Monday, December 22, 2014

English Language Learners and Math

The language demands of the 2011 Massachusetts Curriculum Framework for Mathematics leave many math teachers wondering about how to best serve their English Language Learners.  The following EdSource article highlights strategies of teaching English Language Learners (ELLs) in the math classroom.  The author stresses the importance of group work and connects each mathematical concept to the real world.  Teaching English Learners the Language of Math is written by a 7th grade math teacher in Oakland and focuses on the importance of interaction in the math classroom.

Looking for a more local resource? The Office of English Language Acquisition and Academic Achievement (OELAAA) unit at DESE has begun the process of creating 10 Model Curriculum Units (MCUs) that are ELL specific.  All of the units will be under the broad theme of social justice, and will be linked in some way to an existing MCU.  Local Greater Boston districts are taking the lead on creating various math and science MCUs.  The goal is to have the units completed by the end of the 2015 summer with the pilots starting in September.

Our final resource focuses more specifically on the power of starting math class with an application problem.  The author, Liana Heitin, channels Dan Meyer when recommending that math class begin with a word problem that is rooted in an image or a video.  Making Math Word Problems More Accessible speaks to the difficultly that many ELLs have with word problems and suggests ways of addressing this challenge.

Monday, December 15, 2014

Focus on First Grade Fluency

A few months ago, I posted about early numeracy without focusing on a specific early elementary grade level.  This week, I decided to narrow the focus on first grade.  We'll start with a resource out of the Department of Elementary and Secondary Education.  Did you know that many of the Model Curriculum Units (MCUs) now come with videos of the MCUs in action? The 1st grade unit, 'Math Detectives! Using Properties of Operations to Find Change Unknown' has an excellent video of the MCU in action!

Our second video comes from the 'Great Kids Milestones' website.  This site is an excellent resource for both schools and parents.  It offers a collection of videos for grades K-5 and walks you through grade level standards in writing, reading and math.  I am including the video, How Easily Does Your 1st Grader Add and Subtract?

Our final resource is the article, Responding to Critics of the Common Core Math in the Elementary Grades.  This article takes the three most widely used criticisms of the math Common Core State Standards and explains why the critiques are not valid.  The first criticism is surrounding a highly debated 1st grade math standard.  The standard (1.OA.C.6) requires students to demonstrate fluency when working with numbers within 20.  The authors do an excellent job of explaining why this standard is cognitively complex yet grade level appropriate.

Monday, December 8, 2014

Edwin: A Way to Integrate Initiatives

I attended the Edwin roadshow both last year and this year and have been very impressed with the progression of this tool.  Many kinks have been ironed out and Edwin can now truly be considered a one-stop shop.  When utilized fully, Edwin can be a place to track DDMs, access curriculum, create and analyze both formative and summative assessments, conduct interventions, and generate data graphs.  Although most of us are very familiar with how Edwin Analytics works, Edwin Teaching and Learning has remained a mystery to many.  The intent of this week’s blog post is to demystify this tool and give you some concrete Edwin Teaching and Learning resources.

The first resource is the most traditional: ESE's Edwin Teaching and Learning website.  If you would like your district to be an active Edwin user, this is where you need to start!  The website includes nuts and bolts of SIF compliance, archived webinars, and quick overview videos.

If your district has already committed to Edwin, you have access to live webinars as well.  Here is a list of the upcoming live webinars:

·         Entering External Assessments-What Makes it Quick 12/9 at 12:00pm, 3:00pm, and 4:00pm

·         Sharing Classroom Assessments-Grouping and Intervention 12/10 at 12:00pm, 3:00pm, and 4:00pm

·         Assessment Results for Teachers-Images and Addendums 12/11 at 12:00pm, 3:00pm, and 4:00pm

Our final resource is a link to Thinkgate TV.  Thinkgate is the mastermind behind Edwin Teaching and Learning and they have taken a Khan Academy type approach to their trainings.  Thinkgate TV offers dozens of specialized tutorial videos that support Edwin Teaching and Learning users through every step of the process.  This is a brand new resource that has the potential to be extremely valuable.

