Envisioning Change to Better Serve Our Students

In fall 2015, I attended the AMATYC (American Mathematical Association of Two Year Colleges) Conference, focusing on a symposium on the Mathematics Pathways being developed across the country.  The problem has been identified roughly as follows:  Of all the community college students (nationwide) who place at least two levels below “college level” math, about 15% complete a college level math class within 2 years.  We can do better.  And many efforts have been explored nationwide.  The take-away from that symposium was that efforts proved successful, in those cases where the college was “mobilized to support the student.”  The challenge was for colleges to envision systemic changes that could be leveraged to better serve students.

One key feature of that support was integrating support services into the classroom.  For example, counselors would talk briefly with students during lab time or call them aside to develop or update ed plans.

Another key feature was scheduling assistance.  First year programs supported students by addressing the “paralysis” that the most vulnerable students experience when confronted with the myriad decisions needed just to register for classes.  One program director said she called up each student and asked a single question, “Do you want to come to classes in the mornings or in the afternoons.”  Based on their answer, she enrolled them.

Another key feature was some type of embedded algebra support:  either through co-requisite courses, increased classroom hours, or a lab component.

Another key feature was addressing the human side of the problem, tackling head on issues like deficit thinking and growth mindset.

This year, while on PDL, I have had two types of interactions with colleges.  I, myself, have gone through the process of applying to colleges and registering for classes.  I have a master’s degree in math and consider myself to be resourceful.  But I did not consider that process very easy and I sometimes got tangled up with things like prerequisite verification.  My other interaction was through my daughter, who went through the same processes.  My familiarity with academia allowed me to answer a lot of her questions.  Each time, I reflected on what a student might be experiencing if they had no one to help them with this navigation.

We value choice.  A lot.  But it’s possible that our own appreciation for choice leads us to put students in a position where they have more choices than they care to have…too many to even allow them to remain functional in our system.

It’s time for us to focus on the individual.  When a student enters our college, what do they have to do?  What decisions do they have to make?  To what extent do those decisions serve as a barrier?  How are we supporting students through that process?

I feel at times that our system is based on the assumption that an incoming student is a self-actualized adult who has a pretty good idea of what they want to study and how to navigate our system.  And that may be true of some our students.  But I’m sure that it’s not true for many others.  And based on that symposium of alternative math pathways across America, it seems that in order to better serve these students we need to seriously reflect upon our systemic assumptions and processes and ask ourselves how we can remove some of the barriers that are currently in place.  How can we envision systemic changes that could be leveraged to better serve our students?  What might that look like at Foothill College?


Immersion Style Learning

When a neighbor told me that her daughter was going to a dual-immersion (Spanish/English) elementary school, I experienced bewilderment (thinking “Why?”), followed by judgement (thinking “That doesn’t seem like a very good idea to me.”), followed by curiosity (thinking “They seem very pleased with their choice; I should find out more; maybe there is something to this.”)  I was unconvinced, but the experience created an opening and long story short, three years later my daughter started kindergarten at that same dual-immersion school.

Nothing in my 35 years had prepared me to comprehend immersion style learning.  It was actually a huge leap of faith fueled primarily by a single positive campus visit and the perception that the alternatives were worse (based on a single negative visit to each).  That was about 12 years ago and I now have an appreciation and respect for the immersion approach, mostly based on 8 years of having children in that school.

My education was systematic.  My education was a series of demonstrations.  Hour by hour, day by day, week by week, month by month, year by year.  My teachers showed me what they wanted me to do and then asked me to do it myself.  They encouraged, answered questions, and made corrections.  The chores I did at home were much the same.  “Do what I do.”  “Follow my directions.”  “Do it this way.”  I learned very quickly that there was one right way of doing things.  I had a vague knowledge that that “one right way” somehow depended on the teacher.  The more I did EXACTLY what I was shown, the more I got praised and rewarded.   I learned to look for patterns and search for understanding, not because that was suggested or taught, but because I needed a strategy; it was simply impossible to memorize everything.

