Math Instruction for ALL Students

This blog post is a work in progress! Be sure to come back and visit in a few weeks, as I will be adding to it over time…

It can sometimes feel overwhelming when we look at all of the individual and group needs of our mathematics learners. Building readiness to learn, along with ensuring that we meet the individual needs of students might give us the impression that we need to create an individual lesson plan for each and every person in our classrooms. That sounds exhausting…

But what if we can create structures and use a variety of math instructional strategies within those structures? What if we can create diverse learning experiences that encourage mathematical thinking and growth over key concepts? This is an idea worth investigating!

I am still learning

Our elementary and middle years math curricula in Saskatchewan cover a number of topics, from number to patterns to shape and space and statistics. Ironically, when you look at the skills needed for students to be READY to engage in these grade-level concepts, there are only a handful of pre-skills. These pre-skills are the math concepts that are applied and used in new learning.

For example, when we are learning about adding and subtracting fractions, we need to know about:

  • addition and subtraction
  • multiplication and division, multiples and factors
  • what a fraction is, finding equivalent fractions, improper fractions

When you analyze grade-level outcomes in mathematics, you will often see combinations of the following pr-skills:

  1. Number Sense and Place Value
  2. Addition and Subtraction
  3. Multiplication and Division
  4. Parts of a Whole – Fractions, Decimals and Percent
  5. Algebraic Thinking

So, how do we teach and reteach each of these key concepts in our classrooms? You can find a large number of curated resources in this Google Drive: https://bit.ly/2zrNfqd which contains folders of resources designed to help you to teach through these continuums, as well as:

  • What is an instructional sequence and strategies for teaching each concept?
  • What are some common misconceptions and how might we address them?
  • How might we infuse technology into our mathematics instruction?
  • What are some fun ways to engage in mathematics?
  • How might we use math with a purpose to gain a deeper understanding of social issues?

Concept Continuums

When we look at our Saskatchewan curriculum, we can see how concepts grow over time in these math Curricular Through Lines:

We can also pull out specific concepts and see how they grow. The following concept trajectories were created by a province-wide math leadership group a number of years ago, and show the language, strategies and concepts over time. Each continuum has four instructional strategies listed.

Routines, Puzzles and Games for Math Fluency

Math fluency is the ability to perform mathematical operations quickly and accurately. Math automaticity with basic facts is part of fluency. John Munroe (2011)  indicates that we as learners have a finite amount of working memory. It is important that student working memory is available to learn new math concepts, solve complex problems and think creatively in mathematics, rather than being used to recall basic math facts.

So, how do we promote automaticity of basic math facts without endless worksheets, mad minutes and text-book assignments? Math games, puzzles and routines related to grade level concepts allow for flexibility in thinking, practice and student engagement and fun. The following documents can help us connect practice with curricula:

Math Routines

There has been a significant amount of research in the area of mathematics routines to enhance learning, building automaticity and fluency. There are a number of key resources that are helpful to teachers from grades 1 to 10.

Routines Resources.PNG

Productive Mathematics Discussion

Margaret Smith (2011) has created a structure for planning for and implementing classroom discussion in a mathematics classroom. Discussion and sharing mathematical thinking is the key to most mathematics routines.

Math Discussion

This sequence of thinking can be applied to a teaching strategy, Learner Generated Examples (Crawley, 2010), to create a powerful way of sharing student thinking in mathematics.

Learner Generated Examples:

Brian Crawley, a teacher from Saskatchewan, did extensive research on learner-generated examples. Overlaying the Five Practices, you create a cycle that can be applied to many number routines:

Learner Generated Examples

Move through this cycle three times. This allows students to push beyond the knowledge that they find easy to access and move to more and more complex ideas.

Examples of Math Routines

There are several powerful math routines gathered from many Math Routine Resources that can be adapted to different concepts over grade levels. The following is a short list:

The key to math routines influencing math fluency in your classroom is to choose appropriate concepts and numbers related to your curriculum. For example, in the routine “Today’s Number”, if you are in early primary, you might choose a number between 1 and 10. If you are teaching ideas around skip counting, perhaps choosing the number 6. If you are working on perfect squares, perhaps choosing a number like 36.

Math Puzzles

Math puzzles allow learners to explore mathematical ideas and practice thinking flexibly. Well-designed puzzles are engaging and logical, with most of the time focussing on solving the puzzle mathematically. As with routines, puzzles can be adapted to the range of numbers and concepts appropriate for a given grade level.

Missing Number Puzzles

Kakooma

  • Examples and explanation are found on Greg Tang’s Kakooma Resources website
  • Kakooma helps students build automaticity with addition and multiplication.
  • There are a variety of number puzzles, with a diverse range of numbers and volume of questions to solve.

Math Squares

Two-Ways

Mazes

Inaba Place Value Puzzles

Math Games

When choosing and setting up games in your classroom, along with considering the math concepts you are emphasizing, it is also important to consider student grouping and classroom norms.

By creating homogeneous groupings, it is possible that some groups will use tools to help them calculate or identify numbers, such as:

In heterogeneous math game groupings, it potentially frustrating for both the stronger student and student who needs more time to compute or recall math facts.

There are many excellent math games sites that include Math online games. As well, there are many games that require few materials and are engaging for students.

Of special note are Alphashapes and Alphashapes Games that can be played to understand mathematics language.

The key to finding and using math games in your classroom is to know the math that you would like to build fluency in, and then search for those concepts. There are literally thousands of great sites that you can access both online and paper copy games.

 

 

 

 

 

 

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