Mathematics Updates

ELEMENTARY MATHEMATICS

1. Rather than providing a context, ask students to write a word problem for a given expression.

2. Have students determine an expression to represent a situation.

3. Require students to provide justifications for their solutions.

4. Challenge students to solve problems using more than one solution method or representation.

5. Have students make sense of provided solution strategies by completing the solution or justifying the steps.

6. Make the task open ended so that multiple responses will satisfy the task. Transform a single-step problem to a multiple-step problem.

7. Include the use of multiple representations in a task.

MIDDLE SCHOOL MATHEMATICS

1. Use comparison questions. (When is one situation greater than, equal to, or less than another?)

2. Ask a question across multiple representations in a task.

3. Validate a solution pathway or approach.

4. Require students to provide justifications for (explain) their solutions.

5. Evaluate the error or reasoning in a student solution and provide a correct solution pathway.

6. Create a context. Ask students to write a word problem that creates a context for the given information.

7. Ask students to determine an expression to represent a situation.

8. Create an open-ended debate-type task, so that multiple student responses will satisfy a solution to the mathematical task.

HIGH SCHOOL MATHEMATICS

1. Find the error in a student solution, and provide a correct solution pathway.

2. Create an open-ended debate-type task (evaluating a student claim, for example) so that multiple responses will satisfy the task.

3. Rather than providing a context, ask students to write a word problem for a given expression or graph.

4. Ask students to determine an example to represent a situation.

5. Require students to provide justifications for their solution pathway or strategy (such as when comparing two quantities).

6. Challenge students to solve problems using more than one solution method or representation.

7. Ask students to make sense of provided solution strategies by completing the solution or justifying the steps.

8. Create the task as open ended so that multiple responses will satisfy the task.

9. Transform a single-step problem to a multiple-step problem.

10. Include the use of multiple representations in a task.

The brain is malleable, and ability is not a fixed asset. Students who believe that with effort and persistence they can improve their performance are working with a growth mindset. Educators and parents can help students build a growth mindset by providing specific and accurate feedback about students' efforts followed by an opportunity to improve results.

Praising the process, not the person, is key to informative and productive feedback. Emily Diehl, a Mindset Works trainer, suggests some great prompts teachers can use to promote a growth mindset.

When a student is struggling despite a strong effort:

• "If this was easy, then you wouldn't be learning anything new!"
• "You can do this! Let's break it down into some smaller chunks."
• "Look how much progress you have made!"

When a student is struggling and needs help:

• "What parts of this was hard for you? Show/tell me ..."
• "Let's do one together. Describe your process out loud so I know your thinking."
• "Let me show you another way to try ... Maybe this will help you solve it."

When a student is making progress:

• "You are using the strategies we discussed. Keep it up!"
• "You have really stuck with this and persevered!"
• "Your hard work is really evident!"

When a student succeeds with strong effort:

• "All that hard work and effort paid off!"
• "What strategies did you use that contributed to your success?"
• "Congratulations! I am very proud of you for not giving up!"

When a student succeeds easily without effort:

• "You're ready for something more challenging!"
• "You really have that down. Let's find something that will challenge you a bit more."
• "What skill do you need to work on next?"

Free resources are available at Mindset Works. Download a copy of the poster about mistakes, in color or in black and white, to print and post.

Before we know it, April will be here, and it will be time to celebrate math! Mathematics Awareness Month began in 1986 with a proclamation by President Reagan to celebrate the importance and applications of mathematics to a wide variety of fields.

Planning ahead will allow you to plan some activities to celebrate math during the month of April. The Envision Blog lists some possibilities, and these calendars provide students with grade or grade-band appropriate challenges for each day of the month.

March 7, 2017 - K-2 Math Webinar - 3pm - 4pm

Avoiding Math Misconceptions in Grades K-2

Children try to make sense of what they see and hear in terms of numbers, measurement, shapes, money, and time. And they can develop misconceptions that create issues for conceptual understanding. This session will examine some common math misconceptions children have in K-2 and discuss instructional ideas and activities that can be implemented to address these misconceptions. Register by 4 p.m. on March 6 at https://goo.gl/forms/8k010ZtYKbZEakNs1 to receive an invitation to join this session.

March 21, 2017 - Smokey Road Middle - 4pm - 5pm

Determining Power Standards

Teacher teams will apply the criteria of endurance, leverage, and readiness to grade level math standards, along with the state assessment blueprint, to determine a draft list of power standards. Teams will vertically review draft power standards at each grade level for gaps and redundancies in order to create the final list. This work is in preparation for the creation of 2017-2018 course pacing guides later in the spring. Participants are asked to bring their Chromebooks. No registration is required.

March 28, 2017 - 3-5 Math Webinar - 3pm - 4pm

Avoiding Math Misconceptions in Grades 3-5

Aside from making careless errors and having incomplete mastery of basic facts, the other mistakes students make are due to misconceptions. This session will examine some common math misconceptions children have in grades 3-5. Instructional ideas and activities that can be implemented to address these misconceptions will be discussed. Register by 4 p.m. on March 27 at https://goo.gl/forms/SgF8aASErIVH6r533 to receive an invitation to join this session.

Briars, D.J., Larson, M.R., Kanold-McIntyre, J. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, grades 6-8. Bloomington, IN: Solution Tree.

Dixon, J.K., Adams, T.L., Nolan, E.C. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, grades k-5. Bloomington, IN: Solution Tree.

Dweck, C. (2014). The power of believing that you can improve. TEDxNorrkoping. Available from http://www.ted.com/

Envision Blog. (2016). Mathematics awareness month. Retrieved from https://www.envisionexperience.com/blog/mathematics-awareness-month

Luna Productions (Producer). (2012). Don’t give up: Plan, persevere, revise. Available from https://www.teachingchannel.org

Mindset Works. (2015). Free resources. Retrieved from https://www.mindsetworks.com/free-resources/default

National Council of Teachers of Mathematics. (n.d.). NCTM Illuminations. Reston, VA: Author.

Readdean, C. (Producer). (2012). Student-generated questions for exam prep. Available from https://www.teachingchannel.org

Sun, K.L. (2015). There’s no limit: Mathematics teaching for a growth mindset. Doctoral dissertation. Stanford, CA: Stanford University. Retrieved from https://purl.stanford.edu/xf479cc2194

Teaching Channel (Producer). (2013). Math journals: A record for students and teachers. Available from https://www.teachingchannel.org

Teaching Channel (Producer). (2015). Highlighting mistakes: A grading strategy. Available from https://www.teachingchannel.org

Toncheff, M., & Kanold, T.D. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, high school. Bloomington, IN: Solution Tree.