Math Lit at Achieving the Dream Conference

I am currently on my way … to Anaheim for this year’s Achieving the Dream conference.  On Wednesday, I will have a poster at the “Emerging Ideas” event (11:00am) about the Mathematical Literacy course (and the AMATYC New Life work); Thursday, I am part of  a workshop (1:45pm) on developmental math … my part is the Math Lit course, and we will have extended time for discussions and questions.  This is my first “AtD conference”, and I am really looking forward to the opportunities and dialogue.

So, I have been thinking about how progress is made in academia — about how a basic change is accepted by large numbers of faculty and implemented at their college.  The AtD “mantra” uses phrases like “move the needle”, “acceleration”, and “progression with completion”; within the official communications of AtD and related foundations (Lumina, Jobs for the Future, etc) these phrases are repeated, and much conversation centers around engaging faculty in this work.  Parallel to this, the groups provide some outstanding professional development on theory and practice related to developmental education.

My hope is that the work of the New Life project touches and excites the values and beliefs of mathematicians and math educators.  Certainly, part of this is developing a better set of vocabulary phrases to communicate about our values and beliefs; the name ‘mathematical literacy’ is one effort to develop such a phrase.  However, vocabulary alone does not produce any change of significance; many prior efforts have failed because a new phrase was layered on to an existing curriculum (like ‘basic skills’, ‘application focused’, ‘mastery learning’).

I am convinced that our survival depends upon basic changes in our curriculum — and in our ideas behind the design of the curriculum; I believe that these basic changes will only happen as we all engage in conversations and even arguments about what things mean and what is really important.  Sure, we will need some resources, which means that we need to convince foundations and grant sources that our work is important; this will mean the strategic uses of phrases like “algebraic reasoning” and others like we use in the New Life work.  However, this is much more about our profession and our work together than it is about better words.

Progress occurs after dialogue; progress will happen when we actively seek to engage all members of our profession in a deep conversation about purposes and values, goals and beliefs.  Indeed, nothing can stop progress from happening if we can do so.

If you are coming to AtD 2013, I hope we have an opportunity to have some of that conversation!

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Important Things First … And Repeated

Like most faculty, I encounter times in the semester when I have to wonder “how did we get to this point?” — such as when a student in a course like intermediate algebra does not recognize a product versus a sum, or can not recognize a right-triangle distance problem in context.  I could follow the path of blaming previous bad teachers (all of them except me [:)] ), or on students who do not study; there might even be some truth in these explanations.  However, the professional response is to explore how my course enabled these problems to survive until the end of the semester.

I am concluding that we (and I) stop working on ‘basics’ too soon; I (and we) presume that a passing score on an assessment like a chapter test shows that a student has the basics.  However, I suspect that I depend too much on closed-task items on assessments, which enables some students to simulate appropriate knowledge without its presence.  In addition, I am concluding that I need to design classroom interactions to constantly build literacy and analysis of mathematical objects.

People often say ‘mathematics is a language’, and promptly teach mathematics as if it was a set of mainline cultural artifacts.  We can learn much from our colleagues in foreign language instruction, who tend to constantly use basic literacy into all work in a language and to deliberately address the cultural components of the language.  I see most of my student’s basic failures within mathematics to be cultural issues (context, norms) along with language literacy within mathematics.

The implication I see for my own teaching is that classroom time needs to deal with ‘sum or product’ as an issue every day; nothing is more basic than this issue.  In algebraic classes, there is an added layer of work on symbols and syntax which needs a similar focus (sum or product).  I’m also seeing a need to deliberately address reading skills applied to a math textbook, and hope to coordinate these types of efforts.

I am constantly reminded of this notion:  Novices do not automatically see the critical features and structures that experts see without effort.  Our students are capable of more, and can reason mathematically.  We need to deliberately show the features and structures we see, and provide scaffolding for students to become more expert.  We do students no good if they leave a math class in the same novice mode as they started, with some limited problems they can solve.

