The Project

The students and teachers of Millarville Community School wrote the first question and posted it for the students of Dr. Gibson and Red Deer Lake to respond to. They wanted to write a question that would be a real life question that could actually happen in the area where the children lived. The math that they wanted to discuss to gain an understanding was area, perimeter, scale, fractions, and geometric shapes. They new that there might be more as the problem evolved.
A threaded discussion was set up through email for the students to begin their conversation. There were 4 groups in each of the schools. Group A took part in a discussion with the other group A's from Dr. Gibson and Red Deer Lake School. There were 13 students talking together in group A. They were not able to see or take part in the discussion that was taking place with groups B,C or D. There were 13 students in each of these groups.
The students from Millarville started the conversation and their role was to keep the conversation going by answering questions and posing new ones. The students would log on twice a week and either start a new email or respond to a previous email that had been sent. When they got their plans finalized, they scanned them, then resized them and sent them as attachments to the students at Millarville Community School. The teachers also took part by responding to emails, talking part in the discussions of the math and checking to see if proper etiquette and respect was being used.
When the students finished their plans and submitted them to Millarville Community School, it was then the job of the students at Millarville to compile the different threads of the conversation and post them. When they got the finalized plans, they also had to summarize the thoughts of the different groups that went with each plan.
This same project was repeated by the students at Dr. Gibson School when they posted their math inquiry problem. They wanted to focus their conversation around the understanding of perimeter.

Planning the Project

When we worked on our project we wanted to build it using the "Indicators of Engaged Learning" (NCREL North Central Regional Educational Laboratory). We feel that this project was able to include many of the following indicators.

INDICATORS OF ENGAGED LEARNING

VISIONS OF LEARNING

Responsibility for Learning:
Students take charge and are self-regulated learners. They define learning goals and problems that are meaningful to them and understand how specific activities relate to these goals. Students are also involved in setting and using standards of excellence to evaluate whether they have achieved their goals

Strategic:
Students continually develop and refine learning and problem solving strategies. They apply and transfer knowledge to solve problems creatively.

Energized by Learning:
Engaged Learners derive excitement and pleasure from learning and are intrinsically motivated.

Collaborative
Students have the skills and value the opportunity to work with others. They understand that learning is social, and they understand that many problems/issues have multiple points of view.

TASKS

Authentic:
Tasks bear a close relationship to real world problems in the home and workplaces of today and tomorrow. They build on life experiences, require in-depth work, benefit from frequent collaboration and are of relevance and interest to learner(s).

Challenging:
Tasks are complex and typically involve sustained amounts of time. Students must stretch their thinking and social skills in order to be successful.

Multidisciplinary:
Disciplines are wholly integrated in order to solve problems or address issues.

ASSESSMENT

Performance-Based:
Assessments are meaningful, challenging experience that involve presenting students with an authentic task, project or investigation and then observing, interviewing or examining their artifacts and presentations to assess what they actually know and can do.

Generative:
Teachers create the assessment criteria and tools together with their students so that they are meaningful and generate knowledge

Seamless and Ongoing:
Instruction and assessment are integrated; assessment of the process and products occurs throughout the instruction.

INSTRUCTIONAL MODEL

Interactive:
The course of instruction responds to student needs and interests and students can make key decisions regarding their learning.

Generative:
Students are encouraged to construct and produce knowledge in meaningful and deep ways. They solve problems, conduct meaningful inquiry, engage in reflection and build a repertoire of effective learning and problem solving strategies.

LEARNING CONTEXT

Collaborative:
The school is conceptualized and designed as learning community where students learn to work collaboratively

Knowledge Building:
Learning is made public so that the learner can get input from diverse perspectives and build on that knowledge

Empathetic:
Diversity and multiple perspectives are valued and utilized to build on the strengths of all students

GROUPING

Flexible:
Groups are formed and reformed according to the purpose of instruction. Groups are formed based on common needs and interests, usually for short periods of time.

Equitable:
Groups are organized so that over time students have opportunities to learn from all other students.

