By Joe Dostilio, Kristin Klingensmith, Beatriz Strawhun,
and Laurie Speranzo
Institute for Learning Math Fellows
As we start another non-traditional school year, it is vital to take an asset-based approach to teaching and learning. This requires us to resist the notion that students have not been learning during the pandemic. Students have been learning and they bring assets back to our math classrooms. Students enter a math classroom filled with their own ideas, lived experiences, and knowledge from previous math classes and math from everyday life. Educators who believe that every student has meaningful ideas to contribute are taking an asset-based approach to mathematics teaching and learning.
Practices like repeated cycles of testing, reteaching, and remediating are “just-in-case” teaching practices that stem from a deficit-based perspective about students’ knowledge and abilities. Deficit-based practices are often driven by and perpetuate instructional inequities and negatively impact student engagement. “The educational literature is inundated with reports of studies and theoretical discussions…[that] portray students of color, students who live in poverty, and students whose first language is not English as deficient and inadequate in comparison to their White counterparts” (Milner, 2010). Teachers and school systems operating from this perspective find it difficult to create learning opportunities that are cognitively challenging, especially for students from historically marginalized communities.
If students return to deficit-based teaching that assumes that they do not know and are not able to do math, their mathematical identity will be shaped by the assumed deficits. From there, the all-too-common math anxieties and self-perceptions of “I am just not a math person” may become what students come to believe about themselves, impacting their lives in and out of the classroom.
While a deficit-based approach reinforces the notion that “some people are just not good at math,” an asset-based approach conveys that EVERYONE IS ALREADY A MATH PERSON!
Asset-based teaching counters the deficit approach by centering student thinking and reasoning, works to solidify mathematical understanding, and bolsters positive math identities.
Here are three practices that work in combination to foster safe, student-centered learning environments as students return to school having unique and varied lived experiences. Applying these practices provides opportunities for each student to use and be honored for their assets, engage in learning as doers of mathematics, and develop positive mathematical identifies.
Our position is that it is entirely possible to hold high expectations for all students, address unfinished learning in the context of grade-level work, and dial into the assets students bring with them in order to unlock the creativity and energy they bring to the joyful work of learning something new.
Student Achievement Partners (2020). 2020-2021: Support for instructional content prioritization in high school mathematics. Retrieved from achievethecore.org
1. Center Student Thinking with Cognitively Demanding Grade-Level Tasks
The tasks we use convey not only what we think about mathematics but also what we believe students are capable of doing.
By using cognitively demanding tasks on a regular basis, we message that mathematics is about exploration and reasoning and that it requires sense making. Because such tasks have multiple entry points and can be solved using a wide range of representations and tools, every student can draw on their lived experiences and prior knowledge to make sense of and reason about the situation. This will look different by grade and content being explore. Here’s an example of what it might look like in a grade 1 classroom.
As students try to determine the unknown addend in a story situation, some will reason about the part-whole relationship without really thinking about addition or subtraction. Some will apply reasoning related to subtraction, while others use reasoning related to addition. Students will strategically make use of tools, using those that make sense to them instead of being told which to use. Some might use manipulatives, while others are drawing a picture. Some will use a number line, others their fingers, and some may play with the quantities in their head.
All these pathways are valid, valuable, and decided upon by the students. When students use multiple pathways, they can then spend time connecting their work to the work of others.
By working in collaboration with others on cognitively challenging mathematics tasks, students discover their own strengths, grow confidence to push back, and experience moments of joy and excitement that come with the perseverance of figuring it out.
Through regular use of grade-level cognitively demanding tasks, teachers can
- formatively assess students’ knowledge assets, diverse ways of knowing, and areas of solidified understanding along with their use of mathematical practices, and
- surface any areas for additional “just-in-time” learning opportunities.
Centering student thinking through the use of cognitively demanding tasks creates a community in which students recognize and believe that their ideas and problem-solving approaches are a critical part of the mathematics discussions. Doing this sends the message that mathematics requires critical thinking and reasoning and that we trust our students are doers of math.
Check out this quick read from the national Council of Teachers of Mathematics for more information about and examples of cognitively challenging tasks.
2. Center Student Thinking with Lesson Routines that Position Students as the Authors of Mathematics
There are a lot of lesson routines out there, some are designed to tell students what to do and think about in mathematics, and other routines position the students as the thinkers and doers of mathematics. When making a decision about the lesson routines to use in your classroom, look for those that provide space for students to ask questions, develop and use models, plan and carry out explorations, analyze and interpret data and the work of others, construct explanations, and engage in constructing arguments from evidence, all of which are critical practices (Windschitl, Thompson, Braaten, & Stroupe, 2012).
One such routine is the SMART lesson routine. We recently started calling it the SMART lesson routine to emphasize that Students engage in Math Authoring, Reasoning, and Talk. It is specifically designed for students to learn from the work that has been authored by their peers.
During every phase of the SMART lesson routine, students are reading, interpreting, authoring, and revising their mathematical understanding.
- Set-Up Phase: Students and teacher read the task, often times aloud, and interpret the situation or information provided. The students take stock of what they know and consider how their prior knowledge relates to what they are now solving.
- Explore Phase: Students begin putting their thoughts into action and on paper, at first on their own and then alongside others. They actively discuss and compare their thinking to the thinking of others. The teacher poses questions to further elicit student thinking and leaves the group with a question to advance their work. This combination of peer-to-peer discussion and teacher pressing results in revision and/or refinement for their written work.
- Share, Discuss, and Analyze Phase: Students critically consider and discuss the written work of their classmates that has been intentionally selected and sequenced by the teacher. During this discussion, they make comparisons across the work of multiple peers and generalizations based on patterns they notice. Students often will add to their written work by engaging in Stop and Jots or Quick Writes.
