Teachers know their students best. They spend the most time with them and get to see the evidence of their thinking.
The rest of us do not.
If students are to succeed then the most important math skill they need is to communicate their thinking on paper so that a stranger can understand exactly what they know and don’t know.
And at the end of this article, you’ll find a sign-up and download for Grade 3-8 Math Exam questions organized by standard and searchable.
Communication in Math
For everyone not in the classroom, we rely on grades and numbers to know how students are doing, and sometimes there is a disconnect between what the student knows and what they are able to communicate
It is a skill to communicate your thinking to someone that doesn’t know you, and teachers work very hard with students so that they can do just that in their writing, but in math (as a whole) we are not as good.
We need to find a structure to math writing that helps students communicate their solution. An right answer is never enough. First, let’s acknowledge the structures we have in place for ELA.
ELA Constructed Response – Short
We’ve come up with many different strategies to answer constructed response questions. Some of them acronyms and some just a way of organizing the answer. Here are just a few.
- RACE: Reword -> Answer -> Cite Evidence -> Explain
- Text proof -> Explain -> Extend
- Answer -> Support -> Evidence -> Evidence
- Hamburger: Restate and Answer -> Support with Evidence -> Close
I’m sure you could find many more, but the concept is always the same. Here’s a sample Pinterest Search Constructed Response where you’ll see all the charts teachers create, and they are all ELA.
We structure student’s written language so that the language doesn’t limit getting the right idea across. @4SquareRubric
ELA Constructed Response – Long
Standardized test essays also have their own structure, but in the below case the test actually provides the structure students should use.
All students have to do is a write a 4 paragraph essay: introduction, how paths are similar, how paths are different, and conclusion.
The test tells them exactly how to communicate their answer.
Math Exam Data Trends
This graph shows the average points earned in each of the three sections of the NY state math test. The green bar, the highest in every grade, shows the average percentage of correct multiple choice questions.
Students always do the best when math is just about finding answers.
The blue bars shown the average percentage of points for the 2 point constructed response questions. These questions usually are two step problems. Usually 1 point for the work and 1 point for correct answer.
Finally, the lowest by far in every grade, by far, the yellow bar represents the average for 3 point constructed response questions. In three grades, 5, 6, and 8 students average less than 1 point a questions across NY state. In the other grades it’s not much better.
The takeaway: If you want your students to do better in math you MUST focus on word problems with written responses and HOW students communicate understanding in math.
Instead of an answer based perspective on math focus your students on communicating in math with the same commitment to structure as writing. Here is one suggestion for students, but use whatever language you already use. For many students shifting from a mindset that math is about answers to common core math exams are about communicating thinking is difficult. You have to break it down to build it back up.
Have your students start by identifying the knowns of the problem. Write out the details of the problem and label values. This can be seen as an introduction.
To teach this part use a close reading strategy with students. Here’s a good resource from ASCD to get started.
Make sure students understand what information is given in the problem and make them tell you everything in their own words or models. (Models are always an acceptable method of demonstrating mathematical understanding.
Students clearly state what they are looking for in each specific step. They write it out.
Just these first two steps let you know if students understand the problem.
This is an extra box if necessary to your specific grade. It’s good for younger students who solve simpler problems. It’s also good when your math keywords don’t align with what the math problem is looking for.
This is the body of the students essay. It is where they demonstrate to their reader they know how to problem solve. You wouldn’t let students jump from their introduction to their conclusion in an essay so don’t let them do it here.
You need to see each step they take and how they calculate everything. You accept pictures, labels, and drawings. If students think something isn’t clear then let them label it. They are not restricted to paragraphs like in an essay. If it’s mathematically sound then let them do it.
For most problems students can solve another way or plug their answers back into the problem. They can use the knowns/unknowns boxes to ask themselves if it makes sense.
Success on Common Core Math Exam
We’ve gone over why data can’t drive instruction. It’s student work that drives instruction and data just helps you know where to look.
Do less problems and get more out of them. If students were to solve problems worth solving in this way you’d get more insight into student’s math proficiency than a 30 question multiple choice test. Focus on the process, the thinking, and the communication. Review your State’s released test questions. You’ll notice many examples of students not getting full credit with the right answer because they didn’t communicate effectively.
Sign up below to know when my blog posts come out and I’ll see you a free test bank of all NY Common Core Math Questions organized by standard and searchable. You can take your data, student work, you have now and choose targeted examples to give your students. Practice only a few at a time.
3-8 Common Core Math Test Banks
Free Download of the past two years worth of common core math questions.
They're organized by standards
Examples of Exemplary Answers
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