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The Logic of Change: Do the same, expect different results

You have likely heard the quick definition of insanity:  Doing the same thing, and expecting different results.  Presenters often apply this statement to teaching, frequently stated as “Why should we teach it the same way as they had before, when that obviously did not work?”.  The interesting thought in this logic is the ‘same’ descriptor can be applied to many aspects of the current environment; in spite of this, most discussions focus on the pedagogy and on the teacher behavior in particular.

What about the content?  Perhaps we can improve our results if we first improve the content.  The appropriateness of the current content is questionable, and some have argued that the current content is damaging.  You might take a look at the New Life course outcomes (MLCS Course Goals & Outcomes Oct2012  and Algebraic Literacy Course Goals & Outcomes Oct2012).

However, perhaps we are tragically over simplifying the conversation.  What do we mean by content?  “Algebra” does not always refer to the same content, nor do we use it to refer to the same assessment standards.  We also ignore, I believe, the issue of student perceptions of content.  If you want to trigger a uniform reaction to content, put a simple problem that involves fractions and variables in front of students; in developmental courses, most students will perceive this type of problem as a threat and as something they can not understand.    We could improve our courses tremendously if we would invest time in improving the accuracy of student perceptions of content.  Yes, this takes time, and we would have to give up something … look at it this way:  Most students do not achieve deep understanding of most topics anyway; perhaps the net result would be better if we went a lot slower, with fewer ‘topics’.

You might try this experiment:  After you have covered a topic in a class like you have usually done, where the class went as well as you normally see, ask your students to write their answer to this question: “What are we learning about?”  [I ask individual students this question, and suspect that your students will struggle to provide a good answer just as mine do.]

I see still another over simplification in this conversation: is our content described by objects and procedures, or is our content better described by concepts and relationships?  We do not share perceptions of content, which makes it harder on students.  My hope is that we can, through many professional discussions over an extended period, involving all parts of the country, develop shared language to communicate our perceptions of content.  Of course, I would like us to emphasize reasoning and mathematical problem solving (beyond ‘real world’ problems).  In any case, our students would benefit from our accurate use of a shared language for content.

In many cases, speakers who use quotes like ‘do the same, expect different results’ are using this as a rhetorical device in their efforts to convince us to adopt their solution.  Our profession needs us to take a deeper look at the situations and problems.  If simple statements could solve the problems, they would have been solved long ago.  Making progress at scale (in location and in time) depends on broadly shared conceptualizations and collaboration on solutions.  We each are part of the solutions.

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Innovations in Developmental Mathematics — Getting Past Go

Innovations — large, small, and between — are common in developmental mathematics.  Most of us do not establish ‘Being innovative’ as a goal; rather, we figure out something to do that promises to solve a problem, and this creates the innovation.  Some innovations are very context-dependent, while others are transferable and scalable.  The New Life project (AMATYC Developmental Math Committee) describes innovations that can be locally adaptable and scaled.

The Next Dev Challenge (from Getting Past Go) seeks to gather information on innovations in developmental education, and have the larger community rate the ideas.  The web site is http://gettingpastgo.edthemes.org/ , and we are now in the rating stage of their work.

I encourage you to rate innovations at  the Next Dev Challenge link (http://gettingpastgo.edthemes.org/) . You will need to register in order to rate ideas.  Once you are registered at that site, you can submit your ratings of some innovations (they have far too many for you to rate all of them 🙂 ).  To find entries of interest to you, open the Next Dev Challenge link and then read submissions. (Be sure that you are logged in.)  You can search for phrases, and narrow the results down to one of four categories (assessment & placement; instruction & delivery; continuous improvement; student supports.  Note that you need to click on “View” for each innovation in order to rate it. In addition, you need to choose each rating (adaptability, evidence, and overall) at the end of each innovation’s page.

We have a professional responsibility to participate in projects like the Next Dev Challenge.  I hope you will be able to share some ratings of innovations.  Clearly, I hope that you will support the innovations related to the New Life project in particular; whether you do this or not, please participate in the rating process!

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