Taking a Giant Step in Mathematics
Take a moment to look back at how you were taught math when you were a student. It was probably a time when you would open your textbook to the specified page and answer the questions listed on the board. If you didn't finish, it was to be done for homework. The lesson was probably taught in a rote fashion where the teacher told you step by step how to answer a question. He/she would model these steps on the board so you knew exactly what you had to do to get the right answer. Sound familiar? I know that's how I was taught math when I was a student, and I'm not that old, so it really wasn't that long ago that this was how mathematics was taught in the elementary classroom. We have taken some great steps towards bettering ourselves as math instructors through a new structure commonly known as The Three Part Math Lesson. This new way of looking at mathematics and how to teach it to our students requires a lot of planning, reflecting, and new learning for the teacher as well. It is demanding. It can make you want to cry in frustration sometimes, and that's how you know it's working: we are finally taking the time to understand the why behind mathematics, rather than just the how; and we are taking even more time allowing our students to explore these concepts with us.
What is a Three Part Math Lesson?
A Three Part Math Lesson is drastically different from the model mentioned above. It is designed to encourage students to think about what they know, and use the resources around them to solve a math problem in a way that works for them.
Getting Started
This first part should take between 5 and 10 minutes and it includes the participation of the whole class. Some teachers refer to it as Minds On; in my classroom, we sometimes do little Quick Flashes. I'll explain that in a minute. In this phase, the teacher introduces the students to the problem and together they discuss the task. This is a perfect time for teachers to model different strategies or to verbally remind students about what resources they could use to solve the problem. This is where my quick flashes come in. I will show a series of short questions that force the students to think quickly about how to determine the answer. For example, I would show the following questions on the Smart Board:
Teacher shows question: 10+10= ____
Students: 20!
Teacher: How do you know?
Students: I know my doubles and 10's double is 20
Teacher: Very good. *shows another question: 10+11=____
Students: 21!
Teacher: How do you know?
Students: If I use my doubles to figure out 10+10, then I just add one more, so it will be like 20+1 .That's 21!
Teacher: Excellent strategy, using doubles plus one.
The teacher hasn't explicitly told the students to use this strategy, but has reminded them of how useful it is to solve certain questions. The idea here is to have students keep these strategies in mind as they solve their own math problems.
Working On It
This phase involves the students working independently or in pre-determined pairs on a question very similar to the one modelled in the Getting Started portion. As the students work, they are encouraged to use any resources and manipulatives they need to help them solve the problem. The teacher should be monitoring the students' work by conferencing, asking questions, and taking observational notes. This is a great time for the teacher to learn about his/her students' abilities, which students should be paired together for the next task, and which students should have their work modelled for the next portion of the lesson. This sense of freedom in solving a problem builds a sense of independence amongst the learners in the classroom.
Reflecting and Connecting
In my classroom, I refer to this as The Congress. It is when everyone has finished the task and comes back together to discuss strategies that worked and those that did not. The teacher has taken the time during the Working On It phase to choose which exemplars to use. The teacher guides the discussion to help the class see what others had tried to achieve the answer. The chosen work doesn't always have to have the right answer either; as long as the strategy being modelled is what you are emphasizing to the students. I like to congress with 2-3 examples to show how different strategies can be used, and how one way may be more efficient than another. In the younger grades like mine, I like to congress right after my quick flashes the next day so the kids have the discussion fresh in their minds.
Little Ones with Big Ideas
Maybe your students aren't so little anymore, but just know that no matter how young or old they are, students learn and understand math much easier if they understand the big ideas. What are big ideas? They are mathematical concepts that concentrate on specific skills. Students who have a strong understanding of the big idea will find it easier to problem solve. "Teachers will find that investigating and discussing effective teaching strategies for a big idea is much more valuable than trying to determine specific strategies and approaches to help students achieve individual expectations" (Number Sense and Numeration, Grades 4 to 6 – Volume 1 p12). Keeping in mind the big ideas you want to explore will help to guide your planning.
Planning Your Little Heart Out
An effective math program requires a lot of planning. Your students will not get the most out of math class if you haven't put a significant amount of thought into the upcoming year. A teacher has to make long range plans, unit plans, and day/lesson plans. Each plan gets more detailed as you work toward the latter, but the teacher needs to have a strong sense of where to begin and end a school year within the math curriculum.
Long Range Plans
Big ideas are used in other subjects as well, and this is how I determine where I want my math program to go. I look at where I plan my other units for other subjects and attempt to make a strong cross-curricular program. The benefit here is that students will see the connection of skills between math, literacy, and science. Have you ever asked, "When will I ever need to know this?" If you can establish a strong cross-curricular program, you may never hear this question. Long range plans are vague because it's impossible to know where your class will be when you're developing this at the beginning of the year. Keep it brief and don't lose too much sleep over it.
Here is an example of our long range plans for 2012/2013:
Unit Plans
Using your long range plans makes it easier to look at where you are in all subject areas so you can create a fun and engaging unit for your students that connects to other things they are learning about. The most important thing about unit planning is to plan with a Design Down model. That is, determine where you want your students to be by the end of the unit. What do you want them to be able to do independently? What skills should they have? Once you have identified this, go back to the beginning and determine where you will start, and how the unit will progress. How are you going to move the students forward? How are you going to assess them? How will you give them effective descriptive feedback?
Here is an example of a really fun unit plan I did with my Grade Ones and Twos. Say CHEESE! :
Day/Lesson Plans
This is where planning gets very specific. You want to carefully plan where the lesson will go. You will need to consider what the common misconceptions will be, which students will need to have their tasks differentiated, and what skills and big ideas on which you want to focus. This is where the specifics of the Three Part Math Lesson emerge. Keep in mind: you can plan your little heart out, but don't be surprised if your lesson doesn't go as planned. The kids can surprise you. They may not have a clue what they're doing, forcing you to take a step back and revisit previous lessons; or they might astonish you and turn out to be amazing little mathematicians, meaning you have to offer them something a little more challenging. Either way, it's important to have a detailed plan so that you are prepared for whatever the students throw your way.
Here is an example of a day/lesson plan I developed for looking at how to add two numbers together:
Questions For You
I have been so blessed to have two grade partners that love sitting down and throwing around ideas. Often times, we admit to one another that we're stumped and we just don't know where we want to go with a unit. It's nice to have two other teachers to share their ideas to create an engaging math program. What do you do when you're stuck? Do you have grade partners? Do you structure your program all on your own? Do you use a cross-curricular approach? It's easy to get comfortable with your own routines and styles, but it can be really refreshing to take on someone else's approach to planning for your classroom.
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