Providing a structure for math problem solving, CueThink offers a range of applications. Read on to learn four ways teachers can embed CueThink into commonly existing classroom routines and structures.
Launching a new technology in your classroom can feel daunting. Teachers have found the most success with embedding CueThink into their current classroom routines and structures. Designed around mathematician George Pólya’s 4 Phases of problem solving, here are four ways to succeed in integrating CueThink into your mathematical instruction. The goal is to make minimal changes to your routines and enhance what you already do.
1. Launch a Unit with CueThink: Pre-Assess and Preview Content
Start the unit by engaging students in upcoming concepts and collect formative data around students’ prior knowledge and current misconceptions. Emphasize to students that this activity aims to capture the variety of strategies and knowledge the class currently has and to collaboratively build upon their repertoire.
Review the unit content goals as well as your goals for developing mathematical thinkers. Mark Chubb’s blog post on “What Does Day 1 Look Like?” explains how the roles you and your students take (teacher-directed, teacher-guided or teacher-facilitated; student active or student passive) can support your goals.
Select a rigorous problem either from the CueThink Bank or your own collection that addresses the unit's most important standards and interests students. Consider alternative resources such as the Mathematics Assessment Project for Middle School and High School students that specialize in formative assessments relating to the Common Core Standards. Assign this problem to your CueThink class and pose it to students to introduce the unit. Once students have completed their thinklets, focus peer annotations on unit exploration and making connections to prior concepts using sentence stems such as “Something I’m looking forward to learning more about is…” or “A connection I see to a prior unit is…”
🕒 Working on a launch problem within CueThink will take about 30-40 minutes.
View thinklets and keep notes on students’ prior knowledge and strategies to share during the course of the unit, and misconceptions to be addressed at the start of the unit.
Return to this problem at the end of the unit. Matt Coaty notes in his blogpost, “4 Ways to Encourage Student Self-Reflection in Math Class” that student-led conferences based on formative assessment is a way for them to reflect on their own growth.
2. Problem Solve with CueThink: Provide a Structured Framework To Facilitate Deeper Learning
In a brief on “Why Is Teaching With Problem Solving Important To Student Learning?” NCTM (2016) cites research that teaching problem solving stimulates engagement as students learn concepts, reasoning and communication skills. The structure of Polya’s 4 phases guides students as they solve multi-step problems which enables the teacher to take on a facilitator role to lead discussions that foster deeper conceptual understanding.
Select a complex and engaging problem from the CueThink Problem Bank or your curriculum. The first problem posed should address concepts that at least 80% of students understand but has multiple solution paths or possible answers. This will reduce students’ cognitive overload while learning a new technology tool. Also keep in mind Mark Chubb’s blog post on “Is That Even A Problem?” where he references Polyá’s idea that problems should require some degree of difficulty where reasoning skills are needed to consciously search for an appropriate course of action.
Use the four phases within CueThink to structure short discussions throughout the process. Use the Think-Pair-Share model where students work alone for 5-10 minutes, then explain their work to a peer, followed by sharing their partner’s work with the whole class. Lance Bledsoe’s blog on “I, We, You vs. You, Y’all, We” references Magdalene Lampert’s twist on the Think-Pair-Share model.
🕒 Working within CueThink and debriefing each phase will last about 40-50 minutes.
Conclude by having students spend 5-10 minutes viewing and annotating two peers’ thinklets, encouraging them to give one compliment and one improvement that is kind, specific and helpful.
3. Target Instruction with CueThink: Address Misconceptions Through Student Error Analysis
Targeted small group instruction has been proven to positively impact student learning, particularly with respect to problem solving (Jitendra, Dupuis, Rodriguez, 2012). Using an error-task analysis allows students to demonstrate their conceptual understanding of mathematical concepts involved.
🕒 Each guided math group lasts 10-15 minutes; hold 2-3 groups in one class period.
Arrange students into small groups targeting specific skills based on the assessment data at hand. Assign students to watch and discuss a thinklet demonstrating a misconception as well as an exemplar thinklet about the intended skill. The discussion can start with students’ noticings and wonderings about each thinklet and then progress to comparing the similarities and differences of the two solutions. The goal is for students to notice where in the problem solving process mistakes were made.
Check in on the rest of the students on their assignment(s), while the guided math group is evaluating the assigned thinklets.
Return to the guided math group to discuss observations. Focus the discussion around the similarities and differences between the two thinklets. If students are able to explain which thinklet contained an error and what the error was, conclude the session with a short exit ticket of a similar problem to assess students’ understanding. If students remain confused focus them on the error and explain the misconception. Then work through a similar problem together and highlight the correct steps to solve the problem. Note students’ level of understanding at the conclusion of the session to plan future guided math groups.
4. Diversify Homework with CueThink: Digitally Extend Your Classroom
Vary and enhance homework to create a digital extension of learning. Youki Terada (2015) asks, “How can we transform homework so that it’s engaging, relevant and supports learning?” Here are some strategies that our teachers use to answer that question. At home, students can:
Preview a problem that will be worked on the following day in class. Students can begin to create their thinklets and choose not to submit their thinklet to the class gallery. Focus class time on completing and revising thinklets to submit to the class gallery.
Annotate peers’ thinklets with kind, specific and helpful feedback. This helps students to independently practice giving effective feedback centered around your classroom discussions on what is kind, specific and helpful feedback and the importance of digital citizenry.
Find two thinklets that model different strategies. Dr. Matthew Beyranevand wrote “the more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes.” Comparing multiple strategies support students in learning how to plan their solution as well as evaluating the effectiveness of a strategy in relationship to a specific skill. Assign a problem for students to review or let students choose from the Gallery. After watching both thinklets, students compare and explain which strategy is most effective and why. Comparisons can be written using the annotations feature or on paper.
Revise a thinklet based on peers’ feedback to promote a growth mindset. In an article, Educating the World said, “Good formative assessment celebrates the student’s successes but also offers strategies for improvement and advice on how to develop a greater depth of knowledge and understanding.” The annotations process provides peer-based formative assessment that students should use to improve their work. After students receive peer feedback, give students time at the end of class to review annotations and ask clarifying questions. Then for homework, students iterate on their work to address peers’ feedback.
Conclusion… Your Next Steps
Providing a structure for problem solving, CueThink offers a limitless range of applications. In this article, CueThink enhanced a range of commonly used classroom routines. Select a starting point, evaluate the current strengths and weaknesses of the routine, and select a CueThink plan to improve the practice.
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Jitendra, A. K., Dupuis, D. N., Rodriguez, M. C., & Society for Research on Educational Effectiveness. (2012). Effectiveness of Small-Group Tutoring Interventions for Improving the Mathematical Problem-Solving Performance of Third-Grade Students with Mathematics Difficulties: A Randomized Experiment. Society For Research On Educational Effectiveness.
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