Starting Monday, Feb. 22, 2020, at 9:00 AM EST, our community will hold an asynchronous discussion on this thread about equity, and access in the adult education classroom. This opportunity to have three guests discussants will allow for each of you in the community to pose questions, comment, and participate.
Our three discussants are:
- Cynthia Bell: She is the Director of Workforce Development & Numeracy Services and the Numeracy and Workforce Specialist at the Literacy Assistance Center, where she facilitates workshops for adult basic education (ABE) and high school equivalency (HSE) instructors on standards-based numeracy instruction, as well as on integrating academic and workforce skills. When she’s not leading trainings, Cynthia is providing customized coaching to instructors on curriculum design and the best practices of teaching and learning mathematics. Cynthia has presented at international, national, state, and regional conferences, and is an active board member of the Adult Numeracy Network (ANN), an affiliate delegate of the National Council of Teachers of Mathematics (NCTM), and a national LINCS numeracy trainer.
Sarah Lonberg-Lew: She has been teaching and tutoring math in one form or another for over twenty years. She has worked with students ranging in age from 7 to 70, but currently focuses on adult basic education and high school equivalency. She has taught in two different programs in the north of the Boston area. Sarah’s work with the SABES numeracy team includes developing and facilitating trainings and assisting programs with curriculum development. She is the treasurer for the Adult Numeracy Network.
- Mark Trushkowsky - He started his adult education teaching career in a small basement classroom in Queens, NY in 2001. Since then, he has taught classes in adult basic education, adult numeracy and HSE math. Since 2009, Mark’s work has focused on teacher training and curriculum development with the CUNY Adult Literacy and HSE PD Team. Mark is a founding member of the NYC Community of Adult Math Instructors (CAMI), a math teachers’ circle in New York. He was the lead writer for the CUNY HSE Math Curriculum Framework: Problem-Solving in Functions and Algebra. Mark is on the Adult Numeracy Network Board.
This thread will be the placeholder for the discussion that will start on Monday. If you have questions, ponderings, or musings you may go ahead and post them below. I look forward to learning from them and our discussion with other community members.
Welcome to our discussion on equity and access in the math classroom. To get us started, I’d like to share a story about my early experience in adult education:
When I started teaching math to adults, I saw that my students were discouraged and afraid. They thought that math was hard and they would never be able to do it. I made an effort to be gentle with them and to show them that math did not have to be scary. By slowing things down and breaking procedures into manageable pieces, I showed my students that they could learn math. My students told me I was the best math teacher they’d ever had because I broke things down and made math easy for them.
- What do you see happening in this story?
- What does this story have to do with the title of this discussion (My Students Can't so I Will...)?
- What does this story have to do with equity and access?
Thank you for sharing this, Sarah!
What I hear happening in the story is a teacher breaking down procedures for students. These students will rely on their teacher in the future when they see math they don't know. Students appreciated the teacher's kind, patient demeanor and that the math seemed easier. But was it their math anymore?
It's tempting to want to make things easier on our students (and our own children), but if we do things for our students/children that they need to learn to do themselves, they will always need us.
When I think of equity, I think of providing more opportunities for students than something to memorize. Math is about so much more than that. When I think of access, I think of providing challenging problems that can be approached differently by learners of different math experience levels and problems that don't have a specific, 'right way' to solve them. Maybe these problems don't even have a single right answer.
Thank you, Connie!
When I read your definition of equity, I thought of an activity I do with students every semester I am in the classroom. On the first day, I have students brainstorm a list of characteristics of what makes a good student. It is always a great list filled with all the things you'd want to see: Never give up, Ask for help, Be patient and kind with yourself and each other, etc.
Then I ask them to brainstorm what makes a good math student. Without fail, a switch flips and every semester the list looks something like this:
A good math student....
- Knows their multiplication facts
- Knows the formula/rules/procedures
- Gets the right answer
- Gets the right answer quickly
I find it a good way to begin to talk about mindset with students. The first list is about learning, the second is about memorization and already knowing everything. Put another way, the second list defines students for themselves as bad math students.
To me, our work is two-fold:
- Being explicit with ourselves and our students about what it means to do math. What kinds of experiences do our students need to have to shift the idea that math is memorization?