Monday, November 24, 2014

How To Bring Students' Real Needs Into the Classroom

It may seem on the surface that this week's blog post does not directly connect to mathematics education, but I would argue that it does. Although all three of the following articles have the underlying theme of understanding students' non-academic needs, they link these needs to student learning and Common Core State Standards.  These resources focus on the importance of collecting input from students and serving the 'whole' child.

Our first article has been referred to a lot throughout Massachusetts over the past week.  There is a buzz about the connection between social emotional learning and Common Core. Social Emotional Skills Can Boost Common Core Implementation highlights 5 social emotional learning skills that  students need to develop in order to succeed in college and beyond.  I urge you to read this article by Maurice J. Elias and to consider explicitly teaching social emotional skills in conjunction with the Common Core State Standards.

Our next resource follows chief academic officer, Jenna Ogudipe through her own struggle of connecting equity and the Common Core State Standards. She recognizes that these two foci may be perceived as completely unrelated, but has linked them together in At the Crossroad of Equity and Common Core by shifting her our mindset.

I recently came across a fantastic KQED article that explicitly addresses race and cultural competency as a factor in student learning.  It speaks to students' desire to feel that their teachers know who they are on an individual basis and provides 6 practical tips on how to address race issues in the classroom.  Facing Race Issues In the Classroom: How To Connect With Students acknowledges the achievement gap and offers ways to combat the distressing trend.

Tuesday, November 18, 2014

Title II-B: Massachusetts Mathematics and Science Partnership Program

Are you from Cambridge, Chelsea, Everett, Framingham, Malden, Saugus, Somerville or Waltham?  If so, you are eligible for the new Massachusetts Mathematics and Science Partnership Competitive Grant!
The purpose of the program is to improve student achievement in science, technology/engineering, and mathematics (STEM) particularly in the middle school level through intensive, effective professional development activities that focus on deepening educator's knowledge of subject matter standards, disciplinary practices and student learning. This grant program is also intended to promote the advancement of District Determined Measures (DDMs) to assess student growth and inform educator development.

The Proposal due date is Monday January 26, 2015.  Feel free to check out the link for the Title II-B Grant for additional information. 

Monday, November 10, 2014

High School Mathematics

This week’s blog post is devoted to secondary mathematics.  Although the blog has centered around early numeracy in the past, higher level math has never been a specific focus.  As a former high school math teacher myself, I am always looking for relevant high school level math news and resources. 

I run a network called the Greater Boston High School Math Leaders Network.  Many of our districts have multiple elementary and middle schools where teachers and leaders can communicate with each other across schools.   Districts tend to have only one high school, and for this reason collaboration becomes much more difficult at the secondary level.  If you are interested in joining our high school network, please feel free to email me at
The majority of high schools across the state still stick to the traditional sequence of Algebra I, Geometry and Algebra II.  Some high schools are starting to see the value behind a more integrated approach to teaching mathematics.  Education Week has explored this very topic in today’s article titled, In Transition to Common Core, Some High Schools Turn to 'Integrated' Math.  If you're looking for specific modules that utilize the integrated approach, check out the Mathematics Vision Project.

Although MCAS is still being administered at the high school level, many secondary educators have been requesting PARCC resources to continue the process of shifting their instruction.  PARCC recently released a Tutorial Version of PARCC High School Mathematics Test Booklet.  The
test booklet is paper based and provides hints for every question.

Thursday, November 6, 2014

Next Generation Assessment Practice

Readers seemed to appreciate the last time I blogged about a website that organized information on next generation assessments.  An even better website has recently surfaced!  I highly recommend you check out Assessments: The Next Generation.  This website is broken down into 3-5th grade resources, 6-8th grade resources and 9-12th grade resources.  Additionally, each grade level category includes: 1) Sample Assessment Items 2) Resources by Tool 3) Resources by Topic 4) General Interactive Resource Sites 5) General Assessment Sites.

As you may already know, DESE has been organizing PARCC Practice Test Regional Sessions.  Because the first set of dates proved to be so popular, DESE has gone ahead and added two additional sessions.  One of the new sessions will be held at Revere High School on December 3rd.  This session still has space, but they are filling up quickly.  I urge you to sign up soon!

