Student and Teacher Roles in Contemporary Classrooms

Parts of the ‘Contemporary' Mathematics Lesson	The student . . . . .
Before: Activate	Students develop an understanding of the problem Students recall prior learning Students ask questions and participate in discussion for further clarification Students develop possible strategies and discuss them with their peers
During: Acquire/Apply	Students share their work within their small groups, check answers and strategies, ask questions to provoke further clarification and elaboration All students share their strategies, listen to the ideas of others, question what they do not understand and defend their thinking Students are working with hands-on-material such as manipulatives Students are discussing using mathematical language  Students find ways of displaying their information
After: Connect/Reflect	The class gathers strategies by watching presented strategies Students defend their strategies or develop new ones based on what they have seen Students engage in discussion on key concepts and ideas STudents make connections between key concepts and ideas Students can participate in a gallery walk where they can examine and comment on the work of their peers

Parts of the Contemporary Math Lesson	The Teacher...
Before: Activate	Sets up classroom and materials up and ready to go before students enter Prepares a variety of manipulatives and materials to work with  Begins the lesson by asking the student to draw upon their prior knowledge or brain storm  The teacher may stand at the front of the class, circulate, or sit in a visible place (desktop) to maintain conversational tone.
During: Acquire/Apply	Teacher groups students for the task as required Teacher provides instructions regarding the problem that focus on higher order thinking Teacher circulates during task to correct and assist where necessary Listen for discussion and use of academic language Understand student strategies  The teacher is visible and available for help
After: Connect/Reflect	Facilitates student-driven discussion  Helps students reviews solutions and discuss what works and what doesn’t work Suggests areas for improvement and further opportunity to apply learning to other problems The teacher organizes student work

Lesson Ideas

For information on how to conduct various interactive problem-based math lessons check out Edugains.

Problem-Based Learning Exemplars

Junior Exemplar
Grade: Grade 4    Strand: Measurement


Overall Expectations:  determine the relationships among units and measurable attributes, including the area and perimeter of rectangles.

Specific Expectations: 
describe, through investigation, the relationship between various units of length (i.e., millimetre, centimetre, decimetre, metre, kilometre);

select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure the side lengths and perimeters of various polygons;
Big Idea: attributes, units, and measurement sense


Materials:

• Chart paper/powerpoint/overhead
• Markers
• Ruler
• Pencil
• Handouts

Challenge

Tomorrow I am going to go to Canadian Tire with my family to buy Christmas lights for our house. Before I go, I have to figure out how many meters of Christmas lights I’ll need to buy in order to frame the front of the house. I have a basic blue print of the house that gives me some measurements. Since the blueprint is old, some of the measurements are missing and the measurements that are provided on the blueprint are in centimeters. I need you to help me figure out how many meters of Christmas lights I need to frame the whole house. 

Intermediate Exemplar
Grade: Grade 8   Strand: Measurement


Overall Expectations:
Research, describe, and report on applications of volume and capacity measurement. 
Specific Expectations: 

Research, describe, and report on application of volume and capacity measurement. 
Big Idea: attributes, units, and measurement sense


Materials 

• Bristol Board (tubes)
• Skittles

Challenge

Skittles Inc. is releasing a special tin for their 25th anniversary and has come up with two different tubular tin sizes. They are unsure which tin to use for their anniversary edition BUT they do know they want to use the one that is able to hold the most skittles. You have 2 different tin designs on your table, using your bag of skittles, please help Skittles Inc. decide on which tin design to use. 

The Problem...