- What are the things we each do and say in front of our classes that implicitly encourage and perpetuate the idea that good students know the procedures, know their facts, get the right answer, etc?
yours in productive struggle,
I really appreciate this discussion! As an ABE/GED Instructor, I have gotten much inquiry lately about "how is math racist" and "how can 2+2 have any other answer than 4?" I was happy to read https://equitablemath.org/?utm_medium=email&utm_source=govdelivery to prepare myself with an understandable explanation. For me, the two questions tie together - it has been a racist or white-centric way to present ONE answer with only ONE way to achieve an answer (and show your work!) and, that math is SO much more than arranging numbers in some mechanical and rote, absolute way. When I state, 2+2 can be represented in many different ways, such as <5, >3, 🙂🙂🙂🙂, 3+1, etc. I hear some sputtering, well, those are true, but not the same! And I say, exactly - this is what math is really about, finding many equivalent answers in many equivalent ways!
I have always told my students that Math is a language - a universal one, but it's only after thinking about student's metacognition, that I realized, they need to know they think in mathematical ways nearly all of the time - they just aren't aware of this way of thinking, but it is happening! Everytime they measure something, intake data from any or some of their five senses, their brain is computing, organizing information which is completely mathematical. If they are composing music, drawing a picture, taking a photograph (I use examples specific to the activities my students do), they are calibrating and estimating as quite natural mathematical processes. I think drawing connections between what is relevant to our students, expanding practical applications of what we are working on in math any given day, really enriches our students to be receptive to the new wiring of thinking that learning math provides them.
Math is problem solving, and the ways we can problem solve, the diversity of those ways can be extrapolated to problems other than numerical. This deeper understanding that methods learned in math can be transferred to all sorts of equitable problem solving - personal, social, work, logistical - really the applications are infinite - has caught most of my students on fire for math!
What a juicy conversation. Looking forward to this week, thanks Sarah, Cynthia and Mark.
So much of your story resonates Sarah – starting with students who are discouraged and afraid. I also have definitely had the experience you had with the student frustrated with you – where what I am offering is not what the student expects/wants from a math teacher.
I’d like to pull out a few details I’m chewing on- hopefully in the service of your 3rd question:
- The word *manageable* in your story really sticks out to me. I can read your story up until that point and envision very different kinds of classrooms until that word.
I’m playing with rereading it and replacing the word with meaningful. “Breaking procedures into meaningful pieces.”.
One – Many of my students, especially the ones primarily educated in the US, have spent a lot of their education learning that they can’t manage Math. We know that was never the problem.
Two – It sounds like many people in this thread had the experience, one that I keep having, of coming to the understanding that the opportunity and expectation to make meaning is an essential component of equitable access to the content.
- I really love the word gentle in the third sentence. Though I understand now you are referring to a teacher who mistakes taking away productive thinking/struggle for kindness, in my first read I thought “oh yeah – one can be gentle * and * create a space where students are expected to productively struggle with difficult things.” I don’t believe we *have* to be gentle to provide equitable education, but I like that as a question for my instruction – What can it look like to be gentle and hold students to high expectations – to create an environment that gently, insistently expects them to do deep, complicated thinking?
- Cynthia - I read your post - especially your second question [..would [students] need me there to break things down for them into small easy chunks?] multiple times, so rich. Stretching your question has me thinking about how I decide how to chunk and teach the content.
Today, I feel comfortable identifying content that is definitely too paired down, especially if its stripped of meaning. It’s harder to know the instructional sweet spot.
Our standards and learning targets chunk the content. Right now, I think part of my job is to offer the content in chunks, and like Susan, I’ve also seen the value of students experiencing that something that looked inaccessible can be broken down and understood. [This isn't meant to be about teaching procedures in isolation, more about what segment of the content in any given moment.] I’m wondering how I can get better at identifying when I am paring it down too much (or the wrong way?) or where it shouldn’t be done and what I should do instead.
Mark, maybe this connects to your question about productive struggle?
In literacy, we know that while we often pare down to a component of literacy for some aspects of instruction, it’s not good for students to only be reading highly processed, chunks of texts only designed for instruction. It’s important to also read interesting, robust texts that authentically (messily) pull in words and structures students may not have been 'taught’.
