoring office, and the math department help room.

I encourage you to not assume that students will get help when needed.  Look for ways to require students to get help, especially in developmental and gateway courses.

 
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Hope, Vision, and Developmental Mathematics: Moving towards a Mathematical Literacy Approach

This year has seen a number of reports and articles with very strong negative statements about developmental or remedial mathematics.  As an example, Complete College America issued a report calling remediation a ‘bridge to nowhere’ (see http://www.completecollege.org/docs/CCA-Remediation-final.pdf).  A quick online search will produce many citations of this report; other reports and articles have been published. 

Is there hope for developmental mathematics?  Do we have a role to play in the upward mobility within American society?

If we conceptualize developmental mathematics as basic skills or as ensuring that all students have ‘the math they should have had in high school’, then the answer is probably no to both questions.  These approaches describe a remedial mathematics program.  Since many people see ‘developmental’ as a polite descriptor for remedial, perhaps we should begin to advocate a shift towards mathematical literacy as a framework for our work in colleges.

Policy makers look at the results of our programs and conclude that the investments are not appropriate.  Legislatures see the credits used for remedial or developmental mathematics as an inappropriate redundant expense — they have already paid for students to do this work in the K-12 system.   Researchers find that completion of remedial or developmental mathematics courses is not strongly connected with success in college.  States consider banning developmental or remedial mathematics (or all developmental courses).

I suggest that we can, in fact, drop our traditional developmental and remedial math programs as they are currently designed.  These programs are historical artifacts, dating from an era when colleges and universities held different standards for entering students:  College students had to have been good high school students, therefore students who could not show current knowledge of school mathematics had to complete ‘remedial’ courses.

I suggest that we focus on mathematical literacy as a framework for getting students ready for college work.  A mathematical literacy framework means that we do not fixate on the high school math curriculum; rather, we directly deal with the mathematics needed in college.  Instead of 200 ‘basic skills’ in a remedial program, a mathematical literacy program would have a small set of important mathematical concepts and tools — proportionality, growth and decay, representations, numerical methods, basic symbolic methods.

A mathematical literacy program has the promise of a closer integration of mathematical preparation with other college work.  Most college courses do not deal with dozens of discrete skills with few connections to each other; most college courses focus on a smaller number of big ideas, with a focus on understanding and application.  Students who experience a mathematical literacy preparation will have a shorter bridge to cross in order to reach the demands of other courses.  A mathematical literacy program offers the promise that students will be inspired to learn more mathematics, instead of looking for the earliest exit ramp.

The emerging models of developmental mathematics are steps in this direction, although they sometimes allow the traditional developmental math program to continue.  Our long-term goals should include providing a more powerful experience for all students, not just those in select programs.  Whether it takes 5 years or 10 years, let us work towards the goal of replacing an antiquated remedial math model with a functional mathematical literacy model.

Especially in community colleges, enabling upward social mobility is part of our core purpose.  Far too often, our current model prevents students from achieving this upward mobility due to too-low pass rates and too-low completions of a sequence.  We can … and must … do better.  The vision of a mathematical literacy approach offers hope for us and the students who depend upon us.
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