Common Core Math Not Properly Implemented with Parents
Parent: Johnny really seems to be struggling with math this year.
Teacher: Yes, but he will get it. Just give him some time. He will have a much better understanding of math in the long run.
Parent: But I’ve been trying to help him at home and he keeps saying that’s not the way they do it at school. I can’t even begin to help him form a response when the question asks him to explain why the math works. Math just works. An answer is either right or wrong.
Teacher: You need to stop teaching him the old fashioned way. That is just going to confuse him. If he can explain how he got his answer we will know if he really understands the math. It just takes some kids longer to catch on to the new Common Core math.
This little conversation is being repeated over and over again in classrooms across the country. Formerly highly rated students are suddenly having a hard time with math and teachers are asking parents to just take a seat in the back and trust the teacher to perform her magic with the new math. In fact, one teacher in New York gave this comment to Lyndsey Layton of the Washington Post.
“The kids who come to us are a clean slate,” states Jennifer Patanella, an instructional coach with the Rochester, New York public schools who teaches parents in the strange ways of Common Core math. “It’s the adults who have to be retrained.”
The teacher in my sample conversation isn’t even going to try to retrain the parent. She, like so many, is simply telling them that their participation in the education of their child is no longer wanted. Their jobs as their child’s teacher have been permanently outsourced.
So let’s take a look at the kind of math parents are seeing and complaining about that is being taught under common core. I’ll use an example given by illustrativemath.org of a 1st grade math problem that falls in line with the newest new math.
1. On Saturday, there were 5 girls and 5 boys in the pool. How many children were in the pool?
2. On Sunday, there were 5 girls and 6 boys in the pool. Can you use the answer from the other story to help you figure out how many children were in the pool on Sunday?
What the students are supposed to do, according to this lesson plan, is be able to tell you that since five plus five equals ten and six is one more than five, then five plus six equals one more than ten, or eleven. All mathematically true, but does it develop a deeper understanding of the math?
The best that can be claimed about a problem like this is that it is trying to establish ‘number sense.’ This refers to some foundational mathematical concepts that children need to learn in order to achieve long term success in math. They include:
- estimating with large numbers to provide reasonable approximations; There is no estimating in this problem
- judging the degree of precision appropriate to a situation; There is only one appropriate degree of precision for this answer.
- rounding (understanding reasons for rounding large numbers and limitations in comparisons); There is no rounding in this problem
- choosing measurement units to make sense for a given situation; There is no measurement in this problem
- solving real-life problems involving percentages and decimal portions; There are no decimals or percentages in this problem
- comparing physical measurements within and between the U.S. and metric systems; and There is no unit conversion in this problem
- comparing degrees Fahrenheit and Celsius in real-life situations. There is no unit conversion in this problem
I wonder if this problem was trying to gets at Paiget’s concept of subitising which is mind’s ability to form stable mental images of patterns and associate them with a number or, put more simply, being able to recognize the number of objects by looking at them. Piaget believed that even as adults the most our minds can recognize by sight is five. Everything beyond that either involves regrouping the objects into subsets smaller than five and adding, or estimating the total number viewed.
If also asked to draw out his answer, which we do see a lot with CC math, the child is regrouping using that magic Piaget five. He could have also regrouped the number six as three plus three and then added the five. The child would still be adding three numbers together to come up with the solution. The child would need to know all the factors of 6 and recognize that one of them was included in the previous question. If the teacher has not previously covered factors there is no reason for the child to magically focus on the number five from the previous problem. He would have to look at the number previously given, subtract five from six to see that an additional one is needed. This requires subtraction (if the math facts aren’t memorized), not addition and not factorization. This problem also does not relate to algebraic math concepts like orders or operations or distributive, associative or commutative properties.
The base of this problem requires the child to have already memorized that 5+1=6 and that 10+1=11. We really can’t get away from the fact that to perform any advanced level mathematical calculation, a student must have a solid foundation in (i.e. be able to recall with speed and accuracy) basic mathematics facts of addition, subtraction, multiplication and division. How do we gain speed and accuracy in any task – through repetition and practice. Being able to mentally choose from a number of memorized math facts to find the easiest solution to a problem is a great skill, but it can only come after the student has mastered those math facts. Problems like the one I gave may serve some purpose, but they do not lead to that automaticity.
The only real way to use the previous problem to solve the second one is to say, “I took the two numbers provided in the problem and added them together to get a total number of swimmers. In the first problems I added 5+5 to get 10. In the second problem I added 6+5 to get eleven.”
Can first graders get to the proper solution provided in the lesson plan? Some of them can, but they could have stumbled upon the answer the book wanted rather than honed in on the factors of six to form their response. When asked to explain their answers, only the one that recognized the five as a factor of six is correct, even though the other solutions (3+3+5 or 4+2+5) would have also arrived at the same answer. So which answer is the right one? The one that has to do with factors, not the one that asks the child to solve a word problem by using the numbers provided and coming up with the mathematical solution. That would be the only skill noted in Number Sense that has long term implications for math “solving real-life problems.”
The teacher has claimed that learning this way will help the child in the long run. The parent should respond – prove it. There is no research to prove that being able to regroup mathematically in first grade will make a child college and/or career ready eleven years later. There is no research that factorization at age 6 is necessary for long term math success. Parents who regularly use math in their professions but who were not forced to develop this “deeper” understanding of math at an early age are proof that this focus at this age is not necessary for long term success in math. Telling the parent that they need retraining is not only insulting, but shows the unfounded arrogance of education reformers like Ms. Patenella.
Claiming that all students come as a blank slate also implies that any teacher can teach any student any new curriculum with a degree of certainty and this is demonstrably false. It also perpetuates the myth that all educational failure rests with the teacher because they are handed clean slates to fill properly. Ms. Patenella does her profession no favors with her comment.
She has perhaps been most heavily influenced by Horace Mann, whom John Dewey referred to as the “patron saint of progressive education,” who said
“We, then, who are engaged in the sacred cause of education, are entitled to look upon all parents as having given hostages to our cause.”
Gives me a warm fuzzy. How about you?
Mann also said,
Men are cast-iron; but children are wax. Strength expended upon the latter may be effectual, which would make no impression upon the former.
You will likely be incapable of retraining parents, Ms. Patenella. The only question that remains is whether they will continue supplying your cause with hostages.
Post updated 11-6-14 to correct attribution to the Washington Post.