Philosophy

My philosophy/pillars and the Math Practices

(None of this is original, It is all of my favorite, borrowed ideas brought together in one place.)

Math must start as experiences with concrete objects.

-Must have math tools in primary classrooms include - ten frames and counters, math rack, linking cubes, and base 10 blocks.

-Vital math experiences include counting collections that require students to build structure into their collection (starting with 10 or less and gradually gaining to over 100 items) and beaded number lines

-Related Math Practices - Students must have experiences with concrete objects in order to “Use math tools and tell why they choose them” and “Look for and make use of structure” (using 5 and 10 as an anchor and unitizing 10 and using groups of 10 and what they know about simpler facts to solve two digits problems).

Math must continue to be representational/VISUAL before moving too quickly to abstract numerals.

-Students should have visual images of quantities in their mind when solving and discussing math. This begins by including a variety of math visuals as a part of math instruction and activities. Some of my favorites are listed below. Using pictures of the tools mentioned above is also beneficial.

math visual videos

math flips

Subitizing cards

-Concrete experiences and regular use of math visuals allows students to become fluent with addition facts, some of the major work of primary level math. Here is a link for a great video that gives you an idea of the goal concerning fluency. Remember, fluency includes accuracy, speed AND FLEXIBILITY. It is the flexibility with numbers that allows students to use what they already know to make connections independently and solve challenging problems.

-Related Math Practices - Experiences with concrete objects and math visuals gives students an understanding of the structure of numbers and the flexibility to “Think about numbers in many different ways” and “Show their work in many different ways”.

-If a student is struggling with a game or task the best way to assist them is to provide a concrete math tool or encourage them to create a visual drawing to assist them in solving the problem they are working on. If you find yourself explaining a process to follow to a student it means that they do not yet have the building blocks in place to make the meaningful math connections on their own to solve the problem they are tackling.

-Review this article from YouCubed on the importance of visuals in math and this video from Build Math Minds.

Another pillar of the math classroom is Math talk.

-Training students to slow down and take the time to notice and wonder about new math situations helps them to focus more on making meaning than on just getting answers. This allows them to apply what they learn in one situation to other situations as well. (What do you notice? What do you wonder?)

-Asking students to defend their answers to a peer, to you, or to the class improves their depth of understanding and ability to make use of that information again in future problem solving. It also helps to create a classroom culture of shared learning. (How do you know? Prove it!)

Regular number sense routines allow students to make connections through repeated exposure with slowly increasing difficulty

-Number talks (regular routines to practice mental math) and Number string (a series of related problems in which students are able to make connections between easier and more difficult problems and develop strategies for solving complex problems),

-Estimation - Estimation routines give students the opportunity to grow in their understanding of quantity and develop math reasoning. Estimation 180, estimation clipboard

-The "daily collection" number sense routine is one of the most powerful primary tools for math learning. As a class, add one item to the collection each day and display them in an organized way using groups of 5s and 10s. Ask students to report the quantity each day and defend how they know the total. Then record their explanation as an equation. Students may think of the total in many different ways so many different equations can be recorded each day. Slowly over time students can begin to write the equations themselves that match the number of items collected each day. (Possible items could be dots in ten frames, linking cubes with different colors for each group of 5, a paper chain with colors in groups of 5’s, popsicle sticks in bundles of ten)

-Related Math Practices - Number sense routines encourage students to “think about numbers in many ways”, “explain their thinking and try to understand others”, “use what I know to solve new problems”, and “solve problems by looking for rules and patterns”

Problem solving/Productive Struggle activities are the opportunity for students to bring all the pieces together from the other pillars.

-3 Act Tasks and Math Design Collaborative/Formative Assessment Lessons are good examples of such opportunities.

-These tasks are often collaborative, therefore allowing students to discuss their ideas with others. Teacher questioning is an important part of these experiences. (Teachers might say, “What is tricky about this? What could you do differently? Students might say to each other, “I agree with you because…” “Can you tell me more about…”)

-Related Math Practices - “I can solve problems without giving up!” “I can use what I know to solve new problems” “I can explain my thinking and try to understand the thinking of others” “I can work carefully and check my work”

The overall goal of the math classroom is to create a growth mindset about math learning and willingness to approach really hard math problems ,while providing opportunities for students to gain the number sense needed to find a starting point when solving difficult problems. We strive to give students the tools they need to make connections on their own so that math is “caught rather than taught”.

Math Practices with Primary friendly language included

I can solve problems without giving up

I can make sense of problems and persevere in solving them.

I can think about numbers in many ways

I can reason abstractly and quantitatively.

I can explain my thinking and try to understand others.

I can construct viable arguments and critique the reasoning of others.

I can show my work in many ways.

I can model with mathematics.

I can use math tools and tell why I choose them.

I can use appropriate tools strategically..

I can work carefully and check my work.

I can attend to precision.

I can use what I know to solve new problems.

I can look for and make use of structure.

I can solve problems by looking for rules and patterns.

I can look for and express regularity in repeated reasoning,