Monday, February 25, 2013

Follow up to WGBH post - Mathematics Videos

In January I blogged about WGBH resources that will be an integral part of the Edwin Teaching and Learning system Digital Library of resources. As a follow up I wanted to share a some videos that could be used to pique student interest in the beauty of mathematics.

 If a "picture paints a thousands words" what is the video equivalent? 

Patterns and symmetry with numbers.

From the World Science Festival, " a production of the Science Festival Foundation, a 501(c)(3) non-profit organization headquartered in New York City." 
Beat-boxing and STEM?

Also from  World Science Festival is a series of conversations, more suitable for teachers and perhaps high school students - here are just two.

Creative Math: The Heart of Something Complicated

Can Math Be Beautiful?

Monday, February 18, 2013

Algebra in the MA Model Pathways

I recommend reading Rick Hess' February 11, 2013 blog, " Straight Up Conversation: Common Core Guru Jason Zimba

Of particular note is the discussion as to when algebra is addressed in common core math standards:
RH: How do you respond to critics who have argued that one problem with the math standards is that they don't address algebra until high school? 
JZ: It is incorrect to say that algebra isn't covered until high school. There is a great deal of algebra in the 8th grade standards. For example, students in grade 8 are expected to solve two simultaneous equations with two unknowns. I don't see a lack of rigor there. The standards actually invest heavily in algebra because of the way they focus so strongly on the prerequisites for algebra in the elementary grades.
I actually think the questions about algebra are better formulated as questions about acceleration. How will kids who are ready for advanced work accelerate to reach courses like calculus during high school? But those are questions for policy, not for standards. The standards don't speak to this issue. Decisions about acceleration and ability grouping are still the purview of local districts, just as they've always been. For example, I've seen where the state of Massachusetts has provided some interesting guidance for districts showing several different models for acceleration, all of them ending at calculus in the senior year of high school.

Details about ESE model pathways are presented in the full DESE frameworks document. Additionally the Making Decisions about Course Sequences and the New Model Algebra I Course document provides "information and resources to ground discussions and decision-making in three inter-related  areas of consideration:
• the increased rigor of both the grade 8 and Algebra I standards;
• the offering of high school mathematics (Algebra I) in middle school to students for which it is
appropriate; and
• options for high school pathways that accelerate starting in grade 9 to allow students to reach advanced
mathematics courses such as Calculus by grade 12."

ESE has also made available an Enhanced High School Pathway to Calculus document which "presents as a proof of concept that it is possible to accelerate students starting in grade 9 to reach Calculus by grade 12, without “doubling up” to take multiple math courses in any given year. Please note that the Enhanced Pathway has not been approved by the Board of  Elementary and Secondary Education and is not officially part of the Massachusetts Curriculum Framework for Mathematics. It is provided as a resource to assist district planning and curriculum development."

Monday, February 11, 2013


I recommend "What’s All This Talk about Rigor?" a recent post from NCTM President Linda M. Gojak in NCTM Summing Up, February 5, 2013 found at

Of note is Linda's comment that "The word “rigor” is widely used in policy discussions, but it’s rarely understood or defined, and often it merely passes as code for “better.” It is interesting that the term “rigor” does not appear in the Common Core State Standards for Mathematics, although it is certainly implied."   In the Massachusetts Curriculum Frameworks for Mathematics ( the word rigor appears several times.

Pages 3 and 4 Introduction
  •  "As specified by CCSSO and NGA, the standards are (1) research- and evidence-based, (2) aligned with college and work expectations, (3) rigorous, and (4) internationally benchmarked."
  • "A stronger middle school progression includes new and rigorous grade 8 standards that encompass some standards covered in the 2000 Algebra I course."
Page 105 Introduction: High School Content Standards/MODEL PATHWAYS AND MODEL COURSES 
  •  "The 2011 grade 8 standards are rigorous; students are expected to learn about linear relationships and equations to begin the study of functions and compare rational and irrational numbers. In addition, the statistics presented in the grade 8 standards are more sophisticated and include connecting linear relations with the representation of bivariate data. The Model Algebra I and Model Mathematics I courses progress from these concepts and skills, and focus on quadratic and exponential functions. Thus, the 2011 Model Algebra I course is a more advanced course than the Algebra I course identified in the 2000 Massachusetts Curriculum Framework for Mathematics. Likewise, the Model Mathematics I course is also designed to follow the more rigorous 2011 grade 8 standards."
Page 169 English Language Learners 
  • "The Common Core State Standards for English language arts (ELA) articulate rigorous grade-level expectations in the areas of speaking, listening, reading, and writing to prepare all students to be college and career ready, including English language learners."
Page 171 Students with Disabilites 
  • "The Common Core State Standards articulate rigorous grade-level expectations in the areas of mathematics and English language arts."
  • "These common standards provide an historic opportunity to improve access to rigorous academic content standards for students with disabilities."
  • "These supports and accommodations should ensure that students receive access to multiple means of learning and opportunities to demonstrate knowledge, but at the same time retain the rigor and high expectations of the Common Core State Standards."
An ESE Exploration Activity: Connecting the Standards for Mathematical Practice to the Content Standards was written to investigate the rigor in the new MA frameworks.

Other resources on rigor that of interest may also be found at:

What’s rigor and why is it so important? blog post
Rigor and Relevance Frameworks resources

Wednesday, February 6, 2013

ESE Offering Curriculum Alignment & Mapping Series

New Series on Curriculum Alignment & Mapping:
ESE, in partnership with the Governor's Readiness Centers, has developed a new series on curriculum mapping as a core tool for communicating about and aligning curriculum and instruction across grades, subject areas, and schools. During the series, which includes two webinars, a two-day summer institute, and follow-up activities, participants will discuss the status of curriculum mapping in their districts, gain access to exemplary models and other support resources, and use guided planning time to take their curriculum planning to the next level. The series will launch with an introductory webinar scheduled in early March (Thursday, March 7 from 9-10 a.m. or 1-2 p.m., or Friday, March 8 from 1-2 p.m.). To register for the introductory webinar, go to
The complete series, which is funded by a Race to the Top grant, will include:
•           Webinar 1: Introduction (March 7 and 8)
•           Webinar 2: Mapping Common Core Shifts in ELA, Math, or History (May/June)
•           Summer Institute: Guided Team Time (2-day regional institutes, June/July)
•           Webinar 3: Sharing Examples (Fall 2013)
•           Session at 6th Annual ESE Curriculum & Instruction Summit (Nov. 6 or 7, 2013)
•           Wiki with examples and other resources
•           Coaching Support
Curriculum mapping, webinars, institutes, and resources will be made available to all MA public school districts.