I can see a connection to your question, Cynthia, about the detriment of breaking the math work down for students into small, easy chunks – The value of students getting to enjoy and wrestle with a more messy, interesting, complete thing. I’m not always sure what authentically messy, interesting and WHOLE things look like for math, and when I find one, I’m often not sure how to structure instructional time so my students can productively engage with them. How can I get better at that?
Hi there. First off, I really appreciate the comment about asking what makes a good student then asking what makes a good MATH student. Very insightful.
When I read the phrase My Students Can't So I Will.. it is tempting for me to picture an instructor patiently providing so much scaffolding that the student is buffered against any struggle or difficulty. I can instead see the instructor slowing down and breaking procedures into smaller pieces as more of a helpful diagnostic tool for the instructor, a way to parse the students understanding for errors or points of confusion that the student is either too embarrassed to ask about or doesn't recognize yet. In my experience, "slowing things down and breaking procedures into manageable pieces" was often the place where I could find out if the math jargon, symbolic misunderstandings or directional confusion was the source of their stumble, and where specifically this block was. Although it might’ve seemed like a slowing down for their direct procedural benefit (and it's easy to be fooled by the student's praise for such), for me it was chance for a series of quick inquiries into their understanding and abilities that might not have shown up on their intake exams. What the students often "can't" do is often see their roadblocks of confusion from outside their own perspective. Or see them at all.
I think equity and access for the adult learner is often hindered by instructors who downplay the impact confusion can have on the math student, separate from their conceptual understanding. A person can have a conceptual understanding of how an elevator and escalator work and yet still confuse the terms late into their life. Having them just rename one as a moving staircase can help with that and seems like a kind and sensible option to reduce their verbal anxiety. But in the math class, saying bottom number instead of denominator is seen as a setback or temporary embarrassing placeholder.
I want to thank you, Cynthia, and Mark for leading us in this discussion. I appreciate your willingness to help us reflect and talk about equity. I know from my own experience that these can be difficult conversations to start and remain engaged with. Personally, I am feeling motivated to do better and I feel supported by amazing colleagues in adult education, but I also feel an internal resistance to face the blind spots I have and the ways that I might have contributed to inequities.
In your story, I see a new teacher doing their best, using their knowledge of math and empathy for their students. Feeling like I can learn is an essential step. The teacher is doing a lot of work to create this possibility. (This feels familiar to my experience first teaching math, except that I wasn't very good at breaking procedures into manageable pieces, and my students didn't tell me I was the best math teacher ever! I was working as hard as I could, but I had trouble making the math easy for my students. I did my damndest to explain every step, even when I didn't understand it very well myself.)
I wonder about the part of breaking procedures into manageable pieces. I think this means making each of the steps that students should follow clear and easy to follow. A series of steps the teacher explained to the students and helped them master. I can imagine this leading to a certain form of equity, with students independently able to solve a (limited) set of problems. However, it also could to lead to a dependence on the teacher to provide a series of steps for each type of problem.
Access requires opening doors, providing means for students to enter the mathematical conversation. This story seems to illustrate a form of access, but not equity? I think working towards equity means that our expectations need to be higher. Our students can do more than memorize steps.
I appreciate your point about access. As a math teacher I believe in making math learning accessible for all learners. Personally, I subscribe to the "low floor high ceiling" and the multiple entry points methodology of teaching.
However, my goal in life as a math instructor is and was to develop mathematically powerful students. In the anecdote above, as much as Sarah meant well, I don't think that teaching in this way actually does this. Most of my students are BIPOC or lived in "under privileged neighborhoods". Does doing the thinking for them to make things easier really help those students become mathematically powerful?
My students knowing how to read their paychecks properly, or how to calculate the total of the items that are in their shopping cart prior to getting to the register, being able to challenge when and if they are being taken advantage of is what "mathematically powerful" meant to me. Would they be able to do that or would they need me there to break things down for them into small easy chunks?
For me equity in the math classroom is teaching my students how to think, not just how to do math. The playing field becomes more leveled when learners understand, can reason, be skeptical thinkers and can develop their own solution pathways (not just follow mine).
I'm so looking forward to hearing more of what others think and having my perceptions challenged and expand!
I like this post a lot. When I read "breaking down procedures" I did my automatic "Concepts are more important than procedures!!" response... but I also recognized that a more important lesson is "what looks impossible might not be." Teaching students that a procedure that seems impossible *can* be broken down is important. When they have new material, they can look for ways to have it broken down...
