Meaningful Mathematics In the Primary and Junior Classroom By Allison Pottie

What Does Math Mean To You? Before we begin, take a few moments to think: What was your experience with Math as a child? How did you learn math? Was it effective? What do you see a meaningful Math program consisting of in your classroom? What type of attitude do you want your students to have when they think about Math? What are the goals of your Mathematics program?

Minds On: Click Here To Watch Video Let’s think about the elements of a balanced math program in our classrooms. What does a comprehensive program consist of?

Clear Planning for Students As teachers, one of the most important parts of our job is to engage in thoughtful and clear planning for our students. Take a moment to think: What does thoughtful and clear planning look like in your practice?

The Importance of Clear, Thoughtful Planning To be familiar with curriculum expectations and understand how they build upon one another To look for multiple, cross-curricular connections where possible To provide learning opportunities that are meaningful and relevant to students To have a goal of where you want students to be and how you are going to get them there To know your points of assessment along the way To have a chance to talk and co-ordinate with your grade team partners To make learning purposeful and meaningful to students To have the time and resources to develop a balanced math program for your students To create an atmosphere of trust and comfort within your classroom To be able to incorporate authentic learning opportunities for students To be able to set students up with learning opportunities that promote a priority on understanding To look for when to pose meaningful problems, when to teach a mini lesson and when to give students opportunities to play games and puzzles

Student + Understanding = True Learning When students understand the Mathematics they are engaging with, they: Are more apt to take risks Are more likely to develop a positive attitude surrounding math Can build upon their Mathematics knowledge each year, rather than seeing it as a fresh start each year ** enduring understanding ** Can see connections between what they are learning Communicate more about their learning Show more excitement towards learning See how Mathematics is meaningful in their lives Can become critical thinkers, rather than simply “memorizing” facts, processes or equations Can have the time to slow down and truly explore Mathematical concepts Become more effective, creative and confident Mathematicians

BIG Ideas In order to create a Mathematics classroom environment that promotes a deeper understanding of concepts and how they connect, it is important to look for big ideas within strands and across strands.

Big Ideas: Help students see the connections between what they are learning Allow students to develop their knowledge and skills Allow more opportunities for meaningful problem solving Allow students to explore concepts in more depth Help facilitate a deeper understanding of Mathematical concepts Provide students with an opportunity to draw upon their prior knowledge and schema Help students see that Mathematical concepts should not be thought of in isolation Encourage students to draw upon their knowledge in different strands to come to solutions Develop new knowledge and enduring understanding

Sample Planning Template for Big Ideas

Now that we know how important it is to plan meaningful tasks that promote understanding and incorporate big ideas, let’s take a look at day, unit and long-range planning.

Day Planning Here are some questions to consider when planning for a Mathematics lesson: How will I utilize the prior knowledge and students bring with them? What are the concepts and procedures I want my students to learn and understand? How will I structure the learning opportunities to facilitate understanding? How will I know when my students have learned the concepts and procedures? How will I record my daily lesson plan and assessments?

Sample Day Planning Template

Daily Planning: Three Part Math Lesson Students need time to explore, time to share ideas with one another, time to work with manipulatives, time to receive and give feedback and time to build their Math vocabulary. The Three Part Math Lesson provides a structure for planning that enables all of these things to happen in the classroom.

The Part Math Lesson: Getting Started (10-15 Minutes) Usually involves the whole class Includes a task that has students active prior knowledge that will be useful in working with the problem Gets students thinking about concepts, skills, strategies, etc. that are relevant to the day’s learning Could include a review of a concept previously explored Examples of “Getting Started” Activities Use of a personal think time book: Students record their thinking related to the problem. They can draw, sketch, list, etc. questions they have, strategies they think will work, manipulatives they think might be useful Solving a similar problem to the “big” problem

The Part Math Lesson: Working On It (30-40 Minutes) Students share their ideas with a Math partner and listen to the ideas of others Students learn to use “Math Talk” to communicate Students learn to question each other and communicate in solving the problem (e.g., Can you show me what you mean? Could we solve this another way?) Students develop their understanding of concepts and skills Students communicate with the teacher who facilitates discussions Students record their strategies in a way that is meaningful to them Students choose manipulatives that they find helpful in solving the problem

The Part Math Lesson: Reflecting and Connecting (10-15 Minutes) Students share ideas with the class Students solidify their understandings Students give feedback to one another and ask questions Teacher facilitates discussions and highlights key math concepts that he/she wants students to learn and understand Teacher helps to clarify misunderstandings Students learn that there are different ways to approach and solve a problem Students learn to talk like Mathematicians Teachers assess student understandings and make plans for mini lessons, future problem solving activities, etc. that build upon student understanding

Unit and Long Range Planning Unit and long range planning for Mathematics is important for many of the same reasons mentioned in the earlier slide about planning. These forms of planning also allow teachers the chance to look for cross-curricular connections. If we want students to understand the importance of Mathematics (and learning) in their lives, it is important we give them authentic opportunities and that we highlight the idea that Math truly is everywhere. When creating unit and long range planning, think about ways you can incorporate other curriculum areas (e.g., Reading, Writing, Oral Communication, Media, Science, Social Studies, The Arts, etc.). This also allows more time for students to explore each concept. They start to see all the subjects come together, rather than taught in isolation. If we compartmentalize our day into set “periods”, students start to think this way as well. It is our job to help students see the fluidity and connections between all of their learning experiences.

Sample Long Range Planning Template

Sample Unit Planning Template

Burning Questions Take a moment to reflect on all that you have learned. What burning questions are still with you? What goals have you developed that you will take with you to your own classroom? My Questions: Where can we access examples of meaningful problem solving questions that teach a big idea and that are cross curricular? My Goals: To show my students how I use Math in everyday life (through authentic methods) To provide more opportunities for my students to experience Math in other subject areas (I want to make more of an effort to make my day fluid rather than compartmentalized into subjects) To SLOW DOWN and remember enduring understanding is my goal To spend more time clustering expectations around a big idea