I'm writing a series of blog posts about challenging topics in K-8 math standards. I'll post the links to these here as they come out.

March 16, 2015 Overview of Challenging Standards

March 23, 2015 Measurement

March 30, 2015 Models with Mathematics

April 6, 2015 Fractions

# Mindful About Math Education

Ideas from research and practice for teachers and learners of mathematics, particularly in the middle grades.

## Monday, March 23, 2015

## Thursday, September 4, 2014

### Growth Mindset in Teaching and Learning Mathematics

Since I first posted about mindset research in 2010 there has been much discussion and application of this in relation to mathematics teaching and learning so I figured I'd update things with new references. One of the most impressive efforts is that of mathematics teacher Helen Hindle who has created Growth Mindset Mathematics that's chock full of great information and lesson activities! Jo Boaler, mathematics educator at Stanford, has written extensively about mindset and mathematics and has an online course about mathematics learning built around the idea of having a growth mindset. And the research base has continued to grow including this 2014 study showing positive impacts on student achievement after a 30-minute online intervention. Finally, this TEDx Talk by Eduardo Briceno about Growth Mindset gives a great framing of this concept and how it can powerfully drive learning.

## Wednesday, July 23, 2014

### Misconceptions in Mathematics and Diagnostic Teaching

With the adoption of new standards for learning mathematics that place an emphasis on building students' conceptual understanding and using that to inform their development of procedural knowledge, there is a need for teachers to develop skills in uncovering students' thinking and providing opportunities to address misconceptions. This article by Elizabeth Green in the New York Times offers a thorough look at the changes being called for: "Why Do Americans Stink at Math?"

The following set of resources offer some good ideas to start approaching mathematics teaching conceptually by eliciting and building from students' thinking:

Diagnostic Teaching for Grades 6 and 7 (set of 12 problems and accompanying teacher materials)

How Do My Students Think? Diagnosing Student Thinking (research-based guide for teachers)

Learning from Mistakes and Misconceptions PD (slides and guide)

Gaps and Misconceptions in Maths (focuses on subtraction, division, and fractions)

Mathematics Assessment Probes (first chapter of

Chelsea Diagnostic Mathematics Tests (scanned versions of a book of diagnostic assessment from 1984)

Eliciting Mathematics Misconceptions (blog with two videos about fraction misconceptions)

The following set of resources offer some good ideas to start approaching mathematics teaching conceptually by eliciting and building from students' thinking:

Diagnostic Teaching for Grades 6 and 7 (set of 12 problems and accompanying teacher materials)

How Do My Students Think? Diagnosing Student Thinking (research-based guide for teachers)

Learning from Mistakes and Misconceptions PD (slides and guide)

Gaps and Misconceptions in Maths (focuses on subtraction, division, and fractions)

Mathematics Assessment Probes (first chapter of

*Uncovering Student Thinking in Mathematics, Grades K-5*)*Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-12*(free sample chapters)Chelsea Diagnostic Mathematics Tests (scanned versions of a book of diagnostic assessment from 1984)

Eliciting Mathematics Misconceptions (blog with two videos about fraction misconceptions)

## Tuesday, May 13, 2014

### Ideas for Mathematics Education Courses

The ideas in the spreadsheet below came from conversations with mathematics education faculty in the California State University system. It's far from a comprehensive list but is at least a start! You can add your ideas using this form.

## Monday, April 14, 2014

### Technology that Supports Meaningful Mathematics Learning

At the NCTM Annual Meeting in New Orleans last week I had the chance to talk briefly with a few folks about their use of technology that supports meaningful mathematics learning. Some criteria we agreed were important to keep in mind when deciding whether to use technology and, if so, which technology, included:

- Helps students see things differently (within constraints - e.g. microworlds)
- Is simple to use but promotes deep cognition/challenge
- Gives students better access to concepts (reduce/remove barriers)
- Allows students to connect mathematics to aspects of their culture/community
- Puts students into the role of creators rather than consumers of knowledge

## Friday, February 14, 2014

### Piloting Smarter Balanced in California in Spring 2014

I was asked recently by some colleagues for details about California's piloting of the Smarter Balanced assessment in spring 2014 and thought others might find the information I compiled helpful. Feel free to add comments/clarifications. And if you spot any outright misstatements, certainly let me know!