Finally, if you haven't already registered on PARCC's Educator Leader Cadre website, I highly recommend you do so.  I recently facilitated a workshop at the Curriculum and Instruction Summit and used an activity from this website.  The activity was well received by math directors, superintendents and teachers.   Very few people had heard of this valuable resource which prompted me to reference the Educator Leader Cadre website in this week's blog post.

Saturday, October 25, 2014

New MCU Grant Opportunity

Looking for an opportunity to strengthen alignment of curriculum to the MA Curriculum Frameworks? Look no more.  DESE is offering a new Model Curriculum Unit (MCU) grant! This non-competitive grant supports teams of teachers to adapt and implement selected MCU(s) and is available to district levels 3, 4, and 5.  The grant deadline is November 14th.  For further details and submission instructions, click here.

Friday, October 10, 2014

In the PARCC

Do you have questions about PARCC?  You are not alone.  This week's blog is devoted to getting you the information you need.

Let us begin with the twelve state-wide PARCC practice test regional sessions. DESE has teamed up with various Readiness Centers from across the Commonwealth to support stakeholders in exploring the online PARCC assessments.  For more information on where the sessions are taking place click here.

Planning to attend the Curriculum Summit on October 27th or 28th?  I will be leading a workshop on the Implications of PARCC Math Assessments for Math Instruction in Grades 3-8.  We will be categorizing Illustrative Mathematics tasks in order to better understand what a balanced math classroom looks like.

Did you know that PARCC has monthly Twitter Office Hours?  The first session on September 22nd was a tremendous success.  If you'd like to read the tweets from this session, you can check them out on Storify.  The next office hours session will be on October 23rd from 5:00-6:00pm.  Each month will focus on a different PARCC topic.

Thursday, October 2, 2014

Early Numeracy

I have to step a bit out of my comfort zone for this blog post.  As a former middle and high school math teacher, exploring ratios, proportions, algebra and geometry has always been less daunting than early numeracy.  Kindergarten was not where I felt most at home, but I have learned a lot from my early numeracy peers and it has become a huge part of my job and my passion.

The picture above was taken yesterday at an elementary school in Somerville.  We explored the three-legged rigor stool that balances procedural, conceptual and application.  This kindergarten teacher wanted to create a poster that she could hang on her classroom wall that demonstrated this important balance.  The poster also does an excellent job of highlighting the three aspects of numbers: quantitative, verbal and symbolic.

The Center for American Progress has made an early numeracy video defending the Common Core State Standards.  Robert Hanna, the Senior Education Policy Analyst, has broken down a particular standard that's been under fire in the video, What Would Kindergarteners Learn?

Illustrative Mathematics, the website that brings us free standard aligned math tasks, has now begun a virtual lecture series.  One of the fall lecture series is titled, Working with Number in the Elementary School Classroom.  The series includes an hour long session each month and has excellent speakers lined up!

Monday, September 22, 2014

Registration is Now Open for the 2014 STEM Summit

This year's STEM Summit will be held on October 22, 8:30am to 5:00pm at the DCU Center, Worcester. Sessions include workshops on Bootstrap, Engage with Engineering, Growing up WILD, The STEAM Engine, NASA Resources in the Commonwealth and much more!

For a full event schedule, including agenda and session descriptions, please visit:
To register, please visit:
See you in Worcester!

Friday, September 12, 2014


DESE has a new grant opportunity, the Massachusetts Mathematics and Science Partnership (MMSP), to improve student achievement in science, technology/ engineering, and mathematics (STEM). Districts and institutions of higher education may apply to collaborate in professional development opportunities that increase the subject matter knowledge and improve the standards-based instructional practices of STEM educators. To learn more about the grant, go to

The due date for the application is September 15th.  Feel free to contact Anne DeMallie at with further questions.

Additionally, you might begin hearing people use the acronym STEAM instead of STEM.  If you're curious about what it means and why this change is occurring, make sure to check out the Stem to Steam website.

Tuesday, September 2, 2014

Practice Using Online Math Tools

Many of you have been asking for on-line resources that could help prepare students to use PARCC's technology enhanced items.  Before now, I had not seen a website that offered a comprehensive list of resources.  Ohio, another state in the PARCC consortium, has created a Pearltree that organizes the resources by technology tool.  This is one of the best systematic lists of interactive online activities that I have found. 

