Common Core critics argue that some of the standards are not developmentally appropriate for young students. Earlier this year I published this post by Edward Miller and Nancy Carlsson-Paige about how the standards smack in the face of what we know about how young children learn. Here’s is a new post with concerns about the developmental appropriateness of some Core math standards. This was written by Carol Burris and John Murphy.
Burris is the award-winning principal of South Side High School in New York who most recently wrote about a ridiculous Common Core first-grade math test for students, which you can read here. Burris has been chronicling on this blog the many problems with the test-driven reform initiative in New York (here, and here and here and here, for example), which was one of the first states to implement Common Core and give students Core-aligned standardized tests. She was named New York’s 2013 High School Principal of the Year by the School Administrators Association of New York and the National Association of Secondary School Principals, and in 2010, tapped as the 2010 New York State Outstanding Educator by the School Administrators Association of New York State. She is the co-author of the New York Principals letter of concern regarding the evaluation of teachers by student test scores. It has been signed by more than 1,535 New York principals and more than 6,500 teachers, parents, professors, administrators and citizens. You can read the letter by clicking here.
Murphy is an assistant principal at South Side High School. He was recognized by the Harvard Club and Phi Delta Kappa for his teaching and outstanding leadership. John is South Side’s International Baccalaureate coordinator.
By Carol Burris and John Murphy
Why are New York parents reporting that their elementary school students are having such a difficult time doing Common Core mathematics? Burris’ last blog post presented an example of a first-grade test, created by Pearson, the author of New York’s 3-8 tests. Some readers commented that perhaps the problem was not the Common Core standards, but rather their implementation at the school level. In the case of New York, rushed implementation is certainly a factor.
There are far too many reported problems, however, for us not to consider both. Are these only the result of rushed implementation, or, are the standards themselves problematic? What follows may provide insight into that very question.
A few days ago, our superintendent shared a Common Core assessment question from a PARCC website, which directed viewers to the Mathematics Common Core Toolbox. This site “offers examples of the types of innovative assessment tasks that reflect the direction of the PARCC summative assessments.” He was interested in a question designed for fourth graders, who are typically 9 or 10 years of age. You can find the question that he shared here: under elementary tasks, fourth grade, “Number of Stadium Seats.” Part A of the assessment task is a straightforward question that asks students to put three, 5 digit numbers in order. Part B is a very different kind of question.
Part B provides students with the following information:
The San Francisco Giant’s Stadium has 41,915 seats, the Washington Nationals’ stadium has 41,888 seats and the San Diego Padres’ stadium has 42,445 seats.
It then asks the following question:
Compare these statements from two students.
Jeff said, “I get the same number when I round all three numbers of seats in these stadiums.”
Sara said, “When I round them, I get the same number for two of the stadiums but a different number for the other stadium.”
Can Jeff and Sara both be correct? Explain how you know.
Three administrators in our district brought that question home to their children—one 4th grader and two 6th graders. All three children are good math students who attend different, excellent Long Island schools; all are adept at rounding whole numbers; all were able to do Part A, but got Part B wrong. This response by one of the 6th graders, an 11 year old, provides insight into how this age group thinks:
No, I know this because they all round to 42,000.
We know her response is typical for her age group (7-11) because of the work of one of the greatest childhood psychologists of all time, Jean Piaget. Piaget carefully and systematically studied the cognitive development of children. Before him, it was assumed that when it came to thinking, kids were not as adept as adults, but their thought processes were essentially the same.
Piaget disagreed. He discovered that the development of thinking is far more complex. He identified distinct stages of cognitive development that children go through as they mature, including, the ‘Concrete Operational’ stage (ages 7-11). Students in this stage can engage in some inductive logic, but deductive logic, which is needed to solve problems such as the one described above, is beyond them. Matt Baker does a nice job of summarizing the stages of cognitive development here.
When we gave the Part B question to high school students they had no difficulty answering it correctly. Here is one 14-year-old’s answer.
Yes, they can because it depends on the way a person rounds. Jeff is right if you round to the nearest thousand and Sara is right if you round to the nearest hundred.
Only one tenth-grader said “no.” Her reason was, “Why would someone round the number of stadium seats—it makes sense to round decimals, but rounding whole numbers makes little sense.” So much for ‘real world’ problems!
This question is not an outlier. The question entitled, Deer in the Park, which you can find in the fourth grade sample, requires complex thinking skills as well. Here is what the aforementioned site says about this question:
The task asks students to demonstrate their ability to model with mathematics (MP.4) and reason abstractly and quantitatively (MP.2)—thus making it a “practice forward” task.
This task is innovative because students go much deeper than just demonstrating their ability to solve area and perimeter problems. They reason about the model and the relationship between area and perimeter. Students must move in and out of context as they create a coherent representation of the problem, consider the units involved, and attend to the meaning of quantities.
Please keep in mind that this ‘task’, or sample test question is designed for 9 year olds. They must respond in words, numbers and symbols.
Many of the other tasks involve less abstraction, but are highly difficult. They are interesting questions that make adults stop and think. But as Piaget told us, children are not “mini-adults.” If a child is not developmentally ready, these problems will likely lead to frustration, discouragement and negative emotional reactions—which is exactly what parents are reporting.
Standards matter. We have always been a proponent of challenging learning standards. But they must be high quality and match the development of the child. They should be vetted through field testing, and developmental psychologists should weigh in on their appropriateness.
Repeated exposure to such problems is not the answer. It may be possible to teach them to parrot the tasks for the tests. But what will our students gain? And what will we not be teaching instead? Art? Music? Level-appropriate math skills?
There is time to help our students to develop high-level thinking skills that require the manipulation of multiple symbols and the use of deductive logic. That time is adolescence. To everything there is a season—let’s not rush (or ruin) the most important season of all-childhood.