Check out the NCTM Principles to Action.  Facilitate more “teach” less.

In the first OPA Mathematics Newsletter, we introduced the type of task that can be engaging for students at many different skill levels.  It is called the Border Problem.  It is from a website called youcubed (link included below) in conjunction with Jo Boaler and the Mathematical Mindsets course.  This site is full of mathematical growth mindset tasks for all different grade/skill levels.  These tasks are meant to be done over time.  They may even take more than a week.  The students can work on it during free moments during math class – rather than having the students read during math class when they are finished with their math, they should be working on a math task that creates deeper understanding of core mathematics standards.  If a student is finishing their math quickly, then it often indicates they are ready for a more challenging question – something that will make them think.

One of the biggest math challenges in school is engaging the student, it is important to create a task that students at any level can enter and be successful.  Many of our students are only experiencing math learning from a teacher or aide who teaches them how to do math processes in front of the class.   They wait for the teacher who holds all the keys of knowledge to give that knowledge to them.  This type of teaching is needed at times, but it is better when students themselves can discover concepts or ideas.  The teacher acts more as a facilitator or guide in the discovery process.  The teacher then picks from the various discoveries of learners in the class to lead the class instruction in a core standard the teacher would like to teach.  In 2014, the NCTM (National Council for Teaching Mathematics) came up with 8 principles to action to be incorporated into mathematics instruction to help achieve student success.  These practices were outlined after the Common Core came out, and as schools tested students some very distressing data about math started to roll out.  These principles aren’t new teaching practices.  They are best practices which have been used in successful mathematics classrooms for many years. They make sense, and have been used in successful mathematics classes for many decades.

NCTM Principles to Action for Mathematics Instruction

Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

youcubed link:



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