Although the website above includes both math and literacy tools, the math tools have proven harder for the students to use.  When looking at the PARCC Lessons Learned and listening to teachers reflect on the field test, the equation editor stuck out as a particularly difficult tool.  Online calculators and rulers look like calculators and rulers that they've used in the classroom . But for many students, the equation editor might as well be written in a foreign language. 

According to DESE's Field Test Update, almost half of students (46%) reported a technology problem during the math test, compared to 31% in ELA.  Although the equation editor is a good place to start, students need to be practicing with all of these online tools.  Students might be savvy when it comes to Candy Crush or even code, but the PARCC technology may not be intuitive.  The purpose of the PARCC assessment is not to judge technological skills, but rather to gauge their subject specific knowledge.  Students must practice using the technology to remove this barrier. 

Thursday, August 28, 2014

Efficiency Does Not Always Follow a Recipe

Although answers are often set in stone in the math classroom, methods of deriving said answers can vary tremendously.  It is a common misconception that the best way to be a mathematician is to follow a uniform roadmap of steps.  In fact, giving students some flexibility in their approaches can make them grittier problem solvers.  Once multiples strategies have been shared, students can compare and critique using concrete examples.  It is critical that we allow students the opportunity to use The Standard for Mathematical Practice #3 and to debate in the math classroom.

Our first resource involves the image at the top of this post.  Students are often taught a set of steps when it comes to solving.  In this set of steps, distributing comes first.  Is this always the ‘best’ first step?  In the problem above, the student followed the traditional steps of solving and distributed first.  Wouldn’t it be more efficient to begin by multiplying both sides by the reciprocal?  Multiplying both sides by 4/3 would eliminate all messy fractions right off the bat and leave the student with a simple one step solving problem.  Different problems call for different approaches and efficiency does not always follow a recipe.  

If you haven’t already spent some time on the Open Middle website, I highly recommend that you do!  Thank you to Barbara Rappaport for reminding me just how powerful this site can be.  The notion is that every problem posted has an open middle.  That is, the beginning and end of the math problem are closed/fixed, but the middle is extremely open for interpretation.  The website includes hundreds of open middle problems organized by domain and ranging from Kindergarten to High School.

Finally, how do we assess argument in the math classroom?  I have created a rubric that specifically examines the Standard for Mathematical Practice #3: construct viable arguments and critique the reasoning of others.   Feel free to download and adapt the rubric from dropbox.

Thursday, August 21, 2014

How to Develop a Math Growth Mindset

Math ability, like IQ, should not be viewed as fixed.  I have blogged about this notion before in last November's post, Can Everyone Learn Math?  What is different about this week's post is the inclusion of resources to help students recognize themselves as capable math learners.

Why is it socially acceptable to say "I'm not a math person" or "I was never good at math growing up" when it's not socially acceptable to have the same reaction to reading?  In fact, I've never heard an adult say that they were not good at reading.  It would clearly carry different weight.  So how come we let our students, students' parents, and even co-workers claim to not be math people?  This is an issue that I come across almost every day.  Thank you to the 5 District Partnership Executive Administrator, Cove Davis, for sending me the article How to Turn Every Child Into a Math Person.

Many of you are familiar with Carol Dweck's book, Mindset.  But did you know that Dweck collaborated with computer scientists to develop resources that link video games, the growth mindset and mathematical learning together?  The proposed video games reward students for effort and perseverance when problem solving.  To learn more about this unique study, read Brain Points: A Growth Mindset Incentive Structure Boosts Persistence in an Educational Game.

Our final resource can and should be used in all math classrooms.  Jo Boaler, a professor at Stanford University, has introduced the Low Floor High Ceiling Tasks as a way to engage all levels of mathematicians.  If all students have an authentic entry point into a task, the activity is said to have a low floor.  If all students feel challenged with thought-provoking extensions, the task is said to have a high ceiling.  It is possible to create activities that offer both and give all students the ability to be mathematicians.

Wednesday, August 13, 2014

Girls Can Do Math Too!