... but I still hope we can get students into understanding the ideas behind the procedures. One of the reasons for inequities is that once a student is on anything like a 'remedial' track, the instruction tends to be all about learning a procedure to pass some sort of assessment and then once you're in whatever you qualified for... hoping you can figure out enough to survive. I think we can do better.
Dear heroes of adult education,
First of all, thank you for getting the conversation started, Sarah. I appreciate you sharing your experience because I see my own first few years of teaching math reflected back to me in your story. I see a teacher reaching out to her students with compassion, wanting to explain herself clearly so that students will understand math in a way that they never felt before. If access to math is a party, you were trying to bring all of your students along as your plus one.
I also appreciate Eric for naming how difficult it can be to focus on blind spots, especially when it comes to students we love and our role in systems of inequity. But as with most challenges in my life, I am inspired by my students who have weekly dates with our math classes, which is to say something they are afraid of. Who am I to not show up? I want to pick up something he said that for me is the key of all of this, which is the idea of expectations.
Anyone in our line of work knows that in every class in every semester, we will have students who say "I am not a math person" or "I am just not good at math". From day one, when I hear students say it, I immediately start to contradict them and tell them of course they are and that everyone is and how much I believe in them. I want to heal them with my words so badly. I believe it is something they learned to say in self-preservation. They are asking us to lower our expectations of them. They are telling us to not believe they can do it, because that is what they already know based on what has been done to them and conveyed to them in their prior education.
I talk to students a lot about their experience in math class because it helps. We definitely have students who have been explicitly told they were stupid, yelled at, thrown out of math class for not getting it. And we also have students who did not suffer those heartbreaks who received the exact same messages about themselves and their abilities.
I am very sensitive to the prior math experiences of my students. Almost all of them are on the spectrum of bruised to traumatized when it comes to math. They bring much self-doubt and a crippling lack of self-confidence, which is why I set up my early classrooms as safe places where students didn't struggle and couldn't fail. I understand why I did it, but looking back on my actions now I see that in spite of my intentions and my explicit contradictions, I believed my students were not math people, I believed they were not good at math. I would have said the opposite and shouted it from the rooftops, but by treating them in that way, I conveyed and confirmed that belief to them. And they didn't mind, because they had accepted that belief as truth long before they ever got to my classroom.
People tease me because I often sign off my emails and letters with "yours in productive struggle," and I laugh but part of why I do it is because I need the daily reminder that for me, productive struggle is the crucible where teaching and learning and healing happen in an adult education math classroom.
It is a term that I hear used a lot, but it is one of those words like "justice" and "love" that can mean so many different things to so many people. I'm curious what productive struggle means to you?
yours in productive struggle,
I really appreciate this discussion and appreciate reading others' posts. Very thought provoking. Like many of you, my journey as a teacher began with passion and care for my students, but a tendency to over-support them, interfering with their growth as independent mathematical problem solvers. I have more recently developed (with enormous support from colleagues) teaching habits that put student voices first, support students in finding their own lines of inquiry, and maybe most importantly, feeling safe and comfortable as they make, share, and explore mistakes. I start my first class and repeat often, "mistakes are welcome here."
Still, I know that I have a lot of work to do to improve access and equity for students in my classroom who have been shut out of mathematical conversations in the past. Something that has come up for me a lot lately is differentiation - giving students with different levels of background knowledge and experience the opportunity to thrive. In my eagerness to help my students develop their comfort as they struggle and make mistakes, I stress that we must be patient with each other as everyone in the class builds a common understanding. This often leaves my "quickest" students waiting, twiddling their thumbs when a handout that took them 10 minutes takes other students 20, and then patiently re-explaining their work to students who haven't mastered an idea yet. I think these peer-led conversations are extremely valuable, but I would like to provide strong students with more of an opportunity to thrive and grow at their own pace while still keeping the classroom accessible to the more timid/less confident. I would love to hear others' thoughts and experience on this.
What a great discussion today! I've learned a lot since those early days. At that time I really was proud of myself for making math more accessible to my students. I do things very differently now and plan to continue to grow as a teacher, so I fully expect to be looking back one day on my current ideas and thinking how much I've learned since then.
