Wednesday, December 26, 2012

Recently Released Draft Model Curriculum Units (Prototypes)

The DESE Center for Curriculum and Instruction's mission is to:

"help schools, districts, and organizational partners build capacity to engage all students in learning to meet rigorous expectations" 

In order to support schools implementation of the new curriculum frameworks they have released a protoype/draft model curriculum units. The mathematics unit is: Grade 6 Ratios and Rates which I have included here and can be found on-line as well (with units for ELA, Social Studies and Science) and other DESE resources at

Released: 4 Draft Model Curriculum Units (Prototypes)
Through the Race to the Top Initiative, teams of educators from across the state will develop more than 100 pre-k to grade 12 model curriculum units in English language arts and literacy, history/social science, mathematics, and science and technology/engineering. Four of these draft model curriculum units are now released to the public and all districts for try-out and feedback, they include:

Wednesday, December 12, 2012

MCAS Transitions Webinar REPEAT DATE Wednesday January 23, 2013 11am-12pm EST


January 23th,  2013, 11:00am - 12:00 pm

Transitions in Mathematics MCAS 2013
Offered in conjunction with the ESE Commissioner’s District Math Network

In 2013, the MCAS mathematics tests will be assessing the new 2011 Massachusetts Curriculum Framework for Mathematics. There are many changes and challenges ahead. The transition plans and assessable standards lists are posted on the ESE assessment website, but you might like further information to understand how the MCAS tests are changing for grades 3-8 and how the Grade 10 test is essentially remaining unchanged.

Topics in this DSAC webinar include:
Challenges inherent in transitioning the Grade 10 MCAS mathematics test
Differences in the transition plan for the MCAS mathematics tests in grades 3-8
Details on how the “assessable standards” lists were determined
Understanding what “assessable” means

If you would like to attend this webinar please contact me, Norma Gordon, via email:       


Saturday, December 1, 2012

Resource sharing and Mathematics UDL

Blogger, Twitter, Scoop-it, Pinterest, Tumblr. Which are you following? Using? I intend to selectively share resources related to GB DSAC districts' initiatives. My twitter feed (see link to the right) will include these and other resources "as I find them".

This week's resources align to the three principals of Universal Design for Learning (UDL) the foundation for supporting robust tier 1 instruction used in many GB DSAC schools and districts.
Provide Multiple Means of Representation

Use to represent (mathematics) vocabulary. Here is an example for "equation"
source: "equation" in

Provide Multiple Means of Action and Expression

Consider offering student assignment "menus"with directions such as, "Choose a variety of activities from the menu below. The activities must total at least ____ points. Place a checkmark next to each box to show which activities you will complete". Examples can be found here,

Provide Multiple Means of Engagement 

Use the TED talks (beta) site for education. Mathematics lessons are at I recommend this engaging Ted-Ed on estimation using powers of 10. Make sure you follow the lesson links for assessing (Think) and extending (Dig Deeper).

Sunday, November 25, 2012


Take a minute to look at this sample assessment question:

 source: pages 56-58

MCAS? PARCC?   It is neither. This is a grade 6-8, language of mathematics sample item from, ACCESS for ELLs® Listening, Reading, Writing, and Speaking. WIDA (World-Class Instructional Design and Assessment. Can you recognize Standards for Mathematical Practice #1, Make sense of problems and perservere in solving them, embedded in this sample question? Last week I asked if grade level teachers are having converstations, this week's I am encouraging ELL and mathematics teacher dialog. I highly recommend looking at "useful conceptualizations of the language practices embedded within the Standards for Mathematical Practice" on pages 20-25 of the Framework for English Language Proficiency Development Standards corresponding to the Common Core State Standards and the Next Generation Science Standards at

The question now might be, MCAS? PARCC? WIDA? Curriculum allignment? Where do we focus our efforts? I propose that instead of dividing time and resources step back and identify the commonalities. One framework to faciliate alligning efforts could be the Massachusetts Tiered Systems of Support (MTSS). The MTSS blueprint outlines "a single system of supports that is responsive to the academica and non-academic needs of all students." Information and resources can be found at  I welcome your comments and thoughts about this!