For the first time in history, a woman has won the prestigious Fields Medal!  It was announced yesterday that Maryam Mirzakhani, a professor from Stanford University, has earned the 2014 International Medal for Outstanding Discoveries in Mathematics. Her research is absolutely fascinating and I encourage you to learn more about her work.  For details about Maryam and her proofs, please check out the following Stanford Report.

Ever heard of Danica McKellar?  No?  How about Winnie Cooper from the Wonder Years?  Now you can place her!  Danica happens to be an internationally recognized mathematician and advocate for math education.  She has written a book targeting young female mathematicians.  Take a look at Math Doesn't Suck for more information.

My final resource is not an article, a book or a famous mathematician.  It happens to be an engineering toy.  Goldie Blox is a construction toy designed for girls.  The picture above is the reason CEO, Debbie Sterling, created this product.  She decided it was time to develop and promote a toy that sparked the interest of young women.  She is committed to increasing the number of women engineers in our world and thinks that Goldie Blox can help with this incredibly important endeavor.

Tuesday, August 5, 2014

I, We, You vs. You, Y’all, We

Everybody I know who reads the New York Times felt the need to send me the article Why Do Americans Stink at Math? last week.  I reluctantly clicked on the link thinking it was going to be yet another political common core opinion piece either for or against the highly controversial standards.  I was pleasantly surprised with the article's refreshing message; it challenged our all-too-common approach in the math classroom of the "I, We, You" script.  Many successful countries ask their students to do most of their practicing outside of the classroom, while leaving the tough investigation for the precious time that the students get with their teachers.  So why do we spend so much time practicing in the United States? And what are some resources that we can use if we want to veer away from the traditional role of teacher as practice monitor? If you are curious about exploring the "You, Y'all, We" approach, take a look at some of these links below.

I can't say enough about Dan Meyer's Three-Act Math tasks. His inquiry-based approach lends itself perfectly to the "You, Y'all, We" script.  Act 1 serves as a hook where students watch an engaging video during which they formulate their own math specific questions. Act 2 requires students to work through at least one of their original questions by being provided with the important numbers and information. Finally, act three is where answers are revealed and discussed.

Teenagers across the country (and maybe even the world) have been playing the 'would you rather' game since the beginning of time. Now math teachers can leverage the power of this age-old game by using scenarios from the Would You Rather? Asking Students to Choose Their Path and Justify It website.

If you work with middle school math students, be sure to check out the PBS resource, Math at the Core: Middle School.  This website offers various videos and interactive tools that can be used to spark interest and excitement in the math classroom.  Incidentally, the advisor of this collection of resources is holding a webinar next Monday called Make Math Visual: Strategies and Resources for ELL Students. If you're interested in this webinar, register here

Friday, July 25, 2014

Dividing Fractions

I attended professional development (PD) this week entitled, Developing Proportional Thinking with Connections to Linear Algebra. The PD has inspired me to further explore the division of fractions.  How, you might ask, is the division of fractions related to proportional thinking? Well the ratio is simply a secret division problem in disguise.  The deeper your understanding of fractions (and the division of fractions in particular) the deeper you will be able to go with ratios and proportions.

Take the picture above as an example.  What we are really trying to figure out here is how many one halves fit into three fourths.  When we look at the fraction bars provided, we get a better sense of how many one half servings fit into our new total of three fourths.  This visual model offers an alternative to the commonly used 'invert and multiply' trick.  There are even more ways to divide fractions while maintaining a conceptual understanding of the mathematics involved. Take a look at the Math Playground video, How to Divide Fractions, for a glimpse into the common denominator method.

Our final resource for the week is homemade.  When we were math students we learned a rather simple trick when dividing fractions.  When given two fractions to divide, we were told to invert the second fraction and multiply straight across.  I was never told WHY this trick works every time.  Were you?  The answer is likely no.  For this reason, I felt inspired to create a ShowMe video entitled, Why Does the Invert and Multiply Trick Work? Check it out to see an algebraic proof of this childhood trick.

Thursday, July 17, 2014

Formative Assessments for the Win!

There is more and more research coming out in support of formative assessments in the math classroom.  Due to the sequential nature of mathematics, it is imperative that we as educators have data to prove when our students are ready to move on to new concepts and explorations.  The following three resources range in their uses, but all relate to formative assessment.

