It is the stated goal of every teacher across the country to support all students in achieving mathematical proficiency. This is key, in helping to develop students who feel confident and proficient in using their math skills to solve real-life challenges once they move past their classroom and school years.

When thinking about what makes for a mathematically proficient student what comes to mind?

A student’s ability to…

• – explain to themselves the meaning of a problem and look for entry points to its solution.
• – make sense of quantities and their relationships in problem situations.
• – use assumptions, definitions, and previously established results in constructing arguments.
• – apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
• – consider all available tools when solving a mathematical problem.
• – communicate precisely to others.
• – look closely to discern a pattern or structure.
• – notice if calculations are repeated and look for general methods and shortcuts.

To achieve this level of math proficiency and confidence students need to be supported in…

(a) strengthening their dispositions and perseverance in how they work through provided mathematical tasks

(b) developing a conceptual understanding of math skills and how to apply them

(c) increasing students’ abilities to be strategic thinkers when problem-solving

(d) improving their adaptive reasoning skills.

Teachers need to understand that there are many benefits to instruction that embraces the Five Strands of Proficiency as well.

The Five Math Proficiency Strands

Kilpatrick, Swafford, and Findell (2001) define the five intertwining strands that teachers need to understand and be able to apply with their students.

Conceptual understanding is knowledge about the relationships or foundational ideas of a topic. For example, comprehension of mathematical concepts, operations, and relations.

Procedural fluency is the knowledge and use of rules and procedures used in carrying out mathematical processes and also the symbolism used to represent mathematics.  For example, skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Strategic Competence is the ability of a student to formulate, represent, and solve mathematical problems. For example, in solving problems, do students design a strategy? If it doesn’t work, do they try something else or do they get stuck knowing only a limited set of approaches that might be used?

Adaptive Reasoning is the capacity of a student to demonstrate logical thought, reflection, explanation, and justification when it comes to problem-solving. This capacity to reflect on their work, evaluate it, and then adapt, as needed, is the adaptive reasoning.

Productive Disposition is the habitual inclination of your students to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. For example, do your students have a “can do” attitude? Are your students committed to making sense of and solving challenging performance tasks, knowing that if they keep at it, they will get to a solution? If so, then your students have a productive disposition. This relates to perseverance.

The development of student mathematical proficiency takes time. In each grade, students need to make progress along every strand mentioned above. Each strand is important and interwoven with the others. Additionally, the last three of the five strands develop only when students have experiences with solving problems as part of their daily learning in mathematics.

Because the issue of student proficiency and confidence in math is such a central factor in providing a successful math instructional program, TKL has put together many resources for teachers and schools to leverage.

Here are a few which you may want to consider:

1. Creating Learning Classrooms for Today’s Students
2. Creating Meaningful Math Engagement
3. Creating Student Innovators
4. Developing Mathematical Expertise in a Problem-Centered Classroom
5. Developing Students’ Mathematical Habits of Mind
6. Equalizing Mathematics through Differentiated Instruction
7. Increasing Student Engagement and Motivation
8. Increasing Student Engagement: Planning Outside the Box
9. Supporting Mathematical Proficiency in Struggling Learners