I'm still proud that I gave my students a chance to be successful, but I see now that I could have given them so much more and that one thing I didn't give those early students was the chance to think of themselves as reasoners and thinkers. By failing to do that, I reinforced the idea that real mathematical achievement was not for them - math was just something they had to pass a test in so they could move on with their lives.
More recently, I had an interaction with a student where I was pushing him to explain his reasoning and asking him deeper questions after he had already answered one correctly. He got quite angry with me because I was not behaving in the way he was used to math teachers behaving. According to his experience, after he gave a correct answer, the teacher should leave him alone. But when I explained that I was pushing him to help him grow as a thinker, his anger disappeared instantly. It was a learning moment for both of us. He learned that there's more to learning math than answering a question with a number, and I learned that even if students need a push, they will embrace real learning when given the chance. Sometimes it takes a lot of pushing, but that may be because I am pushing against a heavy history that the student has carried into my classroom. And I may be the first person ever to push back against it. It's not surprising that students sometimes cling to their mistaken ideas about what relationship they can or can't have with math. They've lived with those ideas for a long time.
Pushing students to engage with productive struggle and to hold their own reasoning to high standards doesn't mean I can't still be gentle, supportive, and encouraging. And making my classroom a safe place for students who have been injured by their previous math education doesn't mean I can't have high expectations for them. Failing to have high expectations is siding with the system that hurt them in the first place.
So important that he could learn that you weren't pushing him to make him look bad ... that you were on his side ;) How many students think we're trying to trap them... *find* a way for them to be "wrong..." I see this too, especially in students who have been convinced that their job is to get the right answer and put up a shield so that nobody discovers just how "stupid" they are. It's a nasty spin on 'imposter syndrome.'
At the last ANN Under 10, Minnesota ABE teacher Abby Roza gave a ten minute talk about Expectations and Outcomes. I have returned to the video of her talk over and over again. Abby’s wisdom has helped me identify several truths. Among them are the ideas that Students see themselves as the problem and Systems can be changed.
In her talk Abby said, “Long racist, classist, ableist, sexist histories and current realities, create an environment where policy makers, educators, and worst of all the students themselves, are encouraged to believe that the problem is the students themselves, rather than systems that can be changed.”
Change is hard when dehumanizing narratives are all around us like a smog. Adult education teachers don’t rule the world (yet). We don’t all have the same level of privilege as each other, but we have privilege our students do not.
We’d like to open up today’s discussion with the following questions:
- What is one concrete thing you can do in your classroom to increase access and have high expectations?
- What is one concrete thing you can do outside of your classroom?
yours in productive struggle,
Thanks, Mark, for the challenge to identify concrete steps.
One thing I've identified as useful for increasing access and having high expectations in my classroom is the routine of doing number talks. This is a routine I already have been using and love, but this discussion has helped me pin down some of the ways that it promotes equity and access through being open and communicating high expectations. Here's a very brief description of a number talk in case you're unfamiliar (read this excellent book if you want to know more):
- The teacher poses a computation problem (for example 18 x 5).
- Students think quietly and come up with an answer, usually using mental math.
- Students share their strategies and the teacher records them on the board with the students' names.
Here's why I think this routine promotes access and communicates high expectations. Everyone can participate and is strongly encouraged to do so. I always made sure to pick a problem that I knew all of my students would be able to come up with at least one strategy for. For example, with 18 x 5, one student might write out 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 +5 + 5 + 5 + 5 + 5 + 5 and count by fives until they got the answer or even draw an array and count the dots whereas another student might multiply 18 x 20 and subtract 10. As long as I know every one of my students knows what it means to multiply, this question will work. I make it clear in the routine that I want to hear everyone's answer and everyone's strategy and that they all contribute to the conversation and to advancing the learning of the group. Wrong answers or strategies that didn't work are also valuable. Students hearing from each other and getting credit for their ideas works to push against the narrative that all knowledge comes from the teacher and the narrative that there is no room for creativity or different strategies in math. Where high expectations comes in is in the expectation that students will justify their thinking and continue to explore new strategies. I have occasionally needed to push a student on that, but mostly they have grown into it on their own from seeing the examples set by their peers.
