Today’s guest blogger is Carolyn Felux, Director of Education for Math Solutions, a longtime educator and an expert in the Common Core State Standards for Mathematics. In this post she shares a list of resources that helped her dig deep into the Common Core Standards for Mathematical Practice. Hopefully you’ll find them useful as well! This post originally appeared in On Our Minds @ Scholastic.
I remember sometime in the fall of 2010, I launched into my study of the Common Core. With colleagues at Math Solutions, we decided the place to start was with the Mathematical Practices, listed below.
Standard 1: Make sense of problems and persevere in solving them
Standard 2: Reason abstractly and quantitatively
Standard 3: Construct viable arguments and critique the reasoning of others
Standard 4: Model with mathematics
Standard 5: Use appropriate tools strategically
Standard 6: Attend to precision
Standard 7: Look for and make use of structure
Standard 8: Look for and express regularity in repeated reasoning
These mathematical practices describe the expertise and habits of mind that we should develop in students over the course of their K-12 study of mathematics.
My first encounter of the practices was with an abbreviated version, similar to those listed here. I remember feeling pretty comfortable that I knew something about these . . . until I began to study the expanded version of each practice. There was much more to each standard than these short versions convey. Elaborations for each of the practices can be found on the Common Core State Standards website (page 6). It was when I began to study the elaborations of each mathematical practice that I knew I’d need to call on colleagues and other resources to help me make sense of it.
I’ve included a few questions that have guided my study and a few resources I found helpful.
- What does each mathematical practice mean?
I am still working on making meaning but have made progress because of willing colleagues who will share their thinking, experience and resources. Here are a couple of links that have been especially helpful to me.
Core Standards.org: This site has the Common Core Standards for Mathematics and Standards for Mathematical practice. Elaborations of the practice standards can be found here.
MathSolutions.com: I am proud to say colleagues contributed to a collection of videos on our site called “Explain It to Me Videos.” These provide a brief video introduction to the Standards for Mathematical practice and the big ideas behind each of the eight practices. A new feature on our website that started in October is a focus on each Mathematical Practice. Check this link to see the Standard 1: Make sense of problems and persevere in solving them.
- What is my role as the teacher in supporting students to develop these ways of thinking?
I bumped into an interesting resource as I was preparing for this blog. I don’t know who developed the resource linked below, but I found it a nice place to start in thinking more specifically about what students proficient with a particular practice might be doing along with what I, as the teacher, might be doing to support their development with that practice. There is no authorship identified, but by posting, hopefully we can find out.
As a mathematics teacher, I choose experiences that will help students build their content understanding and proficiency, as well as their mathematical habits of mind. I find examples are helpful to me when I am in the process of learning something new and making sense of it. The Inside Mathematics site has helped me by taking me into the classrooms of other teachers. Via video, I can see how another teacher approaches the content and the mathematical practices. This is a site that is aligning its abundant resources to the Common Core State Standards for Mathematics.
- How do I connect the mathematical practices to the mathematics content standards?
This is work that everyone must do to weave these two aspects of mathematics into a cohesive support for student learning. One resource that could be helpful was developed by the Arizona Department of Education. On that site you will find the mathematics content standards at each grade and the mathematical practice or practices that can be developed at the same time.
I hope you find these resources useful. Let us know of other sites you have found in your journey to understand and implement the Common Core State Standards for Mathematics.
(Flickr photo by adactio)
Most of us know sudoku
, a sort of mathematical crosswords puzzle that has a goal of arranging numbers in a 9 x 9 grid so that each row, column, and 3x sub grid each contain a number 1 through 9.
However, many of us have not heard of ken-ken
, or futoshika
Playing these games is often done by adults with the goal of maintaining mental acuity. However, if played by children, these games may be able to help develop thinking skills that will help in mathematical ability. Perhaps most importantly, pen and paper math games are educational tools that doesn't feel like homework – so students may be self-motivated to complete the game. For the skeptical, take a look at this 2011 study from the Journal of Mathematics Education which outlines how to incorporate sudoku in math education with the Common Core State Standards in mind.
A great classroom activity could involve students independently working on one of these puzzles at the beginning of class, or as a supplementary homework assignment. Alternately, it can be a useful activity for students to help fight summer slide.
Scholastic offers a variety of educational resources based around pen and paper math games. Super Suduko Math: Fractions and Decimals offers reproducible worksheets focusing on suduko with the goal of teaching fractions and decimals. Super Suduko Math also makes a multiplication and division version, as well as an addition and subtraction version.
Have you used sudoku or other pen and paper based math games as a supplement in primary math instruction? Do you feel that this is an effective tool for increasing math and number sense?
When students are underperforming in math, teachers start the intervention process by asking them, “Why?”
Many teachers want feedback, formally or informally, from their students. And according to a new article in Teaching Children Mathematics, the role of diagnostic interviews as a form of math intervention has been shown to be effective.
One-on-one meetings between a student and a teacher can help to determine what teaching techniques work best. The article points out that this approach is not about evaluating the student or teacher, but an opportunity to let the student speak. While diagnostic interviews may include an assessment of a student’s academic level, the goal is to discover the deficiency and the reason for it.
For help developing a diagnostic program that can be applied in your classroom, refer to: How Do My Students Think: Diagnosing Student Thinking published by the American Psychological Association. Scholastic offers information about incorporating diagnostic Interviews into math assessment as part of the Math Reasoning Inventory.
Have diagnostic interviews worked in your experience? How can they best be implemented in schools where personalized lesson plans and individualized assessments are more challenging to create?
Share your thoughts below.