Thursday, November 22, 2012

PARCC updates Mathematics Content Frameworks

Version 3.0 November 2012

Updated document now available 
Full PDF


PARCC Frameworks Browsers  to access and search online versions of the Model Content - Mathematics Frameworks.

Changes from earlier version are highlighted in this document

Thursday, November 8, 2012

Are your teachers having (math content) conversations?

Last week I suggested you could use the K-8 crosswalks, and create a “sidewalk” with your school or district’s 2012 MCAS test item analysis report. 

Here is an example using from the 2012 Grade 8 MCAS mathematics test.

Question #1 Multiple Choice
Reporting Category: Patterns, Relations, and Algebra(2001/4) Standard: 8.P.9 - Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. (Note: This standard is intentionally the same as 7.P.6.)

A cooking instructor stated that 5 pounds of roast beef is needed to serve 8 people. Based on the instructor’s statement, which of the following equations can be used to find r, the number of pounds of roast beef needed to serve 12 people?

The MCAS test item analysis report does not map this question directly to a new standard however if your students did not perform well on the question it still warrants consideration. Proportional reasoning and the ability to use multiple representations (words and equations or equivalent equations) are foundational concepts in mathematics.   A search in the crosswalks document for 8.P.9 brings up cross references to several new 7th and 8th grade standards. Furthermore you might see that this specifc test question most closely relates to, 7.RP.2c Represent proportional relationships by equations and 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.   So my question is, “Are your 7th and 8th grade math teachers having conversations?”

This is just one example and over the next weeks I’ll add others. Information, if you haven’t already looked, for MCAS Assessment Transition can be found at and ESE common core resources are available at

Moving forward I hope this blog becomes a forum to share our best practices so I encourage posting comments, questions and ideas. You can also reach me directly at If you use twitter, follow me @gbdsacmath for more news and resources supporting mathematics engagement, learning and excellence.

Friday, November 2, 2012

Using ESE School Profiles and EDW School Test Item Analysis Summaries
Did our students learn the [mathematics] content we wanted them to learn?
Why do we think this happened or didn’t happen?*
Do these questions come up in your instructional leadership, coaching, or team meetings?  To facilitate a data-rich dialog a place to start might be your school’s 2012 MCAS test item analysis report.  The report provides:
 - “live” links to the released MSAC question(s)
- school to district comparisons
-  a “sidewalk” connecting 2000/2004 and 2011 standards.
Here is one route to your school’s data.
     Using the pull down menus select, School (the default is district), any grade from your school (the default is grade 10) and Mathematics (the default is ELA) select (click) on the orange arrow.
    Next, scroll the list of schools (alphabetical by town) and select (click) your school. From here navigate using the left side “menu” to view content and grades results.
These reports are accessible to the public. A school can also obtain the information from ESE’s Education Data Warehouse (EDW). Depending on your school/district there may be one or several individuals with access.  If you have access, then the EDW report is IT401 (school level data) or IT301 (district level data). Advantages to EDW reports are additional details, for example standards by domain and cluster  and that data can be sorted by cluster, domain, question type, etc.
 Did our students learn the [mathematics] content we want them to learn?
Why do we think this happened or didn’t happen?*
Now you can begin to address these questions. Perhaps the team can:

      -   Identify strengths and weakness by question type or content.
-    Dig deeper into student learning.  For example, obtain formative information by analyzing common student errors.
-    Have richer conversation by using the “sidewalk” in tandem with K-8 crosswalks,, to inform curriculum framework grade shifts and highlight potential trouble spots.  If this last suggestion sounds intriguing then make sure to check my blog next week for more details!

  *Adapted from Small Steps, Big Changes: Eight Essential Practices for Transforming Schools Through Mathematics, Chris Confer and Marco Ramirez 2012 Steinhouse Publishers

Tuesday, October 23, 2012


Welcome the the Greater Boston DSAC Mathematics blog. Please check back soon for commentary and resources to support students' learning and achievement in mathematics.