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Introduce problems that can be solved in more than one way

Use think-aloud to solve a problem with different strategies

Encourage and help to facilitate discussion around the different strategies (efficiency, clarity, similarities, differences)

Provide worked examples in addition to practice problems

More information here (pg 32)

Example:

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A framework for helping students solve word problems using strategies and techniques to help students remember steps or a sequence

Mnemonic should be taught explicitly and teacher should model problem-solving with each step or sequence following by opportunities to practice

Should be a framework that can be generalized and used on a variety of word problems

Typically accompanied by a visual (see below)

More information here

Example:

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Math Peer-Assisted Learning Strategies (PALS)

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Math Peer-Assisted Learning Strategies (PALS)

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Whole-class peer tutoring program in which mixed-ability pairs are formed to practice mathematics skills

Pair consists of a Coach and Player

First 15-20 mins of class

Coach reads a prompt

Player begins working through problems

Coach provides feedback when needed

Players take turns as Coach and Player

Remaining time

Students work independently then work together to check practice work

More information here

Example:

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Used to help facilitate understanding of new concepts

Helps students visually organize their thinking

Can be used for a variety of math topics and modified to meet the needs of the lesson

Some use cases include vocabulary, processes, classification, Frayer Model,

More information here

Example:

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Used to enrich math discussions or exploration of a math topic by holding students accountable for keeping the conversation on topic and promoting deep thinking

The teacher should consistently (on a daily basis) be modeling what accountable talk looks like

Some moves for accountable talk:

Building on prior knowledge

Marking the conversation

Challenging students

Keeping the channels open

More information here

Example:

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Allows students to learn by actively engaging in real-word projects or scenarios for an extended period of time

Includes answering or exploring a complex question, problem or challenge

Helps to promote critical thinking, communication, problem solving, collaboration, and higher-order thinking skills

More information here

Example:

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Setting: Small group or individual

Scripted curriculum that helps to facilitate good problem-solving skills

Students participate in a series of steps that allow them to show their thinking and higher-order problems solving skills

After 3 days of learning the procedures, students engage with Solve It! strategy 30 minutes a week

More information here

Example (scripted curriculum):

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Whole group 15-20min activity in which students are presented a problem, find the answer in their heads, then justify their answer / explain their reasoning

Teacher's role is facilitator, recorder and encourager while students own the thinking aloud and reasoning

Example of a middle school prompt: Have students mentally find 35% of 160

More information here

Example:

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Number Talk: 5th & 6th Grade Part 1 | Inside Mathematics

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Fran Dickinson and his students had done two previous number talks involving "guess my rule?" The difference in this day's number talk was the graphing of the coordinate values. In his planning, Dickinson and his colleagues decided to set parameters for the learner guesses to keep all of the points in the first quadrant.

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The act of incorporating games or gaming elements into a learning activity

Benefits to students are increased engagement in learning and productivity as they making learning feel fun and voluntary

Incentivizes students and increases information retention

Some examples include Quizizz or Gimkit

More information here

Example:

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An approach that teaches that a growth mindset leads to better performance in Mathematics

Key concepts:

Praise the process - not the final product

Mistakes are valuable and grow your brain

Value diligence over speed

More information here

Example:

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Encouraging Students to Persist Through Challenges

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Multiple Problem-Solving Strategies
Improving Mathematical Problem Solving in Grades 4 Through 8 NCEE 2012-4055 U.S. DEPARTMENT OF EDUCATION. (n.d.). https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/MPS_PG_043012.pdf

Word Problem Mnemonics
Word Problem Mnemonics - Evidence Based Intervention Network. (2014, February 18). Evidence Based Intervention Network. https://education.missouri.edu/ebi/2014/02/18/word-problem-mnemonics/

Math Peer-Assisted Learning Strategies (PALS)
Math Peer-Assisted Learning Strategies (PALS) - Evidence Based Intervention Network. (2014, January 30). Evidence Based Intervention Network. https://education.missouri.edu/ebi/2014/01/30/math-peer-assisted-learning-strategies-pals-2/

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‌Graphic Organizers
Graphic Organizers - Evidence Based Intervention Network. (2014, January 30). Evidence Based Intervention Network. https://education.missouri.edu/ebi/2014/01/30/graphic-organizers/

Accountable Talk
Perusall. (2021). Perusall.com. https://app.perusall.com/courses/summer-2021-rem-and-sup-for-st-w-dis-math-sped-6332-01f-02f/visible-learning-for-mathematics-grades-k-12-what-works-best-to-optimize-student-learning?chapter=s9781506362984.i1084&anchor=s9781506362984.i1138

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‌Project-Based Learning
What is PBL? (2021). PBLWorks. https://www.pblworks.org/what-is-pbl#:~:text=Project%20Based%20Learning%20is%20a,question%2C%20problem%2C%20or%20challenge

Solve It!
Math – Acquisition - Evidence Based Intervention Network. (2013). Evidence Based Intervention Network. https://education.missouri.edu/ebi/math-acquisition/

Number Talks
Georgia Standards. (2019). Georgiastandards.org. https://www.georgiastandards.org/Georgia-Standards/Pages/Math-6-8.aspx

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Gamification
Natural HR. (2016, November 22). Brilliant gamification ideas to put the fun back into learning. Natural HR. https://www.naturalhr.com/2016/11/22/brilliant-gamification-ideas-put-fun-back-learning/

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‌Positive MathematicalMindsets and ProductiveStruggle

‌Growth Mindset: How to Normalize Mistake Making and Struggle in Class | KQED. (2015, August 24). KQED. https://www.kqed.org/mindshift/41700/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class