1. Revisit Jo Boaler’s work: Of course, any discussion on growth mindset has to include Jo Boaler. At the start of the current school year, I had posted and discussed her growth mindset norms with my students and used her “Week of Inspirational Math” which can be found on youcubed.com. While many of my students showed initial change, they began to stall around November. At NCSM, I had the opportunity to talk with her in a small group about the issues surrounding a long-term shift to growth mindset (NCSM 2017, Session 1630). Below is some of the advice she gave me:
- Review the growth mindset norms, and adjust them to fit your student’s needs. Don’t be afraid to deviate from the seven norms laid out in Mathematical Mindsets if they suit your students more.
- Leave time to complete at least one low-floor high ceiling task per week, perhaps on each Friday.
- Have students complete the free YouCubed online course.
- Help other staff members develop their own growth mindsets and encourage them to promote a growth mindset in their classes. It can be difficult for students to get the message if you’re the only one promoting it in your school. A few ways to do this are to try low-floor high-ceiling tasks together during staff meetings, bring in student work from their own classroom tasks, or modify your lessons using the new growth mindset cards. More on this later.
2. Capitalize on social and emotional competencies embedded in the SMPs: Often, we believe that the sole purpose of the Standards for Mathematical Practice is to develop mathematical dispositions and habits. However, Aurelia Milam demonstrated that we can use the social and emotional competencies embedded within the SMPs to help our students improve their self-awareness, social awareness, decision-making, self-management, and relationship skills (NCSM 2017, Session 1720).
In her session, we received a copy of the SMPs and highlighted language that we thought demonstrated opportunities for social and emotional learning. Later, we learned that two groups (University of Texas at Austin, Charles A Dana Center and the Collaborative for Academic, Social and Emotional Learning) had collaborated to create a document that explicitly describes how to integrate social and emotional learning into the CCSS. The full document is worth a read: check it out here.
3. Push your students to “own” the mathematics: Glenn Waddell and Megan Schmidt led a session at NCTM focused on teaching statistics through a social justice lens; however, instead of asking teachers to bend their lesson structure to fit in contrived examples, they advocated for keeping the regular lesson structure and letting students investigate their own ideas about their community or educational system. The act of questioning and changing how our educational system can best offer education to all people is called Critical Lesson Theory. Waddell and Schmidt suggested starting the school year by asking groups of students to develop questions about their community or school they want to answer. Then, as the means to answer one of those questions appear in the curricula, the individual group with that question would collect data. Next, the entire class would analyze the necessary data using the tools they had learned. Once the curricula had been finished for the year and all groups had answered their questions, students would be directed to turn their research into action. One possible timeline is below:
- September: Group A wants to know if food at a local grocery store is more expensive than food at a national chain. They write their idea as a research question.
- October: The class studies sampling techniques, and group A is asked to collect data on prices at two different grocery stores. Other groups collect their own data.
- December: The class studies boxplot design, and half of the class charts the data from group A. The other half of the class charts the data from group D because they also collected one-variable data.
- February: The class studies two sample t-tests, and the entire class analyzes the data from group A. They determine that there is no statistical difference between prices at the two stores.
- June: Group A writes a letter to the local grocery store outlining their findings and presents it to the owner of the store. Other groups complete their own projects.
- Start early and acknowledge that some conversations might be difficult.
- Get your principal or administration on board by talking to them.
- Understand that you won’t know what projects or ideas the learners will create.
- Write each group’s research question, so dependent and independent variables are explicit and discussions focus on ideas and not semantics.
- Disagreement is okay, but listening to and respecting one another is vital.
- Give students time to absorb and think.
- Be sure to listen. It’s okay if we don’t have all of the answers.
4. Follow Peg Smith’s steps for encouraging productive struggle: Although I have read and reread 5 Practices for Orchestrating Productive Mathematics Discussion by Peg Smith and Mary Kay Stein, it is always important to revisit the idea of productive struggle. In this session, Smith played two videos of student discourse and asked us to comment on the moves the teacher made to facilitate student learning (NCTM 2017, Session 574). Through this process, she developed a definition of productive struggle:
The struggle is productive if…
- The intended goals and the cognitive demand of the task are maintained
- Student’s thinking is supported by acknowledging effort and mathematical understanding
- Students are able to move forward in the task through their own actions
- Teachers ask questions that help students focus on their thinking and identify the source of their struggle, then encourage students to look at other ways to approach the problem.
- Teachers encourage students to reflect on their work and support student struggle in their effort and not just in getting the correct answers.
- Teachers give time and help students manage their struggles through adversity and failure by not stepping in too soon or helping too much and thus take the intellectual work away from the students.
- Teachers acknowledge that struggle is an important part of learning and doing mathematics.
5. Develop a flipped self-paced mastery approach that expires within two to three weeks: I like the idea of a self-paced mastery approach, but I dislike the idea of having all of my students working on completely different topics. Nor do I like the idea of putting my students on computerized software that would differentiate for me. Instead, I wish that I could have all my students focus on the same topic, but with different levels of depth, so that they could still communicate and collaborate with each other.
In their session titled Self-Paced Flipped Model: A Twist on Flipped Mastery, Kyle Wilhelm and Shelly Lindsey presented a framework for combining a flipped classroom model with mastery based learning. They suggest creating two to three week mini-units that include a summative assessment at the end. During the unit, students watch videos at home and spend half of their class time attempting formative assessments, reflecting, and completing independent practice. These assignments are presented in a playlist of increasing depth and complexity, and students are encouraged to get as far as they can within the playlist before the summative. The other half of class time is spent completing group tasks or in stations designed to target the Standards for Mathematical Practice in a way that independent work cannot. The key is to develop tasks or stations that are accessible by all students, no matter what part of the playlist they are on.
I like this method, but I have questions about the summative assessment at the end of each mini unit. Students that did not finish their playlist, or did not get to activities with sufficient depth, would probably not have all the skills to perform well on their assessment. Perhaps there is a way to use a scale or rubric to account for these students.
6. [EXTRA CREDIT] Ensure that every dose of aspirin has a headache: To be honest, it would probably be redundant and over simplistic to distill this session down into a snippet at the end of an exceptionally long blog post. So, I’ll just direct you do Dan Meyer’s post.