Illustrated Math Dictionary

Math Dictionary

OECD Report on Time Allotted for Instruction

Does Instructional Time Explain Achievement Gaps Internationally

Instructional time and student achievement

Study Homework and Student Achievement

Hattie's Glossary Influences on Student Achievement

The Need for Speed in Mathematics

Timed Tests and the Gender Gap

Times Tests and Math Anxiety

Rubric Teaching and Learning in Standards Based Classroom

Designing lessons the workshop model

Tasks aligned to common core from illustrative math

Tasks from Inside mathematics aligned to common core

Rich mathematics tasks from nRich

Protocol for looking at Rigor of tasks and student learning

It's About the learning.. not the tools

PreK Math and Common Core

PRE K Math aligned to Common Core

Math Modules aligned to Common Core K through 10

Fixing Classroom Observations

Article Making Thinking Visible

Writing in Science

Writing to Learn Math

Math Poster Placemat Early Years

Effective Fraction Instruction

Building Blocks and Cognitive Building Blocks

Use of the Number Line in the Common Core

The focus of the Math Specialist In International Schools (MSIS) project is to build  teacher conceptual understanding of mathematics. Thanks to last weeks rich engaging discussions of the Amman cohort, I decided to share some thoughts on the importance of what they (all of the cohorts) are doing.  

Recently, a parent asked me why her child was not being taught math the way she had learned it.  I was troubled by the next statement of this young mother ….this “new” math…..   Troubled because this is not “new” math! Teaching math conceptually (teaching for understanding) has been around for a long time!  More recently, in the Principles and Standards for School Mathematics (2000). NCTM, one of the six principles states:  “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.”

In 2001, The National Research Council in its document Adding It Up: Helping Children Learn Mathematics used the term mathematical proficiency to describe the successful learning of mathematics. They broke down mathematical proficiency into five components. Conceptual understanding,  procedural fluency, strategic competence, adaptive reasoning, and productive disposition.

Sadly, after decades of studies on the learning of mathematics, rote learning still appears to be the norm. Rote learning is not the answer in mathematics. Learning only to perform mathematics procedures (algorithms) allows students to find answers to a set of rules. This is not the essence of mathematics.

For example take division, How did you learn to divide whole numbers? Fractions, decimals,  integers? Did you learn a particular rule or did you learn division as a mental process that can be completed using any number of strategies? Division problems can be solved many ways, repeated subtraction, repeated addition, using a number line, using objects, and models. For example the procedure using for dividing fractions, “invert and multiply” is only one of many procedures. The concept of division and the procedure of solving division problems are not the same thing!

It is important we teach for understanding. This does not mean that procedures are not learned. They are learned, but not without conceptual understanding. A great benefit of knowing a procedure (How it works) and understanding the concept (Why it works) is that if you forget a procedure, understanding why it works helps in reconstructing the forgotten procedure. On the other hand, if procedural knowledge is the limit of one’s learning, there is no way to reconstruct a forgotten procedure. Conceptual understanding in mathematics, along with procedural skill, is much more powerful than procedural skills alone. 

Yes, our goal is to make certain students acquire procedural fluency  (the How), the conceptual understanding (the Why), and equally important to experience rich problem solving (Where it works)

Pre K Standards for Math Continuum

Connecting IB to Common Core Math

College Board How Common Core Prepares Students for AP courses

AERO NGSS Alignment to 8

AERO NGSS Alignment K to 4

AERO NGSS Alignment K8 READ FIRST

Homework An unnecessary evil???

Why The Common Core Changes Math Instruction

Great Council City Schools Parent Raodmaps

Publishers Criteria High School

Videos, lessons, practice aligned to Common Core

Math Teaching Resources K to 5 aligned to Common Core

Successful STEM Education A Report

From SEEN STEM Form and Function

Vocabulary Cards G 8 to 12 M to Z

Vocabulary Cards G 8 to 12 A to L

Vocabulary Cards G K A to Z

Vocabulary Cards G 7 M to Z

Vocabulary Cards G 7 A to L

STEM Report, Defined and Goals of STEM EDUCATION

Vocabulary Cards G 6 M to Z

Vocabulary Cards G 6 A to L

Vocabulary Cards G 5 M to Z

Vocabulary Cards G 5 A to L

Vocabulary Cards G 4 M to Z

Vocabulary Cards G 4 A to L

Vocabulary Cards G 3 M to Z

Vocabulary Cards G 3 A to L

Vocabulary Cards G 2 M to Z

Vocabulary cards G 2 A to L

Vocabulary Cards G 1 A to L

Vocabulary G 1 M to Z

Utah Common Core Math Units Integrated math

Georgia Common Core Math Units 9 to 12 Traditional path

Georgia Common Core Units 6 to 8

Georgia Common Core Math Units K to 5

Science and Engineering Practices, NSTA

Publishers Criteria Math K to 8

Article Homework or Not

Mathematics Posters 6 to 12

Mathematics Posters 4 to 5

Mathematics Posters K to 1

Math Practices Posters 2 to 3

Math Manipulatives 6 to 8

Math Manipulatives K to 2

Math Manipulatives 3 to 5

Washington Post
Why young kids are struggling with common core math

Standard Algorithms and the Common Core

Calculator Usage and Common Core

From Atlantic Magazine
Stereotypes about math that hold Americans back