LE1 Summary

Planning, Big Ideas and Other Thoughts

Why Plan?

Planning is one of the core routines of teaching (Kilpatrick, Swafford and Findell, 2001). Developing clear objectives based on what students know and what we want them to know is imperative to a plan’s success. Planning is a process that allows teachers to easily build on concepts. We must have a clear idea of where we want students to go and how we’re going to get there in order to achieve the learning goals. As we plan, we need to ensure that we consider the tools, strategies, lessons, prior knowledge and learning styles of our students in order to help them be successful. Helping students see the connections between one lesson and another will help them understand what and why something is being taught. It also helps us address the individual needs of our students. Once we know what they know, how they learn and what they need, we can build lessons or groups of lessons that address that. When a student or group of students struggle with a concept, we have a record of what has happened so far and are better prepared to develop new lessons or supports to help those students move forward. Planning also helps keep us organized and if we were ever questioned by a principal or parent about what was being taught in the classroom, our lessons and plans would support us. These, coupled with a plethora of student work would attest to our commitment to the planning process. There is documented evidence that shows student learning is correlated to teacher planning. So, if we do it for no other reason, we know it’s good for students. That’s a good enough reason for me. I have chosen a quote that I think aptly describes the importance of planning and backwards design: “To begin with the end in mind means to start with a clear understanding of your destination. It means to know where you’re going so that you better understand where you are now so that the steps you take are always in the right direction.” (Stephen R. Covey, The Seven Habits of Highly Effective People).

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Using a Unit Plan

Why are unit plans important? You’ve identified many reasons already on the discussion board and had an opportunity to critically examine some of the unit plans on the NCTM website. Thank you for sharing these lessons and your thoughts.

We know that we need unit plans. They help us build coherence throughout the year. With them, we can determine what modifications or accommodations need to be provided for our students, as well as help us determine what resources and/or materials we will need to gather in order to successfully execute the unit. Think of all the rich mathematical texts that could be used to help provide a context for problem solving. Ask yourself, “Do I really want to run down to the math room on the day of my lesson that requires the use of pattern blocks only to find that all of the bins have been signed out?” The only way to ensure that resources such as these are included and available is to think and plan ahead.

Before we can even begin a unit, we need to determine what students know. This is where our unit planning should begin. Not only do we need to know what they know, but we also need an idea of what manipulatives they are comfortable using and what kinds of problems they can solve. How you start the unit is up to the individual teacher. Many of the teaching guides available in schools have some very creative ideas on how to do this. However you decide to start, remember that it should activate students’ thinking about the unit concepts and be engaging.

We always have to look at the expectations and the big ideas to determine what we need to teach, but we should also be looking at the needs of the group in front of us. By doing so, we can differentiate for our students and provide additional lessons or practise opportunities depending on their understanding of the concepts. At some point, we will have to assess what students know. When we plan using backwards design, it is much easier to find or create lessons that will help students complete the unit successfully. Throughout the unit, teachers should be creating opportunities to check in with students to assess how they are doing. This should not come as a surprise at the end.

By keeping these ideas in mind, you’ll be able to create fun, engaging and applicable learning opportunities for you students.

Kid Snippets: "Math Class" (Imagined by Kids)

Big Idea Summary

We seem to be in agreement on the importance of the big ideas in mathematics.

Many of you have pointed out the importance to connect concepts, strands, subjects and prior knowledge. In her book, “Big Ideas from Dr. Small: Creating a Comfort Zone for Teaching Mathematics”, Marian Small says, “…many teachers feel like they are going through a checklist, checking off whether students have learned each new discrete concept or skill listed in the curriculum. This is in stark contrast to what we know from research about how much more effective it is for students to learn when connections are explicitly made between new knowledge and ideas that students already know”.

Teachers need to understand the deeper meanings and purposes behind the math. Dr. Small goes on to say, “Another way that big ideas can help is to ensure teachers and students understand the overriding purpose behind a lesson or task… Teaching through big ideas is about teachers looking critically at a task or lesson, asking themselves why they are teaching that lesson or task, and them making sure the purpose becomes clear to students to that the task or lesson can be more effective.”

There is an important connection between planning and big ideas. If we start with the curriculum and analyse the connections so that concepts can be “chunked”, we think differently about how to challenge our students and we become more reflective practitioners.

Differentiation is also key and was touched on by a few people. Again, Dr. Small has acknowledged that differentiation is a key challenge for teachers, particularly in mathematics instruction. Her use of open questions and parallel tasks allow teachers and students to explore core concepts in math regardless of where they are on the spectrum of understanding the big idea. Everyone is included in the same conversation, which makes it a lot easier for the teacher to organize and plan. One of the elements missing from this resource is a clear idea about how to organize and facilitate the discussions that are necessary to focus on the big ideas in a meaningful way. A book that I know of, Classroom Discussions:Using Math Talk to Help Students Learn by Suzanne Chapin, Catherine O’Connor and Nancy Canavan Anderson covers discussions and complements Dr. Small’s work. Another that was mentioned by Sherry Parrish was Number Talks.

A math major talks about fear

Perseverance and Engagement

“So often teacher feel they should give answers or provide procedures to learners. The problem with doing so, however, is that those same learners then come to depend on the teachers and never develop the tenacity to work through the important struggles. Even more to the point, they never learn to appreciate the fun and puzzlement and the exhilaration that comes with their own breakthroughs (Cathy Fosnot, Young Mathematicias At Work:Constructing Algebra). Keith Devlin (2003) once said, “When I’m working on a problem it’s like climbing a mountain. Sometimes I can’t even see where I’m going. It is one foot in front of another. And then I reach a point where all of a sudden the vistas open up and I can go down easily for a while, only to eventually reach another climb.” As teachers, our goal is to build the learner’s capacity to make the climb. To that end, when we confer with learners we need to focus on developing the mathematician rather than fixing the mathematics. Every action we take should develop the novice mathematician in front of us.”


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Thoughts from Marian Small

Marian Small says, “Planning makes it more likely that teachers will make good choices about how students spend their instructional time. Classrooms are complex environments. If the teacher has not streamlined the teaching to make sure that the most important ideas are front and centre, it is easy to lose valuable instructional time and make it more difficult for students to attend to the more important ideas.”

(Making Math Meaningful to Canadian Students)

Marian Small says that a good lesson plan template will remind teachers of:

-what materials they will be using

-what groupings they will use and when

-the amount of time to spend on each activity

-some short notes about each component of the lesson

-what important questions they want to make sure they ask students in the various parts of the lesson

· All of these points will help keep us on track and ensure that we are meeting the needs of our students.

Marian Small - Skills Estimation and Practice

Cross-Curricular Links