October 2017 - Make Sense of Math

Teach your students to master mathematics

Helping Your Students Master Mathematics      
As a math teacher, I can't even tell you how many times a student would excuse their poor math work with the comment, "Well, I'm just not a math person."  What was even more horrifying, is when a PARENT would excuse the poor math work of the student with the comment, "Well, I'm not a math person, so he/she is not a math person."  There does not exist two categories of math people or not math people.  However, I do believe that there exists two categories of people who know how to learn math and people who do not know how to learn math.  The great thing is that these categories are flexible and you can easily teach your students to belong to the "I know how to learn math" category. Here are 7 steps to help your students be successful in the math classroom. 

1) Daily Engagement
Stress the difference between engagement and participation. Participating students may simply be copying notes. Engaging students may be copying notes and trying to internalize the notes by making connections. Engagement encourages the use of higher-order thinking skills.  In order for students to engage daily, your classroom instruction needs to promote critical thinking skills. 

2) Learn from Mistakes
Encourage students to never erase mistakes.  Instead have them leave their mistakes, and with a different color they can mark and explain their mistakes.  Continually model this to students by  marking your mistakes on the board. A safe environment is required for students to feel safe to do this step.  Celebrate mistakes as a step in learning.

3) Ask Critical Questions
An example of a non-critical question is, "What's the next step?"  An example of a critical question is, "How do ratios connect with the circumference of a circle?" Make a poster of words that help create critical questions. You could teach them Bloom's taxonomy, and classify different questions for each level. Consistently point out and praise critical questions in the classroom.

4) Show All Your Thinking
Teach students different way to show their thinking. This can include in writing, with models, diagrams, equations, expressions, etc... Showing calculations depends on the level of the student. Teach students to write in complete sentences. Students should label their models and diagrams. do not accept low quality with this step. Consistently push the students to do more and more. Have them redo the assignment over and over until they are showing quality work. 

5) Don't Cut Corners
Students often just want to "be done" with the problem. To help students to not cut corners, assign fewer problems, but require quality. Cutting corners causes students to make mistakes and not critically think through the problem.

6) Make Connections
When students make connections they will retain the information more easily. Many times connections are not obvious and you will need to guide them to discover different connections. Connections between algebra and geometry are critical to understanding higher-level mathematics. Consistently push them to find connections. 

7) Be Humble
Humility is essential for students to learn mathematics. The students that think they are "bright" are often those students who learn very quickly, mostly because they can memorize. These students often think that they don't need to explain their thinking, because they already have the correct answer. Don't let students cut corners. Push these students to ask higher-order thinking skills. The students who struggle often don't want you to know that they struggle, so they will erase mistakes and try to cover up their weaknesses.  Having a positive environment that values mistakes will help these students.  Students who struggle may not want you to know that they struggle, so they will erase mistakes and try to cover up their weaknesses.  Having a positive environment that values mistakes will help these students.

Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on helping your students master mathematics. 

Teach your students to master mathematics




Implementing Mathematical Practices in Your Classroom

Mathematical Thinking
One of the purposes of math teachers is to help your math students develop mathematical thinking. This is achieved through implementing the mathematical practices.
  • Make sense of problems and persevere in solving them
  • Reason abstractly and quantitatively
  • Construct viable arguments and critique the reasoning of others
  • Model with mathematics
  • Use appropriate tools strategically
  • Attend to precision
  • Look for and make use of structure
  • Look for and express reasoning in repeated reasoning
Technically, these practices are supposed to be taught since early elementary grades, but even as a middle school math teacher, I always took the time to explicitly teach them.

Here are three ideas to teach the mathematical practices. 

Assign a Reading Assignment
That's right, I printed out the mathematical practices and their explanations and I assigned my students to read them.  I had them mark up the text, as though they might do in their Language Arts class.  I had them highlight the text, annotate the text, and write questions about the text.  I had them collaborate in small groups about the text and then we had a large group discussion.  Taking the time to do this, truly made the world of difference.

Practice the Mathematical Practices
An excellent time to explicitly teach these skills is the first week or two of school.  I used logic problems to practice these skills.  For example, I would give a logic problem to the students, I often did this in small groups, and have them work on it together.  Then I would have the small groups present their "viable argument" to the class.  The students would then focus on "critiquing their reasoning."  The purpose of the class was not the answer to the logic problem, rather teaching the mathematical practice of, "Construct viable arguments and critique the reasoning of others."  This is just one example, but can easily be applied to other mathematical practices.  

Post and Refer
I made posters for the mathematical practices and hung them at the front of my room.  I kept them there then entire year.  I included them in my teaching on a daily basis.  I would tell the students what skill we were practicing along with the new material.  I would also have my students tell me what skill they were practicing, and have them write about what mathematical practice skill they were practicing on the assignment.  The key for this to be successful is to refer to them and talk about them on a daily basis.  Let them become part of your vocabulary and the students' vocabulary.

If you need some mathematical practices posters then you are luck.  I created these mathematical practices posters that I absolutely love! 

Click on the image below to check out the mathematical practice posters. 


Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to implement the mathematical practices in your classroom. 

Implementing Mathematical Practices in Your Classroom





Back to Top