Mathematical practices represent a whole group of standards in the Common Core State Standards for mathematics. The standards for mathematical practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010, p. 8). Each of the eight standards identified as mathematical practices focuses on different aspects of mathematics while interweaving with the other standards. These standards describe students’ behavior and are designed to develop students’ reasoning and to help them in building mathematical communication, to empower them in using mathematics Rutherford, (2015).

• Make sense of problems & persevere in solving them.

• Reason abstractly and quantitatively.

• Construct viable arguments and critique the reasoning of others.

• Model with mathematics.

• Use appropriate tools strategically.

• Attend to precision.

• Look for and make use of structure.

• Look for and express regularity in repeated reasoning.

Mathematical proficiency is the ability to understand the content and think in a mathematical way (Abdo and Elsayed, 2022; Qutaifan and Alfayez, 2022). Kilpatrick, Swafford, and Findell (2001) have found five standards that define conceptual understanding.

• Conceptual understanding. Comprehension of mathematical concepts, operations, and relations.

• Procedural fluency. Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

• Strategic competence. The ability to formulate, represent, and solve mathematical problems.

• Adaptive reasoning. The capacity for logical thought, reflection, explanation, and justification.

• Productive disposition. Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. (p. 5)