Characteristics of "Good Problems"

• deals with 'big/important ideas' in the curriculum
• is problematic, meaning that the solution is not obvious or known in advance
• should be authentic
• must be sufficiently broad to be challenging and appropriate to the level of students' intellectual development
• allows for multiple entry points
• has more than one way to solve it
• requires students to interpret and construct their own meaning

Benefits of Problem-Based Learning

• Increases student engagement and ownership
• requires differentiation
• addresses a variety of learning styles
• promotes conceptual understanding
• allows flexibility
• increases self-confidence
• makes math fun
• offers excellent opportunities for assessment 

Implementing this Structure in YOUR Classrooms

• Select or design good rich problems that address the big idea
• Try the problem yourself or with a colleague and tweak the numbers or context to make it more engaging for students
• Allow yourself to reflect on your own understanding
• Have I considered the range of responses the students may provide?
• Students may come up with unanticipated solutions, how can I turn these into learning opportunities?
• Do I have strategies in place to address misconceptions?
• Have I considered ways I can differentiate learning when students continue to struggle?
• Am I prepared to be an active learning partner with the students?
• If I am unable to answer all of my students' questions do I have strategies and/or resources in place?

Source: Peel Schools, Transformational Practices Grades 1-12: A research based resource to support collaborative inquiry in Peel schools

Food TV!

The analogy I used to introduce this blog was that of a food-tv show host and it's audience members. Let me explain this a bit more...

The job of the food-tv host is to develop recipes and demonstrate the recipe to the audience in an easy to understand step-by step format. The audience remains passive, they watch the host prepare the meal, take notes (or get the recipe online) and they attempt to follow that prescribed recipe at home following each step. This is the traditional approach to math. The teacher acts as the food-tv hosts, prepares the lesson, demonstrates the algorithms and concepts on the board while students act as an audience by taking notes and watching. They then attempt to follow the prescribed concepts and algorithms to the mathematical problems. Imagine a food-tv show where the audience becomes the host! They work together and start developing recipes on their own, they experiment, try out new ingredients, figure out what works together and what doesn't.  The host simply presents the ingredients, assists when necessary and asks questions about what the audience is making. That's what should be occuring in math classrooms, students should be developing concepts on their own, experimenting, testing strategies, working with manipulatives and figuring out what works and what doesn't work..

  

Learning Through Problem Solving

A New Way of Thinking...

There has been a significant shift in recent years with the way math is run in the classroom.  Rather than the traditional teacher-centered approach math classes are taking a student centred approach. Students become active participants in the learning process and teachers take on the role of a facilitator.  Allowing students to take on this role and shifting the role of the teacher  occurs when teachers are able to teach through problem solving.  Rather than prescribing certain algorithms and methods of solving the problem, teachers probe, ask questions and organize student work in order to help the students consolidate, connect, learn new algorithms, concepts and strategies. While teachers have certain learning goals in mind they allow students the freedom to attack the problem anyway they wish and encourage them to reconsider their strategies to find better more efficient ones. Students also take much more of an active role. They are able to draw on previous knowledge, test out different strategies, teach each other, ask lots of questions and compare their work to enhance their learning. 

Problem-based learning goes well beyond these short-term instructional instances or simple questions. It encompasses a rethinking of the entire curriculum so that teachers design whole units around complex, "ill-structured" problematic scenarios that embody the major concepts to be mastered and understood. (Bellanca and Brandt 178)

The single most important principle for improving the teaching of mathematics is to allow the subject of mathematics to be problematic for the students. That is, students solve problems not ot paply mathematics, but to learn new mathematics. (Hiebert et al. cited by Van de Walle 11)

Welcome- We Use Math

Hello There! 

Welcome to my math blog! The purpose of this blog is to introduce you to the changing face of math in modern classrooms. This blog is not going to show you how to approach math as television food show host, who simply demonstrates standard recipe for audiences to follow. This blog will challenge you and your students to be active, ask questions and learn in new and exciting ways! Be prepared, because this new way of approaching math is quite messy! In this blog you will find: 

• The type of math learning that is occurring in contemporary classrooms today 
• The roles of the student and teachers in contemporary math classrooms
•  Problem Solving Exemplars for junior-intermediate classrooms 
• Valuable tools and Resources 

For now, I leave you with a video from WeUseMath.org, which discusses the importance and relevance of math in everyday life.