One piece of pushback I've heard both from other teachers and from students on number talks is that it is confusing to have to learn more than one way to approach a problem. One thing I'm taking away from this discussion is that pushing students to engage with the confusion is part of having high expectations. Cognitive dissonance and productive struggle create learning. I shouldn't be trying to avoid confusion for my students but rather communicating my faith in them that they can navigate it and will settle on one or more strategies that really resonate with them... and that I am there to support them in their confusion, but not to take it away.
What about something I can do outside the classroom to increase access and have high expectations? One thing I am doing now is making sure that whenever I am out in public (not that often these days), I am wearing something that says Black Lives Matter. I'm thinking about this decision in the context of equity, access, and high expectations and it is strengthening my resolve on this. (And it did take me time to come to this decision and to build the resolve to stick with it.) I wear it because I believe the message, but also specifically because I want other white people to see me, a white person, strongly saying that Black Lives Matter. In this way I am increasing access to this important message and communicating my high expectation of white people that they will see it, think about it, and embrace it. This is part of changing the destructive narrative that this country has been living for so long.
Thank you, everyone, for all that you have shared so far! I love the richness of this conversation. I could spend an entire dinner discussing each of the individual posts, so I am glad to have a concrete question to respond to. What is one concrete thing you can do in your classroom to increase access and have high expectations?
To increase access and have high expectations, we can build our own content knowledge and approach students as colleagues in that endeavor. The more that we understand about mathematics and different ways to see and understand mathematical concepts, the more often we (as teachers, so authority figures) can say "yes" to students who are sharing their own sense-making process. This begins with the question, "How can I reinforce students' trust in their own thinking?" We can only speak from within our own limitations in knowledge and perspective when explaining a concept or procedure. By listening very closely as students explain their thinking, we can find nuances or new ideas to grow our own mathematical knowledge and widen our own perspective. This widened view will help us do better as we listen or talk to the next student. This new knowledge could involve anything from a new analogy to an unfamiliar procedure to a connection between concepts that we had not yet considered.
It is not possible to know all of the things about math, so we can let that go and focus on working with the mathematicians in our classrooms to continue to make sense of math together. If students know we are doing this, even better! I like to listen for students' conjectures and spend time with them. This week, when discussing where to place the decimal in the product when multiplying decimals, a student and I talked about counting digits after the decimal. We talked about estimating an answer, and then he suggested counting the numbers before the decimal, which was a new idea to me. I tested it out a few times and could not immediately find a counterexample, so I wrote it on a sticky note to be explored further, perhaps with another class. I did all of this processing out loud, with the student.
As we learn more access points to concepts, we can recognize them when students use them. A classroom where everyone's ideas are considered, and when ideas are new, others will listen and expect to be convinced, sets the stage for high expectations.
- What is one concrete thing you can do in your classroom to increase access and have high expectations?
In my classroom, one concrete thing I am doing is welcoming any student to join any activity or lesson.
A few years ago, I stopped assigning who could participate in what work or lesson. I teach in a “one room schoolhouse” type setting where students with any Adult Education students are in my room. When I first moved to this type of setting, I had previously taught in more traditional settings where the whole group was supposed to be working on the same objective at the same time. Now, every student has their own objectives. Early on, I did more directing students as to what small group lesson, center or activity they ought to be a part of, based on their educational plan and my understanding of their skills or knowledge.
Students showed me the better way: A student asked to watch a group he wasn't assigned to and made smart, coherent connections between the content the group was working on and what he was studying. Later, when I found myself talking a different student with emerging skills out of playing some game or activity he enthusiastically wanted to join and I thought, WHAT. AM. I. DOING. ?
Students are now openly invited to join any activity or lesson in the room. (They also still have their own individualized objectives and plan.) There was a learning curve on my end. I’m still learning. There are a number of ways this turns out and it's almost always great.
- What is one concrete thing you can do outside of your classroom?
I’m (slowly) learning more about barriers to diverse teacher candidates becoming (and staying) teachers. Right now, that looks like taking opportunities to learn more about (and support) existing initiatives for increasing teachers of color in the classroom and looking closely at my state’s required tests for teacher licensure. I’m simultaneously looking for ways I can support candidates for whom the exams are a current barrier and learning more about initiatives to remove or replace the tests and other barriers to teachers of color becoming licensed.
will try to show them how.
