Balanced Mathematics FAQ
What is it?
Balanced Mathematics is a differentiated instructional strategy designed to enhance student attitudes towards mathematics and to develop high-level thinking, problem-solving and communication skills.
Where does it come from?
Lee Sparling, a teacher with the SCDSB, developed the Balanced Math Program to create a cooperative learning math community and improve student knowledge and overall understanding. She designed the program with the same ‘balanced’ approach that has been implemented in literacy programs, now referred to as comprehensive literacy. Lee authored a teacher resource called Balanced Mathematics in 2005 to help teachers bring the program into their classrooms.
Over the past several years, the fundamental components of Lee’s program have remained while each has evolved to integrate the SCDSBs essential practices of open questions, parallel tasks, technology enabled learning and teaching through the math processes. Furthermore, the assessment for each component has evolved with our implementation of Growing Success and focused efforts on using a variety of assessment practices to offer students our most current understanding of timely and effective feedback. It is our hope that this program will continue to evolve through teacher input as research and practice lead us to a deeper understanding of student learning.
Who is it targeted to?
The original text was written to support students in Grades 2-5, but we have worked with teachers over the past several years to adapt the program for Grades 1, 6-8 and beyond. Based on the skill sets of Gr. 1 students, full integration of the balanced math centred approach to programming may be more challenging. In the Grade 1 classroom, components of balanced math can be integrated into whole group settings, such as math journals, facts and games, or it can implemented with a “bucket” approach with familiar activities and rotating content. An example of this approach might be five buckets or bins, one per strand, with a math activity in each (counting in one, patterning in another, sorting in a third, etc.). Another example is a consistent activity in each bucket/bin that students learn how to do independently and which relates to the current unit of study. The change each week would not be the activity but the material which is based on current or recent learning goals (a math word wall activity, a matching game, picture & word math journal, etc.)
A unique adaptation for the Intermediate division includes a 100-minute, once per week approach to centres with students choosing activities they’d like to do to acquire the day’s learning goal followed by a journal entry demonstrating their progress.
What does it look like?
Math Journal – Students work independently to explain, respond to other students and justify their own thinking about mathematical concepts and ideas. Using math word walls and personal math dictionaries, students build their mathematical vocabulary, make personal connections to the math content and develop their reflective thinking skills. This leads to a more comprehensive understanding of mathematical concepts. An example might be to ask a student to compare his/her work to the Bump It Up board and to reflect on strengths and next steps. A Bump It Up board consists of student work samples at levels 2, 3, and 4 that have been moderated with students. Between each work sample is an arrow or link that describes how to “bump up” from a level 2 to a 3, and a level 3 to a 4. Journal questions can be used to assess understanding of a concept or to assess readiness and prior knowledge.
Math Games – Students in this group cooperatively play a game that has an underlying math concept. In this group, students develop communication skills as well as strategic thinking skills. Students have fun while constructing and internalizing critical mathematics concepts.
Math Facts – Student knowledge of addition/subtraction and multiplication/division facts is critical, however it is difficult to schedule time in math programs to focus strictly on these facts. Students have a consistent and on-going opportunity to build their knowledge and skills while learning and practicing the basic math facts. The intent of the Math Facts group is to ‘drill’ for the use of strategies rather than to drill for memorization.
Independent Problem-solving – This provides students with an opportunity to apply their knowledge and understanding of mathematical concepts that have already been taught – and possibly assessed – through the 3-part lesson. We know that students acquire knowledge and understanding at different rates, and this provides students who consolidate their understanding post “assessment of learning” with yet one more opportunity to demonstrate this understanding. Independent problem solving provides teachers with a venue to offer their students multiple opportunities for success.
Shared Problem-solving - A small group of students work together to solve a math problem. This grouping gives students the opportunity to explore and build skills for successful problem-solving, and to take on and be responsible for specific roles within a group context. It promotes team work and communication while building individual confidence. Participating regularly encourages students to actively contribute ideas, and to listen to and respect the ideas of others. Problems offered might be challenging higher order thinking problems related to the current or prior unit of study, or problems planned as a diagnostic of student understanding prior to the start of a new unit. At the end of the full rotation groups consolidate their understanding through the sharing of their solutions in an oral presentation called “Share the Wealth”. These sessions invite students to compare and discuss their solutions with the rest of the class, similar to the math congress or BANSHO.
Guided Math This is an opportunity for teachers to focus on a key math concepts with a small group of students. Focus may be on a mathematical process, a challenging concept, assessment prep, exploring a new manipulative, etc. It provides opportunities for the teacher to interact with each student in the classroom on a regular basis and to gain a better sense of individual student understanding.
Why do it?
· Increased student engagement through math games and collaborative
learning teams
· Student choice: differentiated activities & products based on ability
level
· Increased collaborative and independent problem-solving skills
· Increased ability to communicate in math
· Improvement in student attitudes towards mathematics…"Math is fun!"
· Students become more confident to take risks and approach
problems
· Gains for higher needs students who learn best with guided practice
· Multiple opportunities for students to demonstrate their understanding (We know that students consolidate their understanding at different rates; therefore, we work to offer multiple opportunities for success. Independent tasks such as problem solving and math journals are typically based on ‘learned’ skills/expectations. For example, these rotations most often relate to the math strand or expectation most recently assessed, thus these activities provide students with one more chance to demonstrate their understanding.)
Does it take the place of my current math program?
No. It is important to note that this program does not take the place of, but rather supplements, your 3-part math lesson. Therefore, you must have an allotment of 100-min. for numeracy instruction on most days of the week. These minutes need not be consecutive as Balanced Math can stand alone within a 25-30 minute block. It’s the ‘reward’ that students will look forward to in your math program because it’s essentially student-directed. Kids get to play, collaborate, communicate, and enjoy some direct attention from you in guided math.
How would I fit it in?
Each rotation takes approximately 20-30 minutes and can be included in your math block or inserted somewhere else in your daily schedule. It’s supplementary to your regular math lesson, so you have some leeway. Although consistency is important for the success of any classroom programming, if you’re short on time one day, it’s an easy program to bump to the following day. Conversely, you may find that you get in your BM rotation as opposed to your regular math lesson on a day you’re crunched for time because it only requires a short block. A common way to schedule BM is to follow your 3-part lesson (students will be motivated to do so as they will look forward to BM) with a rotation. Students who finish early can work on a BM extension, or follow-up task to that day’s math lesson. Ideally, all students will be engaged in a math task for the entire block.
How long is it going to take me to plan?
In the beginning, it may take you an hour per week. Once you’ve planned a few rotations, and get comfortable with accessing your resources, you’ll likely plan and prepare rotations in 30-45 min. max. For this planning, you’ll have 5 days of rotations completed that are targeted to the needs of each of your learners, and much less to plan for yourself or a supply teacher during the week.
Where do I go for help?
You can access detailed information about the Balanced Math program as well as links to planning resources and sample rotations on our wikispace at http://tllpbalancedmath.wikispaces.com/.