Problem Solving: Is It a Problem?
The Georgia Standards of Excellence comprehensive course overviews make it clear: all three components of math instruction are equally as important. Our instruction must be a balance in order to meet the expectations of the standards.
In many classrooms, textbooks, and tests, application is relegated to the end of the line. Have you considered pushing it to the beginning? That's what Dan Meyer has done with Three Act Tasks. (And for the K-5 grade band, Graham Fletcher has created a set of tasks using the same premise.) Beginning a lesson or topic with a contextual problem makes learning the skills and developing conceptual understanding relevant.
But ... students sometimes struggle with word problems, or they just want to pull out the numbers they see in the problem and ... do something, anything with them. Sound familiar? Brian Bushart has addressed this issue with what he calls "numberless word problems".
Removing the numbers from the problem before sharing it with students activates schema and promotes close reading. Students make sense of the situation before any numbers are introduced, and they conjecture about what the ultimate question might be. This approach lets them become familiar with the structure of problems as described in Table 1 and Table 2 from our GSE glossary.
Brian has created several sets of Google slides, organized by problem structure type. Each set of slides contains ten numberless word problems, scaffolded with this approach. The files are available through Google drive at this link: Numberless Word Problems. A folder of the files is also saved in the Learning Resources shared folder for math at each grade level K-5
Redesigned Teacher Resource Link
In order to plan next steps on this project. the state is interested in hearing feedback from teachers. Please take a moment to complete the short survey at https://goo.gl/forms/p063GZl7xv9LUFo13.
Pre-K - Grade 2
In this lesson, students describe order by using vocabulary such as before, after, and between. They also review and use both cardinal and ordinal numbers.
Pre-K - Grade 2
This article connects geometry activities to research on how children learn about shape and geometry.
Grades 3-5
In this lesson, students explore growing patterns. They analyze, describe, and justify their rules for naming patterns.
Grades 3-5
Asking students to write stories to go with their number sentences can provide a window into their thinking.
Grades 6-8
In this lesson, students complete a chart by multiplying or dividing a given value, compare two categories in a line graph, and identify number patterns.
Grades 6-8
Proportional reasoning helps students understand issues of fairness and whether an outcome is disproportionate or expected.
Grades 6-12
With this interactive, students learn how to represent and solve algebra problems. With the tiles, students can substitute in variable expressions and expand and factor.
Grades 9-12
In this lesson, students interpret the meaning of slope and y-intercept of real-life data, relating them to the slope and y-intercept of the least squares regression line. They interpret the correlation coefficient.
Grades 9-12
In this lesson, students discover the relationship between dimension and volume. They justify their observation by analyzing formulas and identifying the dimension(s) with the largest impact on the volume.
November Math Professional Learning
Thursday, November 9, 2017
HS: Developing Quality Assessments
High school math teachers will discuss considerations for item development and analyze items for cognitive complexity. Teachers will revise items to increase the depth of knowledge. Discussion will also involve universal design, vocabulary/language, and alignment to standards. A blueprint template will be shared. Participants will need to bring sample assessments and Chromebooks to the session.
Tuesday, November 14, 2017
K-2: Identifying and Using Rigorous Tasks
This session, for K-2 teachers and administrators, will focus on what rigor in math means, how to assess the rigor of a task, and ways to increase students’ higher level thinking. Register by 4 p.m. on Nov. 13, 2017, at https://goo.gl/forms/MDsek9gghuf1VAk02 to receive a link to join session.
Thursday, November 16, 2017
3-5: Identifying and Using Rigorous Tasks
This session, for teachers in grades 3-5 and administrators, will focus on what rigor in math means, how to assess the rigor of a task, and ways to increase students’ higher level thinking. Register by 4 p.m. on Nov. 15, 2017, at https://goo.gl/forms/QXKYALSwvUK2jpF22 to receive a link to join session.
Wednesday, November 29, 2017
6-8: Developing Quality Assessments
Middle school math teachers will discuss considerations for item development and analyze items for cognitive complexity. Discussion will also involve universal design, vocabulary/language, and alignment to standards. A blueprint template will be shared. Participants will need to bring sample assessments and Chromebooks to the session.
Research base
Fletcher, G. (n.d.) 3-act lessons. [Blog]. Retrieved from https://gfletchy.com/3-act-lessons/
Howse, T.D., & Howse, M.E. (2015). Linking the Van Hiele theory to instruction. Teaching Children Mathematics, 21(5), 304-313.
McCormick, K.K., & Essex, N.K. (2017). Capturing children's multiplication and division stories. Teaching Children Mathematics, 24(1), 40-47.
Meyer, D. (n.d.) The three acts of a mathematical story. [Blog]. Retrieved from http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/
National Council of Teachers of Mathematics [NCTM]. (n.d.) NCTM Illuminations. Reston, VA: Author.
Simic-Muller, K. (2015). Social justice and proportional reasoning. Mathematics Teaching in the Middle School, 21(3), 162-168.
University System of Georgia [USG]. (2017, September 25). Staying on course: Required high school curriculum. Retrieved from http://www.usg.edu/assets/student_affairs/documents/Staying_on_Course.pdf
