Common Core Math (CCM) Practice Standard 3

Opinion – Parents as Coaches

As the parent of one or more students in grade K – 12 (Kindergarten through the senior year of high school), you may feel that you have recently been thrust into the role of home-school teacher. I say “may feel” because you may have actually been home-schooling your children all along. For many parents, this a new situation. Newspapers and websites are filled with advice from “experts” regarding how to cope with unexpected family confinement and to continue to do our own jobs while making sure that our children are able to do theirs.

Most of us have seen young people on sports teams whose skills were well beyond those of their teammates. And then someone would say, “his father is a high school coach.” That father (or mother) is likely to be the most influential coach in their child’s sports career.

The focus of this blog is mathematics because, I claim, it offers a way of thinking that extends beyond any virus. It is fundamental to numerous activities and careers. Activities: tracking sports; buying and selling; investing; computing times, distances, weights; counting calories; cooking; etc. Careers: biology; chemistry; engineering; medicine; sociology; astronomy; meteorology; fashion design; etc. That is why, throughout their school years, most children study math.

Wouldn’t it be sweet if you were the best math coach in your child’s school career? Even though you may now be a parent, you may at one time have been a grade-school student. During that time, you may have decided either that you liked math or that you were not good at math. If the former, try to remember what brought you to that point. Was it a helpful teacher, parent, or older brother or sister? Was it that you found it useful for computing batting averages, measuring out recipes, or keeping track of savings? Did you like the satisfaction of solving problems? Or was it a combination of those things? If they do not already know about it, your children might find your experience interesting.

On the other hand, did you decide at some point that you were not good at math? Many people love dogs, but my wife has a cousin who, when she was a little girl, was attacked and severely injured by a dog. The experience changed her life and she does not much like dogs now. The reasons in the previous paragraph that might explain why some people like math, while the absence of such experiences in your life might explain why you decided that you were not good at math.

Whatever your story, I have some incredible news. Common Core Mathematics (CCM) is constructed such, if you are willing to invest the time and thought, you can become 1) a “math whiz” and 2) the best math coach your child will ever have. How is this possible if your school days are now a speck in the rear-view mirror? It is because the creators of CCM 1) wrote standards for one grade level to provide the basis for standards at the next level, 2) organized the standards according to such disciplines as algebra, geometry, and calculus, 3) used the “object paradigm” in many definitions and explanations, the same paradigm that enables a structured understanding of modern computer programming, and 4) you and I will walk this road together.

We have already embarked on your path to math stardom. As you continue to learn the standard practices and the K-12 standards, you will be building a firm foundation for you and for your children. Stay with it and numeracy will be your reward. Do that with your school-age child and I will call you “coach.” By the way, starting at level K does not imply that your math competency is at Kindergarten level. Look at it rather as the trailhead to a significant hike. When you start a hike in the mountains, I doubt that you feel self-conscious about being at the beginning, even though you must be aware that others got onto the trail ahead of you, either that day or the day before or … And even though you might use math daily, CCM takes a somewhat different trail.

For most elementary and secondary-school students, a key discriminator for success is parental commitment. When students believe that their parents care and when parents show that they care by investing time and offering encouragement, students perform better.  Good teaching matters and I applaud the dedication and sacrifices of teachers, but just as was true for you and me, your child will be taught by a wide range of teachers with various levels of motivation, experience, and independence. Add to that variability the new classroom and distance-learning unpredictability. You can be the constant coach who offers the continuity your children need to excel at math and to learn to learn.

A wonderful characteristic of math is that it is objective. Your child can excel at math regardless of gender, race, religion, country of origin, or class. And, he or she can literally prove (pun intended) their skill. All they really need is a dedicated coach.

CCM Lesson of the day: CCM Practice Standard 3

Construct viable arguments and critique the reasoning of others.

“Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Students build proofs by induction and proofs by contradiction.  CA 3.1 (for higher mathematics only).”

Comment:

I beg your pardon for my reaction to this step. Years ago, when my son was a middle-school student, the “new math” was introduced along with its little brother, “group math.” His interpretation of the whole endeavor was quite telling. First, he explained that “it isn’t solving for X that’s important, it’s how you feel about solving for X.” And then, after observing the process at work in his algebra class, he noticed that in each group, the best student solved the problem and the others copied her answer. In other words, there was only one learner per group. The point: implementation matters.

Process implications:

make sure that you can define each word in any problem statement

teach others a concept to verify that you have mastered it

Definitions

Notice the use of the word “definitions” within this practice standard, reinforcing our emphasis on definitions in this blog.

Applications and Examples

Let’s offer a children’s riddle about baseball (yes, I was a devoted little leaguer). Before we start, remember that the bases – first base, second base, third base, and home plate – are organized in a square (called a “diamond” in baseball), 90 feet apart. Added information is that the team on defense (“in the field”) traditionally positions their infielders as follows: a first baseman near first, a second baseman near second on the first base side, a shortstop near second on the third base side, and a third baseman near third base.

The riddle is this: Imagine that I am standing at home plate and you are standing on second base. We each beginning running at the same time at the same speed, I from home to first and then to second, and you from second to third and then home. Who will arrive at their destination first?

The answer to the riddle is that I will arrive first. “No,” you say, “how can this be since we will be running the same distance at the same speed?” Remember that we were children when we invented this – children love riddles – but also consider the definitions.

Hint: the clue lies among the infielders. 😊