In a recent Formative Assessment Podcast from the Bill and Melinda Gates Foundation website, ‘College Ready’, Stephanie Emmons talks about her experience as a special educator in co-taught math classrooms in Kentucky.   This podcast is a testament to the impact that formative assessments have made as far as student ownership is concerned.    

The Dylan William book above is an excellent summer read.  William references learning targets and success criteria throughout and offers more than 50 classroom tools and techniques to support teachers and coaches in formatively assessing students.  If you'd like more information, check out the Dylan William's Website.

Many of our districts have a large English language learner (ELL) population and that population continues to grow.  Formative assessments can be used in powerful ways when working with ELLs.  The Department of Elementary and Secondary Education (DESE) is currently offering a WIDA 101 course in Taunton that focuses on the formative language assessment process.  This DESE PD Offering runs from August 4th-August 6th and is free to attend.

Thursday, July 10, 2014

How DO We Problem Solve?

Mathematical Practice #1 might be the most daunting of all the Mathematical Practices!  How can we possibly teach students to make sense of problems and persevere in solving them?  Problem solving has always been one of those skills that we know good mathematicians acquire along the way.  Are students born with these skills or can we support our young people in cultivating them?  This week we will talk about the various ways to help scaffold the art of problem solving. 
Our first resource is a quick two minute video from the Teaching Channel. In this video, instructional math coach, Audra McPhillips, shows the audience how powerful hint cards can be as a scaffolding tool.  Take a look at the video, Hint Cards.
Our second resource is an article from the Association for Middle Level Education website.  The article highlights the benefits of using a graphic organizer in the math classroom and includes samples of student work as evidence.  Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications is worth the read.
Finally, the graphic above is an example that helps students scaffold their own thinking when exploring longer denser tasks.  The DEEP acronym is a rather easy acronym to remember and acts as a self-created graphic organizer that gives students many different ways to first approach a task.  Students can start by redefining the question in their own words, by sketching a picture, by highlighting key details and evidence, or by writing out the steps using prose.  The more students practice using these tools, the less they will need the tools in the future!

Wednesday, June 25, 2014

Multiple Select Items

Multiple select items are quickly becoming the new way of assessing our students in the math classroom.  For those of us who are used to the MCAS recipe of multiple choice/short answer/open response, multiple select items will present a big change!  With multiple select questions, students have the ability to acknowledge more than one answer as correct.  Take the picture above as an example.  Both 1a. and 1c. are correct representations of the fraction 2/5.  This model makes it more difficult to guess the one correct answer and also better demonstrates what a real world dilemma might look like.  

Both PARCC and Smarter Balanced have decided to include multiple select items because being college and career ready often means representing your answer in multiple ways.  Although Massachusetts is a PARCC state, all math educators should feel free to explore the Smarter Balanced Sample Items.  They use the term non-traditional selected response items instead of multiple select and the example above is taken from their large bank of questions.

If you are wondering how to go about creating your own on-line multiple select items, I have the website for you!  Open Ed just announced a new assessment creation tool that includes multiple select response questions.  In order to use this tool, you must first set-up a free login at OpenEd.

Thursday, June 12, 2014

New and Improved PLC Website

The Professional Learning Communities Expansion Project website has received a make-over! 
If you work in a district that participates in the project, please take a few minutes to visit the website and explore the new features.  All modules come with facilitator's guides and lesson plans.  All protocols can be found under the 'tools and resources' tab.  If you were unable to attend one of the institutes, all agendas and powerpoints can be found under the 'home' tab.
Check out it out here.

Monday, June 9, 2014

Traveling Bloom's Taxonomy

Our DSAC team recently conducted a Learning Walkthrough with a focus on characteristic #9: lesson tasks and guiding questions lead students to engage in a process of application, analysis, synthesis and evaluation. The Characteristics of Standards-based Teaching and Learning can be found on DESE's website and serve as the focus of inquiry for all formal Learning Walkthroughs.  While visiting classrooms, I was reminded of the importance of traveling Bloom's Taxonomy and felt inspired to blog about it this week. 

