Common Core Math (CCM) Practice Standard 6

Opinion – CCM  may be Unproven

One argument I’ve seen against CCM is that the standards are unproven. Since they were made up by math teachers, I believe that they are (1) correct and (2) well structured. Therefore, it is hard for me to see how learning them would do any damage. Moreover, to allow the sharing of teaching materials and to level expectations across state lines, they are being widely adopted and implemented in the USA. Therefore, not learning them could put your children at a disadvantage to their peers. Why would you choose to risk their futures rather than help them master the standards?

My children graduated high school before CC Math was introduced. However, if they were still in school, here is how I would approach the above question. I would hedge my bets – on the off chance that the standards would cause them problems, I would show my children the old-fashioned “we’ve-always-done-it-this-way-and-it-was-good-enough-for-me” way – and help them learn both. While comparing old and new, if I or one of my children did discover a flaw in the CCM standards, we would be richer for the experience. Alongside the standards, I would share with my children lessons learned regarding how to “befriend” computers and programming languages. For example, the object paradigm, fundamental to many modern programming languages, can help us formulate problems such that computers can solve them effectively.

Anecdotal reports (available on-line) say that, taken step-by-step, CCM standards are working well for many motivated teachers and students.  Other anecdotal reports say that students are reduced to tears by new problems and unfamiliar approaches (unfamiliar to their parents) inherent in both the CCM standards and the way some teachers are using them.  I will not debate either set of reports, but it is reasonable to observe that any academic discipline requires competent teachers and helpful teaching materials, and that CCM is still relatively new. 

While the standards may have been “vetted” by mathematicians and math teachers, it is not intuitively obvious that all standards are “age-appropriate.” The standards creators do write that, “the development of the standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.” This shows an awareness of the importance of this matter; however, there is not yet enough evidence to demonstrate that the current standards are, in fact, age appropriate. That children mature intellectually at different rates leaves open the question of whether the new standards are right for all students at all times.

This is not a trivial matter, but if your child is one of those for whom certain concepts are out of reach, I suggest patience. It is unlikely that she is “stupid;” it is more likely that she is not quite ready for the particular standard that is part of her homework that day. One issue that is sometimes overlooked during the early primary grades is that students in one class may differ in age by almost a year. Younger students may appear to be slower learners when in fact they are simply younger and less mature than their classmates. By the same token, if your child is older, be thankful but remember, his age advantage will diminish over time.

Teachers’ skills matter, but as I said earlier, children in public schools, private schools, and even home schools will be faced with teachers of varying skill and motivation levels. As a parent, you want the best possible learning environment for your children. However, I believe that you will agree that it is not useful to assess the value of CCM based on the competence of available teachers. Granted, an incompetent teacher increases the challenge to student and parent alike to learn the material. However, overcoming this impediment can be seen as a positive experience.  In other words, while teachers’ skills matter, student and parent attitudes matter more.

The claim of the education community is that, a comprehensive understanding of CCM will be an advantage in college and in the world of business.  It is your right to be skeptical, but if that claim turns out to be true, would you prefer that your children have that advantage or that they compete with other (parents’) children at a disadvantage? Over time, colleges, and universities as well as many businesses are likely to expect that earning a high-school diploma will imply mastery of CC Math standards. However, given the pace of technology change, CCM may be necessary but not sufficient.

CCM Lesson of the day: CCM Practice Standard 6

Attend to precision

“Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other.  By the time they reach high school they have learned to examine claims and make explicit use of definitions.”

My Comment

This step conflates accuracy and precision, terms which do not mean the same thing. It also uses the word precision (underlined in the paragraph above) to explain what precision means. The modal “attend to” is vague enough that we can take this to mean ‘use lots of precision’ or ‘be consistent in your use of precision.’

Process implications:

·         When solving a problem, estimate the solution and compare your result for accuracy

·         When solving a problem, consider the precision you will require.

Definitions

Accuracy and precision are not the same thing. For example, in measuring the distance from your house to the nearest post office, an accurate estimate (to the nearest mile) might indicate how long it will take you to make the trip by car.

However, if you need to lay out cones on a soccer field, you might need a more precise measurement, in feet say, to know how many cones or how much gypsum you will need.

Accuracy: The closeness of a result to the “true” value.

Precision: The degree to which your result must be refined.

Applications and Examples

Accurate: If our gas gauge indicates half a tank, accuracy could be critical so that we realize how far we can go, but it’s unlikely that we can justify being much more precise than to estimate our remaining mileage to within ten miles, as in “we should be able to travel another 160 miles.”

Precise: By contrast, when using a laser to perform a medical procedure, precision in fractions of millimeters may be required to perform effectively and safely.

Accurate and Precise: When preparing to install new flooring material in a room in your house, your measurements must be accurate and precise. You will want to measure accurately (the correct distances, in feet and inches) so that you know how much material to buy. You will want to refine your measurements precisely to 1/8 inch or less (differences between the measurements of floor and flooring material) prior to cutting the material in order to avoid unsightly gaps or bulges.