Common Core Math (CCM) Practice Standard 1

Opinion – Don’t Get Stuck

In the lesson of the day (below), you will read the actual CCM Standard 1. Before you read that, here is a rule from my experience that you might want to let your children in on: “don’t get stuck.” Meaning, don’t allow yourself to be brought to a halt when working on a math problem.

Why? Isn’t perseverance an admirable quality, a character trait necessary to success? Not getting stuck is not the same thing as giving up; it simply means that after investing a “reasonable” amount of time to solve a problem and getting nowhere, I may be missing something critical. Ordinarily, if I cannot find my car keys, I have misplaced them. However, on occasion, if I cannot find my car keys, it’s because someone borrowed them and failed to return them. This is something I can only find out by asking. If that is the case, continuing to look in more and more unlikely places will only waste my time.

While perseverance is part of being an effective learner, effective use of time is just as important. For example, homework not only offers an opportunity to practice solving problems, it can reveal what we do not understand. This is valuable information, because it shows where we need to strengthen our knowledge and problem-solving skills. Exams let students show what they know while at the same time (like homework) revealing what they may not have understood. Learning from homework and exam results is an important element of learning to learn.

Here are three things your son can do when he cannot solve a homework problem: First, ask someone else, a fellow student, a sibling, or you. Even if you are not the one he asks, you can help him learn to ask for help. That means explaining to his brother, for example, where he is stuck and what he does not understand. This should not be the same thing as asking his brother to solve the problem for him. One caveat: some parental oversight may be necessary, at least at first, to assure that help is requested and given in a climate of mutual respect.

Second, some texts offer the possibility of looking up the answer in the back of the book. It takes some ingenuity to use such an answer and then to work backwards. This should not be the usual procedure, because it reduces the value of that answer as a check on the original work; nevertheless, it is a better option than getting stuck.

Third, formulating a question for the teacher can be helpful since it requires an awareness of where misunderstanding has occurred. At times, composing the question will lead a student to redefine the problem, get “un-stuck,” and solve the problem.

CCM Lesson of the day: CCM Practice Standard 1

Mathematical Practice from the CCSSI Math Standards Website

The following is the first in a series of 8 standards which comprise an outline of the objectives of learning the CCM Standards.

Make sense of problems and persevere in solving them.

“Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.”

My Comment

In principle, I see nothing wrong with perseverance since hard problems require time to solve. In practice, I believe that it is important for a student to recognize when he is missing a concept, definition, or value necessary to the solution; this can save valuable time on homework or tests.

Process implications:

• draw pictures

• don’t get stuck and do ask questions

Definitions

Mathematically Proficient Student: Strictly speaking, this is a student who thinks like a mathematician.

Permit me to offer an anecdote which might prove both amusing and helpful. I was lucky enough to be a student in the Advanced Calculus class of Professor Robert Sorgenfrey, a Distinguished Teaching award winner at UCLA. Professor Sorgenfrey often introduced new topics with the words, “now, every cultured person knows …” Why is this introduction so cool? Three reasons: 1) humor is very relaxing; 2) while I may not yet have actually been a “cultured person,” I was about to take an important step in that direction; and, 3) the possibility obviously occurred to many of us that some people who thought themselves “cultured,” might not have ever taken advanced calculus. Are “mathematically proficient students” cultured people; Professor Sorgenfrey (RIP) would undoubtedly answer that with a mischievous smile.

Applications and Examples

You and I live on the same street, one mile apart. You have something I need, so we decide to walk toward each other on that street. We decide to leave at the same time. You walk twice as fast as I do. How far will we be from you house when we meet? Draw a picture for a quick solution.