In yesterday's Saturday session, we discussed 3 🔑 Mathematical Literacy Practices: LEVERAGING FORM, THINKING WITH AND THROUGH, and REFINING IDEAS. These three key practices will serve as the foundation for the rest of our work at the center. Our participating teachers took a deep dive into these practices, considering what they look like across the middle school curriculum. For example, teachers discussed using the fractions, decimals, and percent as an opportunity to discuss leveraging form. They also noticed how multiple representations are most powerful when they are student-selected, or even student created!
In the last Saturday Session we discussed some specific mathematical practices, namely:
seeing concepts as mathematical objects,
seeing concepts as mathematical processes,
and meaning making across different representations.
Rooted in the work of Rachel Gabriel (2023) and Anna Sfard (1991, 2008), we looked at ways in which math literacy practices can be foregrounded in classrooms by making the often implicit ways we make meaning, more explicit for students.
Next time we will dive further, analyzing classroom videos and artifacts to gain evidence of mathematical literacy practices in action!
Gabriel, R. (2023) Doing Disciplinary Literacy: Teaching Reading and Writing Across the Content Areas. Teachers College Press.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University press.
In this month's Work Group Meeting, teacher-participants discussed ways they have incorporated PD learning into their daily teaching. Several teachers mentioned using their document cameras during instruction, leveraging the new tool to support quality classroom conversations.
Teachers also discussed their initial attempts at LAUNCHing tasks. One teacher noted that in her inclusion class a quality launch helped students use math language throughout the lesson. Another noted how important it was to "let them go" by providing students the time and space to wrestle with interesting ideas (as opposed to lowering the cognitive demand of the task by rushing to give students answers).
Lastly, one teacher noted that she had been doing a form for launching for years, discussing the context of a math problem before jumping in. But her latest attempts at launches were "more than just talk" and now included carefully designed student experiences. For example, when introducing least common denominators, a teacher showed a picture of two boxes - one with 8 cupcakes and another with 10 juice boxes. Above the boxes was written "What do you notice? What do you wonder?" Students were eventually led to consider how many boxes they would need to have an equal amount of each. The students talked purposefully about math in ways they simply wouldn't if you started off by giving them the definition of LCD and having them do examples. More importantly, they had a truly mathematical experience!
We look forward to continuing these great professional conversations at our next Saturday Session - Nov 12th!
Today's release of NAEP data ("the nation's report card") continues to highlight the inequities that were exacerbated by the COVID pandemic (see more https://www.nationsreportcard.gov/highlights/ltt/2022/#performance-trends-by-student-group). For example, for 9-eary-olds the white-black achievement gap in mathematics expanded from 25 to 33 points. While there were/are a myriad of factors contributing to these results, what can we do as math educators to on a daily basis to combat such trends?
In our upcoming Saturday sessions we will discuss the role mathematical literacy can play in creating more equitable outcomes for ALL students.
The CEML TEAM wanted to say a big THANK YOU to all the amazing teachers who made our Summer Institute 2022 a success! We wish you all the best and look forward to continuing to learn and grow with you in the coming weeks and months!
Today we thought about what it means to have "DIALOGUE" in mathematics.
We continued to examine mathematical tasks from https://access.openupresources.org/curricula/, first exploring them as students. As we worked through the tasks we thought about the math literacy practices we were using, including connecting to prior knowledge, refining ideas, and learning from the current experience.
The group also discussed some specific teaching practices we might use to support our students as they engage in math literacy practices, including: providing individual think time before discussions, providing students with sentence stems, and fishbowl discussions.
Have a restful remainder of the summer!
We asked participants about their biggest takeaways from DAY 3 of our Summer Institute. Here's what they told us:
"Students should be given the space and opportunity to process their thinking (writing, reading, taking notes/annotating) before starting a task."
"There is no right or wrong way to write math."
"The biggest takeaway I have for today is the appreciation I have for this group community....It almost chokes me up a little... This group is so willing to help...their willingness to help me is staggering."
"Specializing allows students to test new learning with numbers they're comfortable with."
Today we thought about what it means to "WRITE" in mathematics.
As we worked through the mathematical tasks we thought about the math literacy practices we were using, including thinking with and through symbols, annotating, and specializing. The group also discussed some specific teaching practices we might use to support our students as they engage in math literacy practices, including: writing for a particular audience, writing for a particular purpose, and writing to learn.
We're looking forward to a great last day for our Summer Institute 2022!
Today we thought about what it means to "READ" in mathematics.
We looked at some great mathematical tasks from https://access.openupresources.org/curricula/, first exploring them as students. As we worked through the tasks we thought about the math literacy practices we were using, including interpreting common representations and notation, maintaining equivalence, and leveraging form.
The group also discussed some specific teaching practices we might use to support our students as they engage in math literacy practices, including: making connections (text-to-text, text-to-self, or text-to-world), unpacking vocabulary, modeling, providing sufficient time, and providing sufficient “space,” i.e. an open problem.
We are blessed to have such an amazing group of reflective practitioners!
Looking forward to more great conversations and learning tomorrow!
What a great first day!
To get in the literacy mood, we first read the poem Stopping by Woods on a Snowy Evening. Led by Dr. Kane, participants unpacked the often tacit literacy practices used during sense making. Participants noted several things, including accessing prior knowledge, creating mental imagery, double reading, and reading aloud. Then participants contrasted poetry reading with reading a NCTM mathematics task. Participants described using literacy practices including rereading, looking for key words, and making personal connections.
Throughout the day participants tackled more rich mathematical tasks, paying particular attention to the critical role literacy plays in sensemaking. For example, participants noted that different types of graphs required different types of sense making, leading Dr. Kane to describe them as different "genres" of graphs (i.e. bar graph, line graph, etc.)
Participants consistently used their document cameras throughout the day (part of their welcome package they received in the mail), putting on their "student hats" to share work on mathematical tasks with one another. Participants discussed how they could see that their students will benefit from the use of the document camera in their classrooms, likely increasing student ownership and engagement.
In the days ahead we will dive deeper into mathematical literacy, getting specific about what it is and how we support students to engage in the related literacy practices.
Imagine a new student will be coming to your class. As she talks to the other students she asks: "What do I have to do in this class to be successful?" How would your students respond? Take a second and write down your answer before reading on...
This question is meant to get at the current "mathematical practices" in your classroom. By mathematical practices we mean what do students repeatedly do as they engage in mathematics. Research has shown (Stigler, 1999) that in many US math classrooms, common mathematical practices include taking notes, mimicking rigid procedures, and symbolic manipulation. In contrast, recent standards documents (NGA, 2010) describe mathematical practice more akin to what a mathematics professional might do, including leveraging form, thinking with and through symbols, and asking questions.
Here at the CEML, we use the lens of literacy to examine our current mathematical practices and then shift the classroom culture into one that promotes equitable access to powerful mathematical practices.
In future posts we will explore specifics about how we leverage literacy to transform the local definition of what it means to "do mathematics"!
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.
Stigler, James W. (1999). The teaching gap : best ideas from the world's teachers for improving education in the classroom. New York :Free Press,
According to Solomon (2009), to be