"Just because they should, doesn't mean they can. Just because they can't, doesn't mean they can't learn to." (So many missing clauses, but...)
Like many of us on this thread, I have vivid memories of students' visceral reactions to fractions. It was the first piece of math "baggage" set at my feet when I advised new students and reviewed their TABE scores. Those math insecurities were presented almost as an apology by the students, like they owed me some kind of explanation for how they performed on a test or what led them to be in my HSE class in the first place. I usually would assure them that they were not alone in their feelings about fractions and that my job was to create a new (and hopefully more welcoming) experience with fractions and other math topics, too. My 15 minutes of advising didn't leave too much time for really providing the kind of support I wanted to impart before they started my class, but it was a beginning step for sure.
I realized, however, that no amount of assurance on my part could remove the emotional trauma some students carried with them. One student in particular stands out in my mind. She was a woman in her late 50s who was slowly chipping away at passing sections of the GED, knowing math would be her last test. She had been in my class for some time and was extremely helpful and well-liked by her classmates. I could count on her to be my eyes and ears to alert me if someone needed help but wasn't speaking up for themselves. She worked hard on her own skills and welcomed whatever math learning experiences I brought to class. Until we got to fractions.
She shut down. Emotionally. Mentally. Physically. She was a different person. Her hands would shake when she tried working on fraction problems. She often cried. She would apologize profusely for losing control of her emotions, and no reassuring by me (or her classmates) seemed to make a difference. I later learned from her that she had a teacher who believed in cracking her knuckles with a ruler when she made a mistake with her math, and it began when they were doing fractions. Nearly 50 years later, she still responded as if I was standing over her with a ruler, waiting for her to make a mistake on those same fractions. It broke my heart, and everything I tried to do to help her seemed to fail. Until one day when working on angles in geometry.
She came up to me after class with her phone extended to show me some pictures of wooden birdhouses she had made. They were beautiful and showcased her carpentry skills, which I had no idea she possessed. She was beaming with pride and was so delighted that I noticed things like the type of wood she had used and asked questions about her designs. She was alive again. When I pointed out how much math I saw in those birdhouses, she denied using any of those skills or terms. She didn't see how her use of a measuring tape had anything to do with the fractions we'd previously studied. She did concede that the miter cuts on the roof were related to the angles we'd been learning about that week. For her, it was impossible for something as upsetting as fractions to coexist in her woodworking world.
The lesson I took away from that experience was that no matter how many new ways I tried to reach my students on topics they often tried (and failed) to grasp, I was missing one critical tool - my students own lives. Their world and their experiences were missing from my lessons because I had not created space for them. And even if they couldn't see the math in those things that brought them joy, that's where I could help and support them.
So, one concrete thing I can do now (even though I'm no longer in the classroom) is create learning opportunities for teachers and professional developers to experience math beyond the norm so they might invite their students to do the same. It's challenging to find the math in things you know little about, but that's what it means to be a lifelong learner of math, and as Mark mentioned in his post, it's part of my own understanding of productive struggle.
One thing I'm currently doing is working with an amazing team of ANN members to plan the music portion of the ANN Teaching & Learning Institute on March 19th as part of COABE's pre-conference series. I love music, but digging into the math side of this is challenging me in ways I never imagined. It's hard and frustrating, but every now and again the light bulb goes off and I finally see the math that's been there all along despite my denial. I'm discovering new tools and resources I never would have considered looking into that I now recognize would have been fantastic materials for my students who wanted to go into music production. Imagine what kind of lesson I could have created out of a student telling me about his or her love of mixing songs. How fun would it be to start each week of class with a new career or hobby as the focus, and my job is to simply let the students tell their stories and listen and watch for the many ways in which math shows up?
Thank you to Cynthia, Sarah, and Mark for hosting this important and timely topic. The discussion is still open and you may continue to discuss with each other. Cynthia, Sarah, and Mark are still members of our community and may chime in from time to time. I feel that there is more to uncover with this topic. Additionally, many community members who have not had time this week to voice their reflections I would like to hear from you. I want to empower you to add to this rich discussion.
This topic is a great example of how this community can help and support each other to grow - together. If you would like to lead a discussion like this or something else, please email me email@example.com . I can help you to flesh out your idea.
Thank you once again to Cynthia, Sarah, and Mark!
LINCS Math and Numeracy COP