Heterogeneous:
Groups include males and females and a mix of cultures, learning styles, abilities, socioeconomic status and ages in order to capitalize on the range of background knowledge and differing perspectives.

TEACHER ROLES

Facilitator:
Teachers create opportunities for students to work collaboratively to solve problems, do authentic tasks and share knowledge and responsibility.

Guide:
Teachers help students to construct their own meaning by modeling, mediating and coaching. They constantly adjust the level of information and support according to students' needs.

Co-Learner/ Co-Investigator:
Teachers learn along with students and students may serve as teachers.

STUDENTS ROLES

Explorer:
Students discover concepts and connections and apply skills by interacting with the physical world, materials, technology and other people. Often students are encouraged to jump into an open-ended activity in order to stimulate their curiosity, become familiar with the instructional materials and formulate early understandings of the task.

Cognitive Apprentice:
Students observe, apply and refine through practice the thinking processes used by practitioners in specific content areas. They receive ongoing feedback on many aspects of a complex problem or skill.

Teacher:
In order to teach others, students must integrate and holistically represent what they have learned.

Producer:
Students generate knowledge and products for themselves and the community, which synthesize and integrate knowledge and skills.

Reflections and comments about the project:

• We were pleased with the amount of time that the students wanted to spend on the math problem. They were willing to work on the project every math class for 3 weeks reflecting, revising, discussing and posing new solutions.
• Many of the students commented that this did not seem like math because they got to work and talk with other students and plan together. We discovered that discussion about the "math" within the "math" when you are problem solving is very important. It does take time but it is very important when you are striving for understanding.
• The students really enjoyed working online with students in different schools. They were very interested in conversing with them and trying to help them understand the question and a method of solving the problem. This was something that we do not always see during the traditional class room discussion. The idea of using technology and being able to plan and work with another school was very interesting to the students and they were very comfortable with the concept. They did not see the others as keypals but more as learning pals.
• The students really like the story approach to math and voiced their opinion that they would like to work this way all of the time. We do not always take the time to construct math learning in this way as we seem to be bound by coverage and not uncoverage. We know that learning is more meaningful when it is in context of a situation and not isolated.
• They mentioned that this was not like the usual real life math questions where you read the question and then all you do is to decided whether you should divide, multiply, add or subtract. They said that although they used to get answers they really did not understand how they got the correct answer.
• The students liked the idea of taking time to talk about math and do math. There wasn't a series of questions with this math question like you have in a text book where you just go from on to another until you are finished. Then sometimes the only discussion is around the answer and if you got it correct or not.
• We really felt that the students gain a strong understanding of the math that we were focusing on. They were able to talk about what they were doing and why they were doing it. They were also writing new questions that came out of the questions that had been posed. They did not want the process of learning to stop.

Reflections about Math:

When students are learning they attach meaning to what they do. The intent of this project was to do just that to have a question around which meaning could be attached and learning could happen. The students needed to feel comfortable taking risks, asking questions and posing possible solutions. We felt that they were comfortable as they worked their way through the question you would often hear them say.."No that idea does not work I wonder why? Let's try this and see if it will work? I think that it will because this is my thinking to this point."

"Students need to become mathematically literate in order to explore problem-solving situations, accommodate changing conditions and actively create new knowledge in striving for self-fulfillment". (Alberta Learning Mathematics K-12)

The main goals of mathematics education are to prepare students to: use mathematics confidently to solve problems, communicate and reason mathematically, appreciate the value of mathematics, exhibit a curiosity, show an enjoyment, and contribute to mathematical discussions. Throughout the project we saw evidence of all of these goals.

Reflecting on the NCTM Problem-Solving Standards:

The mathematics curriculum should include numerous and varied experiences with problem solving as a method of inquiry and application so that students can:

• Use problem-solving approaches to investigate and understand mathematical content
• formulate problems from situations within and outside mathematics
• develop and apply a variety of strategies to solve problems, with emphasis on multistep and nonroutine problems
• verify and interpret results with respect to the original problem situation
• generalize solutions an strategies to new problem situations
• acquire confidence in using mathematics meaningfully