The idea of traveling Bloom's Taxonomy was first mentioned in 1956 by psychologist Benjamin Bloom to discourage teachers from teaching only rote memorization.  With the popularization of objective-based lesson planning comes the need for action verbs at the beginning of the objective statements.  Clemson University has done an exceptional job of breaking down these action verbs into Bloom's Taxonomy Categories. 

For those of you who are looking for a more math-specific list, please check the Montemath Bloom's Taxonomy Chart that not only lists math-specific action verbs but also lists sample tasks that match said verbs.  The final missing piece is the development of solid questioning techniques that are not limiting students to lower order knowledge retrieval.  Analysis, synthesis and evaluation should not be present only in the humanities classrooms.  You have the power to bring characteristic #9 to a math classroom near you! 

Monday, June 2, 2014

Free Summer Math Opportunities

With less than a month left until the official end of the 2013-2014 school year, you must be filled with excitement and anticipation.  I wanted to devote this week’s post to summer math opportunities that don’t break the bank.  Whether you have a week, a day or even a few hours to devote to math education this summer, these resources can help guide you.

Let’s begin with a student opportunity.  Most on-line student interventions are costly.  Khan Academy is always an excellent choice but this summer our options have expanded! TenMarks is offering a free summer program for students.  The program is personalized, and is based on an upfront diagnostic assessment.  It has embedded instruction, intervention, and points and rewards to motivate.

The Department of Elementary and Secondary Education (DESE) has a number of free math PD courses for educators.  DESE's Professional Development Offerings range from understanding fractions to developing proportional thinking.

Are you part of the 5 District Partnership?  If so, there are some excellent PD opportunities for you!  The 5 District Partnership (5DP) courses are focused on Understanding by Design (UbD) with open enrollment as well as district-selected opportunities with stipends.  Check out the image above for more details and register here.

Tuesday, May 20, 2014

Discovery Before Memorization



It is easier to teach students a formula than to have them discover the formula on their own.  But no one said teaching was supposed to be easy.

Facilitating students through the discovery process takes time, patience and collaboration.  Having parents, guardians, caregivers, tutors or afterschool educators on board with the importance of discovery is absolutely necessary.  It is imperative that the teaching of the standard algorithm does not interrupt the discovery process prematurely.  Deriving a formula and/or algorithm helps build number sense and critical conceptual understanding.

As usual, I have included three varying examples in the weekly blog.  The first example is self-created and includes the two images at the beginning of the post.  Teaching multiplication through the area model/arrays can be an excellent way to build conceptual understanding prior to the memorization of the standard multiplication algorithm.  The second resource is a video taken directly from the Teaching Channel. Challenging Students to Discover Pythagoras shows one teacher’s journey through the teaching and learning of this daunting 8th grade standard.  Our final example is an article from Business Insider.  In There's a New Way of Doing Subtraction-And it's So Much Better Than How You Learned in School, Joe Weisenthal demonstrates how CCSS and number lines turn math into a road map.  He argues that in this particular case, the discovery is simpler than the memorization.

Friday, May 16, 2014

The 'Consumer Reports' of CCSS Instructional Materials, a new nonprofit launching in the fall of 2014 to publish Consumer Reports-style reviews of yearlong instructional materials, beginning with mathematics, is hoping for 10 minutes of your time to complete a short survey with these specific aims:

§  Listen for input on the criteria most important to educators when selecting instructional materials

§  Inform the development of the evaluation tool, instructional material review process and website

§  Validate’s vision, mission and 2014 goals believes that educators need high-quality instructional materials to help students attain college- and career-ready standards. It seeks to be your trusted, independent source to review instructional materials on behalf of teachers, principals, school district purchasers, state adopters/recommenders, parents and publishers. Reviews will be conducted by expert educators from across the country and published on a public website. By producing such reviews, will help educators become more informed consumers of instructional materials, leading to improved quality of materials over time as educator needs are heard.

Please complete this survey by May 30, 2014.
To show’s appreciation for your time, your name will be entered into a raffle for a $15 gift card upon successfully submitting your completed survey. The drawing will take place the first week of June.
Simply click on the link below, or cut and paste the entire URL into your browser to access the survey:

Your input is very important and will be kept strictly confidential (used only for the purposes of research for and not to be shared externally). 

