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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 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
Resources that reflect some number of these criteria were shared in a Google Form, the results of which are below.  These represent the specific interests of the group I was talking with and the list is of course not comprehensive.  If you'd like to contribute additional resources, the form is here.

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!

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.

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).