Wednesday, September 10, 2014

The Truth

I love truth. I always seek after truth. So here is the truth about that common core math problem you've been seeing all over the internet since last Spring.

First and most important truth, Frustrated Parent gets a lot of things right. There are a lot of reasons this is a ridiculous problem to ask a 7-year-old to solve. Simplification should be valued over complication, even in 2nd grade.

Second and equally important truth, this math problem is not a reflection of Common Core. It is a reflection of poor teaching (a mistake we all make from time to time).

Let's dissect those two truths. Why is this question ridiculous? Well, it appears to be assessing four different 2nd grade learning standards (understand place value, add and subtract within 1000, explain why addition and subtraction strategies work, and represent whole numbers on a number line). I'm all about intermingling standards and subjects where appropriate and natural, but when it comes time for assessment it is best if one question equals one standard, not four (and if you want to get technical, the number line isn't an appropriate model for place value, so those two standards are conflicting from the start).

The correct answer, in case you are interested, is something to this affect:
Dear Jack,
You did an excellent job of subtracting your 100s. It looks like you jumped from 127 to 107 though. You forgot to place 117 on your number line, and therefore your answer is off by 10 points. Please remember to double check your work next time.
Caring Classmate

But how in the world is a 2nd grader suppose to know that? The number line is horribly scaled, and you can't tell what part of the problem is Jack's work and what part of the problem is the teacher's. I mean, who really drew that number line? Jack or his teacher? And how is a 2nd grader suppose to try and figure that out? Sure, 2nd graders may love to play "school," but that doesn't mean we can expect their writing to reflect the criticism a teacher would offer a peer. This question fails as a math assessment AND a writing assessment.

I would suggest rewriting this question entirely (at a minimum, drop the number line), but if I was forced to use the same methods to fix the problem here is what I would do.

First, I'd break the problem into two questions. One assessing the math portion of the problem and one assessing the writing portion. The new math question would say, Jack was asked to solve 427-316. He drew the number line below to solve his problem. Can you circle the part of his number line where he made a mistake? Then I'd draw the number line below to scale and in kid friendly handwriting, so that it is clear a child wrote it.

This fixes two problems in the original question. One, it makes it clear Jack wrote the numbers on the number line; and two, it gives the child a chance to demonstrate they understand the math concept being tested, even if they don't understand the writing concept being tested. They'd either circle the dash where 117 is missing (the right answer) or they'd circle some other portion of the line (the wrong answer).

Now, for the second part of the question you could ask the student to write Jack a letter telling him how to fix his mistake. There really is no need for the students to tell Jack one thing he did right and what he should do right to fix it. This new, separate question would give kids a chance to explain how they might do the math problem. Which is fabulous because each kid might "fix" Jack's problem a different way. How enlightening for a teacher to learn! As Frustrated Parent demonstrates, some kids might tell Jack to skip the number line all together and use carry over instead. Other students may tell him to use a base ten formula. And some students may stick with the number line and simply remind Jack a number line goes from 100s, to 10s to single digits. This gives kids a chance to think about what math method is best for them while also giving the teacher a chance to assess their writing skills and learn about their preferred math strategies. Win, win.

Most importantly, breaking the question into two parts gives the teacher a chance to figure out what a student can and can't do. Maybe one student can't figure out what is wrong with the number line, but can tell Jack to use carry over instead. Maybe one student can figure out what is wrong with the number line, but can't write a complete sentence. Whatever the child's struggle is, being more direct in the assessment of standards eliminates a lot of confusion for the students and the teacher.

Now, for dissecting the second truth, why this math problem is not a reflection of Common Core. The most basic explanation is that Common Core is not curriculum. Common Core is a set of learning and teaching standards. Curriculum is the lesson, text, assignment, and assessment used to try and teach each of those standards. Basically, Common Core states what every child is expected to know in the subjects of math and Language Arts by the end of each given school grade. Curriculum is how various teachers and schools try to help students meet those expectations. Lesson plans, texts, assignments, and assessments will vary from school to school and classroom to classroom, all while the Common Core standards remain the same. If a drama teacher is expected to teach students about tragedy and she chooses to study Shakespeare's Midsummer Night Dream to do so, it isn't the standard's fault her students won't understand tragedy! Common Core gives Educators, parents, and students the learning expectations children are suppose to master. Decisions regarding lesson planning, textbook purchases, homework assignments, and exams are left up to individual districts, schools, and teachers.

As stated above, this particular math problem aims to assess four different Common Core standards, two of which should not be combined. Either way, if the student answers the question right, the teacher still wouldn't know if the student has mastered all four standards. The problem with this question stems from poor curriculum, not poor standards. If people want to critique the standards, then critique the actual standards. They are readily available at

Finally, I'd like to point out that Frustrated Parent wrote a lengthy follow up post, explaining the context of this assignment and his actions. He noted that his son is Autistic and suffers from ADHD. He explained that his son excels in math and despises writing. In his exact words, this question "might as well have been a doctoral dissertation." The father noted he supports teaching kids various different approaches to math, but that the multi-layered approach of this particular question frustrated him. He acknowledged that Common Core is a set of standards and that their flaw does not lie in the standards themselves but in their application. I agree with him on that and think it is important to note (though he didn't) that their application will vary from school to school. He is obviously frustrated by the "gobbeldygook presentation (North Carolina implemented) which must be interpreted" and by the way his child's school is forcing teachers to use the standards in a "multilateral way, all day long." But those problems are best addressed at the local level; not through viral Right Wing websites. Each state has printed their own version of the standards, and if their explanation is too difficult for an Electronics Engineer to understand then they need to fix it. If their student's are becoming frustrated by the constant multi-disciplinary approach they have taken then they need to fix it. They do not need to change or drop the standards all together.

Look to Indiana to find out what happens when a State gives in to all the ill informed naysayers. Mid year Indiana let its Legislature decide the fate of its school standards instead of leaving that decision to the experts in Education. The Legislature decided to override Common Core, and that left Indiana's Education Department the huge burden of writing new standards mid year (and teachers and students were put in an odd limbo). The Legislature then had to hire the state's best Educators to create a new set of standards, and guess what? Those new standards look an awful lot like Common Core. And there is a good explanation for that. If you want your state to have the best standards possible, they are going to look a lot like Common Core. You can either accept that or go Indiana's route and waste valuable resources re-inventing what you already have set in place. 

1 comment:

Mom said...

That was an enlightenment for myself, Sissy Sue! Thanks for sharing that. You obviously are your father's child when it comes to brains!!!

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