Mathematics Updates

The autumnal equinox officially ushered in the fall season on Friday, September 22. Soon we will feel a nip in the air and enjoy that certain crispness fall is famous for. Albert Camus expressed it well: "Autumn is a second spring when every leaf is a flower."

Fall signals change in the seasons. It conjures up thoughts of "back to school" (even though school now starts mid-summer). It is harvest time, when the growing cycle of many cultivated crops begins to cease. Even as those rhythms slow, however, the growing cycle for our students is gathering momentum and student learning is on the rise.

This issue of Mathematics Updates contains articles, research, resources, and information about professional learning opportunities that are intended to provide nutrients for professional growth that will lead to strengthening student understanding, academic growth, and higher performance levels.

By Youki Terada

in Edutopia

Our brains are wired to forget, but there are research-backed strategies you can use to make your teaching stick. When students learn a new piece of information, they make new synaptic connections. Two scientifically based ways to help them retain learning is by making as many connections as possible—typically to other concepts, thus widening the “spiderweb” of neural connections—but also by accessing the memory repeatedly over time.

Which explains why the following learning strategies, all tied to research conducted within the past five years, are so effective:

1. Peer-to-peer explanations: When students explain what they’ve learned to peers, fading memories are reactivated, strengthened, and consolidated. This strategy not only increases retention but also encourages active learning (Sekeres et al., 2016).

2. The spacing effect: Instead of covering a topic and then moving on, revisit key ideas throughout the school year. Research shows that students perform better academically when given multiple opportunities to review learned material. For example, teachers can quickly incorporate a brief review of what was covered several weeks earlier into ongoing lessons, or use homework to re-expose students to previous concepts (Carpenter et al., 2012; Kang, 2016).

3. Frequent practice tests: Akin to regularly reviewing material, giving frequent practice tests can boost long-term retention and, as a bonus, help protect against stress, which often impairs memory performance. Practice tests can be low stakes and ungraded, such as a quick pop quiz at the start of a lesson or a trivia quiz on Kahoot, a popular online game-based learning platform. Breaking down one large high-stakes test into smaller tests over several months is an effective approach (Butler, 2010; Karpicke, 2016).

4. Interleave concepts: Instead of grouping similar problems together, mix them up. Solving problems involves identifying the correct strategy to use and then executing the strategy. When similar problems are grouped together, students don’t have to think about what strategies to use—they automatically apply the same solution over and over. Interleaving forces students to think on their feet, and encodes learning more deeply (Rohrer, 2012).

5. Combine text with images: It’s often easier to remember information that’s been presented in different ways, especially if visual aids can help organize information. For example, pairing a list of countries occupied by German forces during World War II with a map of German military expansion can reinforce that lesson. It’s easier to remember what’s been read and seen, instead of either one alone (Carney & Levin, 2002; Bui & McDaniel, 2015).

By Matt Larson

Reprinted from NCTM President's Messages

Recent events in our country have presented educators with challenges that are new to many of us. As mathematics educators we are not immune to the current political climate and emotionally charged environments. In recent weeks I have had some mathematics educators tell me that the political events in our country have no impact on their work as mathematics teachers because “they teach mathematics.”

While the subject we teach is mathematics, we need to always remember that we teach mathematics to students. And our students’ success in the classroom is dependent on our ability as teachers to create an emotionally safe and welcoming classroom environment for each and every one of our students, regardless of their background.

Several organizations have recently called for a reaffirming of the “inclusive values that are the foundation of healthy learning cultures.” Some organizations, including TODOS: Mathematics for All and the American Educational Research Association (AERA) have released specific statements in support of each and every student and against acts that intimidate, harass, or restrict student opportunity. NCTM joins TODOS and AERA in these reaffirmations and calls to action.

As educators we need to simultaneously maintain our commitment to democratic principles and our role in the democratic process, including the constructive and inclusive exchange of differing points of view, while simultaneously always standing against any act by anyone that threatens the well being of students. I encourage you to refer, reflect, and discuss with one another the statements of professional organizations referenced in this post. As Diane Kinch, the president of TODOS recently wrote, as mathematics educators we must “continue to stand by our students and their families, advocate for them, and work in any way possible to ensure and affirm their futures.”

We owe this not only to our students, but also to the society we wish to inhabit in the future.

Thursday, October 12 - Newnan High, 4 - 5 p.m.

9-12: Promoting Mathematical Discourse in the Classroom

Student mathematical discourse reveals how students represent, think, talk, question, agree, and disagree in the classroom. Strategies for increasing student discourse will be explored.

Tuesday, October 24, 2:50 - 3:30 p.m.

K-2: Reading and Writing in Mathematics

This session, for K-2 teachers and administrators, will focus on applying reading strategies to help students decode and comprehend math contextual situations. Suggestions for ways to incorporate writing in mathematics instruction will also be discussed. Register by 4 p.m. on Oct. 23, 2017, at https://goo.gl/forms/AcCcryDzdaMjKn0o1 to receive a link to join session.

Wednesday, October 25 - Evans Middle, 4 - 5 p.m.

6-8: Spotlight on Equity

Using cases presented in an article from Mathematics Teaching in the Middle School, participants will start a conversation about equity and begin to examine practices teachers can change that impact students. Strategies for creating equitable classroom environments will be explored.

Thursday, October 26, 2:50 - 3:30 p.m.

3-5: Reading and Writing in Mathematics

This session, for teachers in grades 3-5 and administrators, will focus on applying reading strategies to help students decode and comprehend math contextual situations. Suggestions for ways to incorporate writing in mathematics instruction will also be discussed. Register by 4 p.m. on Oct. 25, 2017, at https://goo.gl/forms/g8wdx3JydKEgE8032 to receive a link to join session.

Larson, M. (2016). We teach more than mathematics. [Website]. NCTM President’s Messages. Retrieved from http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Matt-Larson/We-Teach-More-Than-Mathematics/

Moore, S. (2013, October 21). A math major talks about fear. [Video File]. Retrieved from https://www.youtube.com/watch/?v=Xs9aGVUZ3YA

National Council of Teachers of Mathematics [NCTM]. (n.d.) NCTM Illuminations. Reston, VA: Author.

Terada, Y. (2017). Why students forget – and what you can do about it. [Website]. Edutopia. Retrieved from https://www.edutopia.org/article/why-students-forget-and-what-you-can-do-about-it

Yenca, C. (2017, April 6). Seeking students who hide. [Video File]. Presentation at NCTM Shadow Con at the 2017 Annual Meeting, San Antonio, TX. Retrieved from https://www.youtube.com/watch?v=yXVYEI7_GGs