CAMPPP+2011+New+Teachers+Artifacts

New Teachers Day CAMPPPers Artifacts of Learning
The following are collective highlights, compiled by the new teacher day campers, from day one of Math Camppp 2011:
 * Beneficial to see the student transcripts and the actual dialogue and thinking that took place when the students were solving math problems. It would be great to see such transcripts included in pre-service math courses;
 * Need for greater exposure to student thinking and reasoning in pre-service courses;
 * We as teachers need to actually use manipulatives ourselves in order to more fully understand the thinking and reasoning that takes place when our students are using manipulatives;
 * It is important to have lists of key questions to elicit further thinking, help students progress to the next level of learning, and consolidate previous learning (eg. open ended questions, scaffolding questions, etc.);
 * AH-HA! Justification framework! The justification framework is the research that should inform and support assessment rubrics in the classroom and achievement charts within the curriculum;
 * Interesting to see the progression of math learning from kindergarten to grade 12 (eg. concepts such as the equation of a line (y = mx + b) can be introduced in earlier grades with such activities as the robot game).

And, our creative piece:



Nikki, Jessie, Boni

DAY TWO

The following are collective highlights, compiled by the new teacher day camper


 * It seemed that after Plenary 4, discussions in the breakouts focused more on possible systemic issues surrounding success criteria for mathematics (i.e. it is easier to visualize how success criteria works within the literacy program but when it comes to math people feel that success criteria may put constraints on what is expected with regards to mathematical thinking). A ceiling is created by the success criteria that may not allow students to explore a mathematical concept and expand their thinking and in turn make those conjectures that Dr. Beatty and Dr. Bruce emphasize.
 * Letting student's ideas and conjectures stand longer, whether they are right or wrong, gives students a reason to learn because if we don't shut them down by "telling" them how to think then they begin to realize their thoughts have value. This in turn may create an environment where the right answer is not the most important thing.
 * As new teachers we don't have enough experience seeing "real" student work samples (actual photocopies not from a textbook) and deconstructing student answers to assess their learning. Through Math Camppp we have learned that being aware of the different generalization strategies that a student might be using to solve a problem and the justification framework are key to deconstructing student thinking and reasoning.
 * Camppp seems to increase teacher content knowledge and the breakouts allow for learning to apply the concepts to new and different problems. Teachers are DOING the math at camp and thus learning (i.e. you are forced to step outside of your comfort zone).
 * Idea of passive VS. active graphing allows for the students to add a new strategy to their mathematical toolboxes.
 * Listen to the answer not for the answers. (i.e. maybe teachers need to actively listen rather than formulating the ideas they expect to hear prior to asking the question)
 * Thinking as a student during the planning phase is key.

So we wonder: Why do some teachers feel the need to stop at a certain point and move on to another topic? Research VS. Curriculum? How do they connect? How do teachers transfer it into practice? Is it even being transferred to classrooms?

Jennifer and Kristin

Day 3

Today we finished up our sessions with Ruth and Cathy by focusing on how to help the struggling learner. We found the following:


 * Use of the three part lesson with manipulatives helps the struggling learner and students with special needs
 * CLIPS has been found to increase the understanding of all learners - []

The inclusion of how to help the struggling learner with math needs to be included in pre-service training.

We then moved to focus on how to give good, in the moment feedback to students. Ideas that stuck with us included:
 * Using focusing questions (to focus on the student’s thinking) rather than funneling questions (come around to the teacher’s thinking)
 * Scaffolding questions can help move the student’s thinking to the next stage
 * Word choice when giving feedback – re-read versus re-state
 * Tying the feedback to the learning goals (this returns to yesterday’s question as to where do the learning goals come from)
 * Using the justification chart to assist with feedback
 * Using mathematical process cards to help both the teacher and students in guiding their feedback
 * Should the teacher’s be inferring what the student’s were thinking?