If you have any questions please email

Tuesday, May 6, 2014

Math MCAS Perspectives and Pump-Ups

It is that time of year again; the time when April showers truly turn into May flowers and the time when we begin summatively assessing our 3rd-10th grade students in the math classroom.

Let’s start our weekly blog by acknowledging how far we have come with stakeholders’ perspectives on standardized testing. Catherine Gewertz, an assistant editor for Education Week, recently synthesized research and surveys that track educator, administrator and student attitudes towards assessment over time.   This fascinating article, Survey: More Teachers Think That 'Just the Right Amount' of Time Is Spent on Testing, offers many charts and graphs as quantitative evidence.

Looking for a way to pump up your students on the day of the MCAS exam?  Look no further.  These four activities offer quick ways for students to practice key math concepts from the year while simultaneously getting up, moving around and pumping blood to their brains!  The four sample activities include Function Foursquare, Pythagorean Hop Scotch, Justification Jump Rope and Rational Red Light/Green Light.  These activities are targeted to an 8th grade audience but can be changed and adapted as you see fit!  All activities have been placed in a public dropbox.

Good luck to all!  

Wednesday, April 23, 2014

Collaboration in Educator Evaluation

"More than anything, evaluation systems should be recognizing, developing, and promoting the most talented and successful educators. We need an approach to evaluation that is all about celebrating excellence, and ensuring that those who excel also thrive in their workplaces, and stay in education."
         - Member of the Massachusetts Task Force on the Evaluation of Teachers and Administrators

With DESE's Spring Convening around the corner, I felt it appropriate to post about educator evaluation.  Come join us in Marlborough, Massachusetts on May 28th and 29th to learn how many districts across the Commonwealth have approached calibration, district determined measures and student feedback.  At the core of educator evaluation is collaborative learning between teachers and administrators.  We look forward to having you as a partner! 

Linda Darling-Hammond recently published an article in American Educator that highlights the difference between teacher quality and teaching quality.  She has titled this article, One Piece of the Whole: Teacher Evaluation as Part of a Comprehensive System of Teaching and Learning.  I've come to rely on Darling-Hammond to fight the good fight.  Her desire to support continuous teacher improvement aligns with Massachusetts' five educator evaluation regulations:
  • Promote growth and development amongst leaders and teachers
  • Place student learning at the center, using multiple measure of student learning, growth, and achievement
  • Recognize excellence in teaching and leading
  • Set a high bar for professional teaching status
  • Shorten timelines for improvement
Did you know that DESE creates a monthly Education Evaluation Newsletter?  Check out this month’s ‘Implementation Spotlight’ to learn how specific schools in the Greater Boston region are focusing on giving consistent and constructive feedback.

Wednesday, April 9, 2014

English Language Learners and the Common Core

Our districts have an increasing number of English language learners (ELLs) and it is critical that we figure out the best way to address their needs.  Many questions arise as we navigate this intricate process.  Can we truly implement a Common Core aligned curriculum when working with ELLs?  How do we best train teachers who work with this population of students?  Is technology going to damage or assist in this process? This week’s blog is dedicated to exploring research and resources for English language learners in the age of Common Core State Standards.

The Institute of Education Sciences has published an educator’s practice guide entitled, Teaching Academic Content and Literacy to English Learners in Elementary and Middle School.  This guide has been recently updated since it was first published in 2007.  There are new foci on the importance of teaching academic vocabulary and writing in all subject areas.  This guide includes 'exhibits' that offer sample lessons, graphic organizers, prompts and sentence starters to use with English language learners.

Guadalupe Valdés, Amanda K. Kibler and Aída Walqui have written a Professional Paper entitled, Changes in the Expertise of ESL Professionals: Knowledge and Action in an Era of New StandardsThey have built on TESOL's work on why it's important to train ESL professionals and how to go about doing so.  This is an extremely well researched paper that focuses tremendously on the evolving role of the ESL professional.

Finally, we must address the fact that technology can and will play a large role in the education of ELLs.  We have already begun to see how PARCC and Smarter Balance intend to support ELLs.  But what does this look like in practice? In the article, English Learners Get Help with Common Core Test, KQED's Ana Tintocalis explains how California teachers have recently been using computers to help support English language learners.