Common Core NUGGET

One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student's maturity, WHY a particular mathematical statement is true or where a mathematical rule comes from (Common Core State Standards for Mathematics, pg. 4).  The student who can explain a rule in mathematics may have a better chance to succeed less familiar tasks such as expanding the rule.  Mathematical understanding and procedural skills are equally important, and BOTH are assessable using mathematical tasks of sufficient richness (CCSSM, pg. 4).


There are 8 Mathematical Practices that all students should be encouraged to use in all areas of math.

1. Make sense of problems and persevere in solving them.  Students should begin each math problem before them by explaining to themselves the meaning of the problem and looking for entry points to the solution.  They analyze givens, constraints, relationships, goals, and unknowns (I added that one!) They also check their answers, and they ask questions like, "Does this make sense?"
2. Reason abstractly and quantitatively.  Students must be able to decontextualize and contextualize their problems.  They should also be able to recreate a coherent representation of the problem, consider the units involved, attend to the meaning of the quantities, compute, and know the different properties of operations and objects.  
3. Construct viable arguments and critique the reasoning of others.  Students must be able to understand and use stated assumptions, definitions, and established results in constructing arguments.  
4. Model with mathematics.  Mathematically proficient students can apply mathematics to solve problems arising in everyday life, society, and the workplace.  
5. Use appropriate tools strategically.  Students need to have access to available tools when solving a mathematical problem.  These tools include pencil and paper, concrete models, rulers, protractors, calculators, spreadsheets, computer algebra systems, statistical packages, and geometry software.  They are able to use these tools to explore and deepen their understanding of concepts.  
6. Attend to precision.  Students need to communicate precisely to others.  They state the meaning of the symbols they use; they use the equal sign consistently and appropriately, they specify units of measure; they calculate accurately; and they express numerical answers with a degree of precision appropriate for the problem context.  
7. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure.
8. Look for and express regularity in repeated reasoning.  Students will notice if calculations are repeated, and look for general methods and for shortcuts.  They continually evaluate the reasonableness of their intermediate results.  

These principles describe the ways in which students of math should engage with the mathematical subject matter as they grow in mathematical maturity and expertise throughout their K-12 experience.  As teachers of mathematics, we should attend to the need to connect the mathematical practices to mathematical content in mathematical instruction (CCSSM, pgs. 6-8)
On a personal note, I am forever grateful for Mrs. Janet Loper Dixon (my high school science teacher) for teaching me many of these mathematical practices in our physics and chemistry class in high school.  She always taught me to start with a list of what I know and what I don't know that was needed to solve the equation at hand.  Now, Mrs. Mosley (my high school math teacher) was great, but she "assumed" too much.  She assumed that we had the skills for math before she got us.  She made a very faulty assumption that I had a mathematical mind by nature.  NO... much of what I know today about math is because Janet Dixon taught me to "learn" the art of becoming a great math student.  It wasn't innate; it was learned for me.