Through regular use of the SMART lesson routine or a lesson routine that centers student thinking the same way, teachers can
- identify each student’s assets and area(s) of unfinished learning as they generate their own solutions drawn from their ways of knowing and using native language (even when it is not the language of instruction), and
- take stock of how student thinking evolves as they work with their peers throughout the phases.
Check out Cesar’s story about how “flipping” a traditional lesson routine to be more like the SMART lesson routine changed the dynamics of his classroom. Cesar is a teacher we work with in Canutillo Independent School District.
A lot of my practices didn’t change much because I asked why a lot before. I always encouraged students to make mistakes and to just try. I would tell them, “I don’t care about the right answer, I care about the process.” I wanted them to know that in-class is where we can make all the mistakes; it is where we practice. It was important for them to know that we make mistakes to make improvements.
What did change was the order in which I teach.
It’s like I do, we do, you do, but backwards.
The first time I flipped my lesson routine was for a task involving scientific notation. Here’s what happened…
During the set-up of the lesson, I told them I was going to push and challenge them to learn math in a new way. That it is going to be challenging at times and possibly frustrating, but I am there to help them. I referred to the phone scenario and then used that to start the lesson. I gave them a problem to work on from the book and said use the text to find patterns, hints, anything to help you solve the problem. I made sure to tell them that I didn’t care that the answer was wrong, but I want them to try. I also told them that they NEED to come up with something. That, “I don’t know, or we didn’t get anything.” was not an acceptable answer. All I cared about was that they came up with an answer and that they could back it up with evidence from the text or their work.
They went off to explore for about 8 minutes. They used the text to find patterns. I heard students point out vocabulary; I saw them test and try different methods based on what they saw. I circulated asking students their thoughts and encouraging them to try whatever they thought was correct. If I heard anything that was on the right track, I had them pause what they were doing and had the group say their thoughts out loud to the class. For example, I had one group notice that the coefficient in scientific notation had to be bigger or equal to one, but less than ten. I had them repeat their claim to the class. That helped the rest of them continue to solve the problems because I heard “OOOOOOH!” many times when that little detail was shared.
After some time, I had them share their findings and methods with the class, as a whole. Then we all shared our answers and conclusions. If something was shared that was incorrect, we worked on the spot together to revise and correct the mistake. We then continued the same process for each of the problems they solved.
Once we finished the section, I congratulated them on being able to find all the details on how to write and convert numbers into scientific notation. They were shocked that they were able to figure everything out on their own. I would even say that they felt accomplished about what they did.
As for me…it was pretty great to see them just go for it. I loved that they were open to trying this method with me and were not afraid to ask questions or try whatever came to mind. I was nervous on how this would go and what it would look like, but I was pleasantly surprised.
Would I do it again? Yes!
I have already started a new topic and began the same way. The students are still getting used to this way of working and still need a bit more confidence and guidance. I’m hoping that if I stick with it, that it will come more naturally to them and soon they will be leading more and more of the discussion.
3. Center Student Thinking Through Meaningful Mathematics Discussions
Meaningful mathematics discussions are intended to be meaningful…both because they are mathematically rich and because learners are invested in the discussion in meaningful ways. These types of mathematical discussions do not typically happen by chance, because being a participant in them, whether as the student or the teacher, is different than engaging in conversations outside of learning spaces.
There is no shortage of posters, place mats, and gimmicky tools designed to support students in engaging in mathematics discussions. Unfortunately, many do not lead to discussions that are mathematically meaningful because they either aren’t mathy enough or they don’t consider the nuanced interactions among students and between students and teacher during conversations.
Facilitating discussions through which learning occurs, especially in mathematics, requires an “unnatural orientation toward others and a simultaneous, unusual attention to the ‘what’ of that which they are helping others learn” and draws on ways of being that are not common outside of teaching (Loewenberg Ball & Forzani, 2009).
Through regular facilitation of meaningful mathematics discussions, teachers can
- invite and honor contributions from students that are linguistically diverse,
- gain insight into what students know and understand and the evidence they use to support their understanding, and
- monitor the dynamics of learning conversations and make adjustments that draw in students who have not yet been heard.
Check out this video from a Grade 1 classroom. As you watch the video, notice how the teachers works to facilitate mathematical discussions as students engage with a cognitively demanding task. This video also shows the SMART lesson routine in action!
As you watch the video, you will notice that the teacher continually centers the thinking of the student or students with whom she is talking by
- asking questions to which all or part of the answer is anticipated,
- probing others’ ideas for further information and reasoning,
- provoking disequilibrium and surfacing errors to deepen
the discussion or explore misconceptions
or overgeneralizations, and
- seeking to learn about and from others’ experiences
and perspectives (without presuming a common understanding
from the start).
Tell Us About How You Center Student Thinking in Math Class
- Which of these ways do you already use? How is it going?
- Which of these ways might you add to your toolbox? Why?
- What other approaches, practices, or strategies do you recommend for centering student in math classrooms.
Tell us here.
Loewenberg Ball, D., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497-511. doi:10.1177/0022487109348479
Milner, H. R. (2010). What does teacher education have to do with teaching? Implications for diversity studies. Journal of Teacher Education, 61(1-2), 118-131. doi:10.1177/0022487109347670
Windschitl, M., Thompson, J., Braaten, M., & Stroupe, D. (2012). Proposing a core set of instructional practices and tools for teachers of science. Science Education (Salem, Mass.), 96(5), 878-903. doi:10.1002/sce.21027