So then, by the time I got into a college Spanish class, I was very analytical.  Identify the patterns; memorize the exceptions.  After completing my college language requirement, I could do everything that the teacher asked me to do, but I could not speak Spanish.  My daughter, on the other hand, shyly and proudly told everyone after a month in immersion kindergarten, “I speak English and Spanish.”

She had acclimated to the demands put on her.  She understood the simple directions that the teacher used everyday, and her vocabulary had grown significantly, through colors, counting, story time, and singing.  If the teacher ever got really stuck with a student, she would ask the child to explain in English what they thought she had said or she would ask in Spanish for a volunteer to explain in English what was happening.  The learning was not based on memorizing conjugations, but on using correct forms in daily classroom interactions.

Now I’m on Professional Development Leave, a math teacher looking for ways to connect with students and choosing Spanish Language Studies as one such connection.  As is frequently the case, I am realizing a second, unforeseen benefit.  Let me explain.

When I researched Spanish programs, I realized that the local colleges no longer distinguish between Spanish and Conversational Spanish.  There were 2 sequences of classes when I was young.  I think a person could have enrolled in both sequences concurrently, taking both a grammar and a conversation class.  In our local quarter schools (Foothill, DeAnza, CSU Eastbay) there is now 1 sequence, consisting of 6 courses:  3 classes in introductory Spanish and 3 classes in Intermediate Spanish.  When I signed up for the first class, I was surprised to find that it was so different from that grammar class I took 30 years ago.  It’s based on an immersion model!  Each week, I’m given resource pages with more vocabulary words than I can possibly memorize. (But I’m explicitly told I don’t have to memorize all of them.) Several short grammar exercises incrementally introduce some usage and the remaining exercises (video, audio, written, partnered work) provide opportunity to practice that usage.  I can’t always express my complicated ideas using the Spanish learned so far, but I can always at least partially express myself.  Before I went through this experience, I didn’t think that I could learn in an immersion environment.  But now I can actually speak and write in Spanish (and not just do trite little exercises).

The unforeseen benefit is the way in which this experience allows me to reframe mathematics education.  Mathematics education is systematic.  Mathematics education is a series of demonstrations.  Hour by hour, day by day, week by week, month by month, year by year.  We teachers show students what we want them to do and then ask them to do it.  We encourage, answer questions, and make corrections.  They learn very quickly that there is one right way of doing things.  (But wait, NO!  We don’t want them to learn that; it’s not true!)  They know, vaguely, that that “one right way” somehow depends on the teacher.  The more they do exactly what we’d do, the better their grade is.  (OK, on rare occasions we are charmed and dazzled by a student’s unique approach…)   The successful students look for patterns and search for understanding.  The students who haven’t developed these strategies think they have to memorize everything.

I recall how I couldn’t speak Spanish because I had very little practice and I was relying entirely on my head.  There was no internalization of the language.  This reminds me of students who can’t talk about their mathematical thinking because they’ve had very little practice.  This reminds me of students who can’t apply what they’ve learned because they’ve had very little practice.  This reminds me of students who are always in “recall” mode because they’ve had very little practice with “thinking” mode.  Their skills are in a box in their head, memorized facts and procedures.  There is no internalization of mathematical thinking.

Over the last several years I’ve worked with materials and pedagogies designed to provide students with experiences talking, applying, and thinking about mathematics.  I didn’t realize until I studied Spanish this year that those efforts are much like creating an “immersion style” of learning mathematics.  In my earlier years, “immersion” sounded scary, much like throwing someone in deep water to teach them to swim.  But now “immersion” sounds wonderful, conjuring up images of nurturing and support and “whole person” learning, where the learning is integrated and internalized and not based on memorization.