This Politico storyfrom Dec 2013 details some of the challenges with online assessments. And this interactive graphic tells the story of
Indiana’s experience with online tests last spring (led by McGraw Hill, not
Pearson as in CA).

As best I understand it, the Field Test in California in spring 2014 will be only computer-based and non-adaptive (each student gets a fixed
set of items) for the purpose of testing out item validity and
reliability. From the 2015-16 school year, the online assessments will be
adaptive (with a student’s response on one item determining what item they get
next). Also, from 2015-16 for a total of three years there will be a
paper-based version of the assessment (non-adaptive with scores somehow equated
to the online, adaptive tests) for schools that lack the technology to conduct
the test online. There is a Technology Readiness Tool each district is
supposed to use to gauge their capacity to support students’ access to the
assessments:

Students will either use computers with a mouse or other
point-and-click device OR a tablet device with touchscreen. Each device must
have the Smarter Balanced secure browser installed
to be used for testing. Specific technology requirements are found here
(along with other field test information).

Students are permitted to have access to certain tools, both
embedded within the secure browser, and non-embedded. This includes
scratch paper on which to do mathematical work and, from grade 6, graph
paper. Any scratch work is to be discarded after the test and is not used
for scoring purposes. The full list of tools is here but note each state
may make modifications to this.

## Thursday, October 11, 2012

### NCTM Dallas Regional Presentation

This is a quick post to share the slides from my presentation today on Common Core Standards for Mathematics Practice at the NCTM Regional Conference in Dallas. I'll update later with more details...

The presentation slides are at this link.

Update (12:45 PM 10/11/12)

The session was well-attended with about 100 folks in the room. I invited them to enter my Socrative Teacher classroom by installing the Socrative Student Clicker app before we got started. Over 30 participants did so and were able to provide input in addition to those who spoke out verbally during the session.

I was impressed with the turnout and the participation. My intent was to provide food for thought about the Common Core Standards for Mathematical Practice as well as what it means, in general, to think about teaching 21st century learners. I hope the attendees found it to be 60 minutes well-spent!

One slide I didn't have as much time to comment on as I had planned is titled "Flipping Out" and features a link to a Kahn Academy video. The point I was going to make is that if "flipping" one's classroom is simply a matter of moving lectures to homework and doing homework in class, we're not addressing the real need to transform what teaching and learning are all about. It's more than rearranging the same traditional lessons that focus primarily on skills and procedures. We need to be looking for ways to shift teaching and learning to place students' reasoning and sense making at the center of all that takes place. Two recent columns discuss this quite well (better than I am able to do!), so I encourage you to check these out:

The presentation slides are at this link.

Update (12:45 PM 10/11/12)

The session was well-attended with about 100 folks in the room. I invited them to enter my Socrative Teacher classroom by installing the Socrative Student Clicker app before we got started. Over 30 participants did so and were able to provide input in addition to those who spoke out verbally during the session.

I was impressed with the turnout and the participation. My intent was to provide food for thought about the Common Core Standards for Mathematical Practice as well as what it means, in general, to think about teaching 21st century learners. I hope the attendees found it to be 60 minutes well-spent!

One slide I didn't have as much time to comment on as I had planned is titled "Flipping Out" and features a link to a Kahn Academy video. The point I was going to make is that if "flipping" one's classroom is simply a matter of moving lectures to homework and doing homework in class, we're not addressing the real need to transform what teaching and learning are all about. It's more than rearranging the same traditional lessons that focus primarily on skills and procedures. We need to be looking for ways to shift teaching and learning to place students' reasoning and sense making at the center of all that takes place. Two recent columns discuss this quite well (better than I am able to do!), so I encourage you to check these out:

- NCTM President Linda Gojak, "To Flip or Not to Flip: That is NOT the Question"
- Teacher and Blogger Shelly Wright, "Why I Gave Up Flipped Instruction"

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