In the afternoon we had new plenary speakers – Marian Small and Amy Lin. They introduced us to proportional reasoning. We had a variety of new problems to solve throughout the plenary. Marian showed us the in between, within and unitizing thinking stages of student thinking that we should look for and effective feedback to move students through the stages. Some of our a-ha moments for the day included:
 * Learning disability versus teaching disabilities
 * Curriculum assessment does not reflect teaching methods
 * Testing/assessment can’t always be done in one day
 * Often teachers teach the way they learn, but we need to teach to all learner type

Catherine and Shari

Observations and questions from Day 4:
 * Terminology and the definition of teacher speak may lead to misunderstanding and disagreement on the meaning of such terms. Different terms, i.e. success criteria, consolidation, learning goals, big ideas, can be interpreted and put into practice in different ways, depending on how the definition of these terms are communicated to educators.
 * At times there seems to be a disconnect between “best” teaching practices and current assessment methods / frameworks.
 * Your insights can only be as deep as your experience. Math CAMPPP has provided us with experiences that can influence our perceptions and insights moving forward.
 * More focus / practice is needed in pre-service courses to build knowledge for pre-teachers to choose appropriate specific feedback strategies, consolidation questions / activities, and annotating / analyzing student work.
 * In breakout sessions a majority of new teachers have noticed that consolidation questions tend to be more general or generic rather than specific. We thought that if one does not understand “the math”, it is very hard to provide quality consolidation.
 * WOW, 30 minute allotted consolidation time according to K-4 breakout. Members of other breakout sessions were surprised to learn this much time should be devoted to consolidation. Many thought that 10 minutes was the norm.
 * We have found discrepancies / misunderstandings between breakout groups regarding ideas surrounding the concept of consolidation. How long should consolidation take? What do you include in the consolidation component? Does success criteria flow out of the consolidation?
 * Success criteria is a VERY CONFUSING term! What was the original intended purpose of success criteria in Ontario? Does the concept of success criteria move teachers away from differentiated instruction? Can the concept of success criteria change as a result of the content being taught, i.e. success criteria for procedural and letter writing vs. success criteria for problem solving?
 * If we want students to think for themselves then you must be careful not to scaffold too much. It seems that success criteria is often scaffolding so a student achieves level 3, i.e. what the teacher would like to see.

Bonita & Jenn

Day 5

Wow! Does time ever fly when you’re having fun!! This past week has been a flurry of activity and our minds are overflowing with new ideas and an increased understanding of math concepts and how to be effective math teachers. We have explored, discovered, and questioned all week and we are excited about the many opportunities that await us as teachers.

Below are a few of our final highlights and comments from Math Camppp 2011, as well as some parting quotes about our experience.


 * We found that having the opportunity to view videos and samples of students’ work and then discuss what feedback we would give these students (both in the moment and at a later time) was extremely beneficial to us as new teachers.
 * We have furthered our understanding of the three part math lesson, especially with regards to the consolidation part and the three sub-parts found within the consolidation part.
 * We feel much more prepared with regards to giving students feedback as a result of the activities and the resources provided to us at Math Camppp.
 * We have enjoyed having the opportunity to network with other professionals who are as passionate about math as we are and it was amazing how willing everyone was to share their experiences and resources with us.
 * It was awesome to be able to see theory put into practice. We have been exposed to a multitude of theory in our pre-service programs and to actually see this theory being implemented in classrooms is fantastic.
 * Multiple Representations = Meaningful Math for All Students. What more can we say?
 * We are excited to create collaborative learning communities in our classrooms where students feel safe to discuss and question the math they are doing and to explore new problems and ideas.

Some parting quotes:

“I can’t wait to apply all the new things I have learned and connect with all the people I have met”

“Holy cow! I thought I had a handle on it but now I realize I only had a small portion.”

“Math Camppp ROCKS!!”

“Math Camppp is essential for ALL teachers”

“This week has been amazing, from the plenary sessions to the breakouts and the awesome participants! Not only have I come away with a firmer grasp on algebraic thinking and proportional reasoning, I have also gained a whole new understanding of the three part math lesson and a toolbox full of fantastic tools to help me give my future students quality math tasks and effective feedback to challenge them and help them to be all that they can be!”

“Proportional reasoning at its finest: a slice of banana chocolate cake for you, two slices of banana chocolate cake for me. A slice of banana chocolate cake for you, two slices for me…talk about a great ratio!!”

We have all had an amazing time this week and we are so grateful to have had the opportunity to be involved in this ground-breaking event. We are honoured to be a part of a community of educators who are actively changing the way students view math and making math accessible and meaningful to ALL students! You have welcomed us into the teaching profession and shown us multiple ways of thinking about both math learning and teaching, and for this we are truly thankful!

Until next time…

The New Teachers (Boni, Jennifer, Jessie, Shari, Catherine, Nikki, and Kristin) Math Camppp 2011

Jessie, Boni, and Nikki