Mathematics Updates

December 2016

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Achievement Level Descriptors (ALDs) show a progression of knowledge and skills for which students must demonstrate competency across the achievement levels. It is important to understand that a student should demonstrate mastery of the knowledge and skills within his/her achievement level as well as all content and skills in any achievement levels that precede his/her own, if any. For example, a Proficient Learner should also possess the knowledge and skills of a Developing Learner and a Beginning Learner.

More detailed and content-specific concepts and skills are provided for each grade, content area, and course in the Achievement Level Descriptors (ALDs). ALDs are narrative descriptions of the knowledge and skills expected at each of the four achievement levels. Use of ALDs in planning for and delivering instruction and assessments will help our students be better prepared to show what they know. Access the ALDs for what you teach.

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What Is Math Rigor?

By Jessica Carlson, curriculum expert at MIND Research Institute

Educational reformers called for a shift toward more rigorous standards and assessments with the intention of developing deeper understanding, perseverance, and creative problem-solving abilities. By viewing rigor in a way that uses procedural memorization and repetition as a means to teach and learn harder content, a disconnect has occurred between classroom learning and standardized tests.

How do we equip our students to be independent, creative problem solvers when facing rigorous material, without relying on rigid pathways or stock formulas as the only means to solving challenging problems?

We need a new shared understanding of rigor. We need to bridge the disconnect between classroom learning and standardized tests. To do this, gaining a better understanding of the kind of thinking and problem solving (i.e., rigor) called for in the new assessments is a good place to start.

Cycle of Rigorous Learning

When students embody the characteristics of rigorous learning, it becomes a cycle of growth and continues to develop their capacity for deeper thinking and increasingly complex problem solving.

Rigorous problem solving should always be challenging. But given the right opportunities, students may just come to enjoy it! Rigor takes students out of their automatic framework of thinking, pushing them beyond the threshold of what they already know. It moves them into creative and effortful problem solving. It is there that they expand their capacity for deeper understanding. As students find success with rigorous instruction, they develop a thirst for challenge and any limitations they face in problem solving begin to fade away.

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This free graphic was created by the Georgia Assessment Center. Download a copy to print for your classroom.
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The Need to Make Homework Comprehensible

By Matt Larson, President, National Council of Teachers of Mathematics

Whether you are an elementary, middle level, or high school teacher, you are likely to have had parents say to you that they can’t help their children with their math homework. At the secondary level, the difficulty is often the content itself; at the elementary level, however, it is often a function of parents’ unfamiliarity with the instructional strategies that we use today to build conceptual understanding.

In recent years, as new standards and instructional strategies have been implemented at the school and classroom level to build students’ conceptual understanding in addition to helping them meet traditional procedural fluency goals, parental concerns about math homework, particularly at the elementary level, have increased. Social media provide a new vehicle by which parents rapidly share examples and express their concerns about math homework and instructional strategies that they find confusing or unnecessarily complicated. Read more ...

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Dynamic Math Resources for Your Students

Pre-K–Grade 2

Dynamic PaperNeed a set of pattern blocks where all shapes have one-inch sides? You can create it and more with the Dynamic Paper tool. Place the images you want, then export it as a PDF activity sheet for your students or as a JPG image for use in other applications or on the Web.

Grades 3–5

Turtle Pond Students enter a sequence of commands to help the turtle get to the pond. The turtle will then move along a path according to their instructions.

Grades 6–8

Playing Fraction Track In this two-player e-example, students take timed turns racing to the end of each fraction line by moving one or more of their markers to sum to a given fraction value. Options include a pass and restart button.

Grades 9–12

Vector Investigation - Boat to Island Students move the boat in the water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Students try to land the boat on the island without hitting the walls.

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Eight Teaching Habits that Block Productive Struggle in Math Students

By Heera King

Productive struggle is the kind of effortful learning that develops grit and creative problem solving. It results in students understanding content at a deeper level and applying that learning to more difficult and complex problems. It's what we want for all students. But did you know that some teaching methods could block students' potential for developing productive struggle?

Here’s a roundup of information on some common teaching habits and their unintended consequences:

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Research Base

Carlson, J. (2016). What is math rigor? It may not mean what you think it means. Irvine, CA: MIND Research Institute.

Georgia Center for Assessment. (2015). Mathematical problem solving steps. Athens, GA: Author, University of Georgia. Retrieved from

Georgia Department of Education. (2015). Georgia Milestones Achievement Level Descriptors, End-of-Grade Resources. Retrieved from

Kang, H. (2016, March 31). 8 Teaching habits that block productive struggle in math students. Irvine, CA: MIND Research Institute. Retrieved from

Larson, M. (2016, November 15). The need to make homework comprehensible. NCTM President’s Messages. Reston, VA: National Council of Teachers of Mathematics. Retrieved from

National Council of Teachers of Mathematics. (n.d.). Bright ideas: Mathtools. Reston, VA: Author.

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