Tuesday, February 3, 2015

Mathematics at BVP

Today is day two of our blog series all about academics

Mathematics is at the heart of a spirited national conversation of late. Anyone who engages in the topic of parenting, kids, and schools on social media has undoubtedly seen otherwise simple arithmetic problems morph into political debates about the content and methods scholars should learn. 

The discourse is lively, and there’s one sentiment that tends to surface with frequency: I didn’t learn it this way, and I turned out fine. 

For some, that is accurate. However, there is a tremendous amount of work to be done when it comes to closing the scientific and high-tech job gap. The education many of us received in the 70s, 80s, and 90s is not the education that will drive our scholars and national economy in years to come.

We at BVP believe that, in order to be competitive in a growing and increasingly inter-connected world, all scholars must possess a strong understanding of mathematics, including the ability to reason logically, attack problems from multiple directions, and solve problems out of context.
Nationally, we are not currently meeting this goal.  According to Achieve, Inc., an American 8th grader who successfully meets expectations will end the year two years behind his or her peers in other countries[1].  One reason underlying our country’s low results is the lack of coherence in our math curricula.  Instead of focusing on a core set of ideas, American schools have historically created endless lists of skills and topics we want scholars to master.  This approach can be referred to as going, “a mile wide, an inch deep.”[2]
We are preparing all scholars for at least one Advanced Placement (AP) mathematics class--calculus or statistics--by the point of graduation from Blackstone Valley Prep. We firmly believe that a strong mathematical foundation serves all scholars on their path to college regardless of their career aspirations.
At Blackstone Valley Prep, the following pillars drive our mathematics classrooms:
1.       Speed
It is no longer good enough to only solve problems.  The length of time a scholar takes to solve a problem is equally important.  This is especially true of simple mathematical operations that scholars are expected to complete from memory.  We set goals around speed at each grade level, and lessons continuously reinforce the importance of completing work with urgency.  All scholars are expected to spend 2,000 minutes annually practicing basic facts outside of the mathematics classroom. (Note: we’ll talk more about how time--what we do with all that extra time, and how it still isn’t enough--in an upcoming entry. Follow the blog to get it first!)
2.      Balance
Accuracy and process matter; it isn’t enough to have the right answer. Scholars have to be able to defend their pathway to that answer.  
3.      Multiple Paths
We are always pushing our scholars to be critical thinkers.  As a result, scholars are regularly expected to solve problems more than one way as part of their mathematical development. Scholars compare different methods and determine which one is the best way to solve a problem, focusing on efficiency and reliability of the method.
4.      Intentional Struggle
Scholars are too often given all of the tools to solve problems up front, being told by the teacher how to solve a problem and what strategy to use.  We intentionally allow our scholars to struggle with problems (the good kind of struggle, not the overwhelming kind).  This allows our scholars to develop all of the skills necessary to solve unfamiliar problems and tackle higher-level mathematics, and it reinforces our value of perseverance.
5.      Real World Application
We all remember the word problems that focused on the shadow cast by a tree, or trains leaving stations, or someone buying 489 apples. As much as they aspired to real world application, they fell a bit short. We aim to improve upon that.

All skills must be connected to tasks or scenarios in the world. Skills are combined together to solve single, multi-step problems that involve drawing on knowledge from other contents in addition to mathematics.  Scholars are expected to be able to identify the skills needed to solve a problem on their own and then employ the skills in coming to an answer.

The next segment of this series focuses on English Language Arts (ELA) instruction at BVP. We hope you will continue following! Engage with us through comments, questions, and shares, and please take this opportunity to shout out topics you’d like to see highlighted in future blog series.

[1] Math Works: Achieve, Inc., 2013

[2] William Schmidt, 2002

By Kate Crowe and Drew Madden


  1. If these are the things you are focusing on, what are you NOT focusing on? In particular, your focus on speed seems inconsistent with what follows. When speed conflicts with multiple processes and struggle, which wins out?

    1. Hey Tom,

      Thanks for the important question. I will take your question in two parts. In terms of what we are not focusing on, we have greatly narrowed our curriculum from what it was in past years. In the past, we have devoted a lot of time to scholars memorizing many mathematical facts, which is no longer a major focus (except in specific areas I will address in a moment). Another example is we previously spent up to a third of our year on geometric concepts at the middle school level, covering everything from basic shapes to coordinate planes to nets of 3-D figures. In reaction to the thoughtful pushes of the Common Core State Standards, we have distilled each grade level into a single focus that strings vertically across grades.

      In terms of your second question about the apparent conflict of speed and multiple paths or struggle, I actually see them as working in concert together. We have specific fluency goals for each grade level (some from the Common Core, some our own) where speed is key. These goals are focused on concepts scholars were expected to master over previous years and should now be able to do quickly. This is the one area where memorization is still emphasized with important concepts, such as multiplication facts.

      Our focus on multiple paths and struggle are intended for new concepts when they are first introduced or when pairing concepts together (especially struggle). For instance, when working with addition, we teach scholars multiple methods, such as number bonds, number lines, and the standard algorithm, among others. Our expectation is that scholars become comfortable toggling between methods, but eventually will gravitate to a single preferred method that is best for them and that allows them to begin to solve problems with speed.

      Here at BVP, our core pillar of more time is very important to our ability to balance these different focal areas in mathematics. Through our extended school day, we have a minimum of 90 minutes of math instruction per day K-8. Each block is broken into four parts (fluency, skill mini-lesson, concept review, and problem solving) and each part has a different focus.

      I’m always happy to talk further and you are more than welcome to come by and see our math curriculum in action. Thanks for commenting!

      Drew Madden, Associate Director, Curriculum, Instruction, and Assessment

  2. Do you develop your own curriculum at BVP; or do you use one of the scripted Common Core-aligned versions (and if so, which one)? I have been curious about this for quite some time, so thank you for posting this blog!

  3. Jeanne - thanks for the great question here and on the other thread. Drew and/or Kate can get back to you with a more detailed answer if you need it, but the short answer is that for the most part we build our our assessments and long-term plans and teachers, often collaboratively, build lesson plans. All of these plans are informed by backwards-mapping from standards and their related tasks along with released items. We pull resources and materials from all over the place (much of what we use is borrowed). Some favorite sources include http://achievethecore.org/ http://coretaskproject.com/ https://www.engageny.org/ http://www.achieve.org/ and of course http://www.corestandards.org/.

  4. Thank you for responding. This is what I had thought, and IMO it makes much more sense to do it this way rather than having to depend on a single source for one-size-fits-all scripted instruction.