Messaging is so important.  It’s far more impactful than we want it to be.  We want to be understood for what we mean.  But sometimes words are inadequate for expressing our ideas.  Or if the right words exist, we may not find them and use them effectively.  Or we think and many may agree that we chose our words perfectly, only to find that misunderstanding ensues anyway.  Colleagues get offended.  “Camps” develop.  We take what we hear and impose a story or a meaning that comes more from our own experiences than from the speaker.  Take a modern catch-phrase, “meet students where they are.”  Some teachers are threatened by this phrase, interpreting it to mean that they have to systematically assess every student and then teach every students in their class differently, depending on their assessment.  Faced with what seems to be an impossible task, they condemn the notion as crazy, unrealistic, and unreasonable.  These feelings may drive a wedge between an excellent teacher and their profession and colleagues.

As ideas about teaching evolve, we want some gems to take back to the class.  Sometimes, an idea resonates and we can see its place within the framework of our own understanding.  Sometimes, we can’t see another person’s success within our framework of understanding.  This can become a problem when we feel like we are being told what to do.

A friend shared an article recently on the importance of creating an environment where everyone is free to create their unique magic in the classroom (as opposed to a system that requires everyone to follow a prescribed plan).  I think that such an environment at least partially addresses the messaging problem.  When it is expected that every individual is at their best when they’re being creative and creating their own unique magic, then successes shared in articles or in the lunchroom may feel more like points of interest and less like suggestions for improvement.

Take our course outlines for example.  They are supposed to guide us in our teaching and provide students and institutions with information about what students learn in a class.   I think that f they are well written, they should leave plenty of room for individual creativity on the part of the teacher.  If they are overly prescriptive, they may have the unintended consequence of stifling what could be a very good class.  I wonder, have you ever felt like a course outline got in the way of you doing your best work with students?

How Does Change Occur?

We are now in the 21st Century.  Several decades ago, academia, government and business started talking about the 21st Century.  What would be needed in the workforce?  What would education look like?  What would students look like?  Now it’s 2017.  17 years into the 21st Century, I’m not sure that we’ve made real significant changes to the education system.  I have changed what I do in the classroom, but the course outlines that are supposed to lay out what I teach haven’t changed much.  So I find myself changing my pedagogy and my thinking, but working with the same curriculum.  Year after year, success data shows us that the traditional pathway of Beginning Algebra –> Intermediate Algebra  –> Transfer Level Math is ineffective.  Only a small percentage of students navigate this pathway successfully.  And it is widely thought nationwide that this developmental math curriculum is a major roadblock to degree achievement.  That’s why the mathematical community has been working for many years on developing alternative pathways.  Several are being implemented nationwide.  And California is in the process of clearing the road for these new curriculums.  But what do we teachers do in the meantime?  What do we do with an outdated Course Outline of Record?  How do we function in a system that is slow to respond to the changing world and the changing student body?  How can we truly serve our students under these constraints?  I think a lot now about how I can interpret a Course Outline.  I ran an experiment last year wherein to better serve students, I used the alternative curriculum called Quantway, developed through the Carnegie Foundation.  To remain true to the Course Outline, I supplemented these materials with traditional curriculum.  That work led me to believe that I would have served them even better had I foregone the supplementation with traditional curriculum.  This belief is reinforced by the following quote coming out of the Dana Center at the University of Texas, Austin:

“After the New Mathways Project was implemented in Texas, 23 percent of students enrolled successfully completed a college-credit-bearing math course within one year, compared with the statewide average of 8 percent. Campuses that implemented the program with the highest fidelity to recommendations had 43 percent of students earn college credit in one year.”


So then, to what extent can I change the Intermediate Algebra Course Outline and still call it Intermediate Algebra?  And to what extent can I use my professional understanding of where we are and what serves my students to interpret the Course Outline in a way that might be seen as unconventional but support me to better serve student?  As I ponder these questions, I think about what happened in Texas in the above quote.  8% to 23% represents an almost 200% increase in the proportion of students who completed a college-credit-bearing class within 1 year; and 8% to 43% represents over a 400% increase.  I think that’s pretty compelling.