Assessing Talking Turkey

The Turkey is all gobbled up! And it was a success. I am so pleased with the math that came out of it.

Once the problems were solved, groups of students came to the front of the class and presented their solutions. They were showing their peers how they solved the problem, reasoning and justifying their thinking and teaching others how to do things such as add fractions and decimals, represent decimals to add, and even introduced mixed numbers and improper fractions. I don't think I could have done a better job. They were drawing out their representations on the white board and using manipulatives to model their thinking.

The picture above shows how one particular student went about solving the problem. He used pictures to help him understand the problem; the circles within circles represent the amount of turkey each person in Sam's family ate, with one small circle representing 1/4 kg. He then took this information and drew a number line to show that he was meeting all the requirements for the problem as he had to prove that Uncle Roy, for example, at the most and Judy the least. He also used the number line to help him get the total amount of turkey that was ate. From there he went on to represent each amount using fractions, including improper fractions and then mixed numbers. He spent the majority of his presentation teaching his peers about these two concepts and most actually understood it. Oh, and did I mention that his mom told me that he did not like math and that he had a lot of trouble with it in previous years!! I was impressed to say the least.

So basically this is how my math year is going to unfold. Today, I am planning a little follow up to see how much students learned from these activities. I plan to do a quick assessment of representing decimals, and then give them a situation where they have to decide if three decimals are ordered correctly. One of the outcomes in Grade 6 is the multiply a whole number by a decimal number, so I will also do a preassessment to see where everyone is with this which will help me decide where to go next in instruction.

Monday we will be starting a new problem called Pumpkin Patch Picking. Stay tuned!

Talking Turkey

Now that things have settled down after the storm, I have introduced the first "real" problem to students in both grades 5 and 6. The problem is as follows:


Sam loves to help around the kitchen. With Thanksgiving approaching, there is plenty to do! Sam offers to help determine how big a turkey the family should buy for the dinner.

He finds some “rules of thumb” for buying turkeys. The suggested weight range is from:
• one kilogram to one and one-half kilograms per adult,
• three-quarters of a kilogram per child,
if the family wants leftovers

OR
• three-quarters of a kilogram to one kilogram per adult,
• one half of a kilogram per child
if the family does not want leftovers.

The people who made the rules of thumb do not know Sam’s family.
• The two teenagers in Sam’s family eat more than most of the adults
• Uncle Roy eats more than anybody else.
• Sam’s sister Judy does not really like turkey, so she will fill up on dinner rolls and just eat a little to be polite.
• It is hard to predict what the three young children (Uncle Roy’s kids) will eat—it depends on their mood.
• Sam loves turkey, but he guesses that the standard amount per child will be about right.
• Sam also knows that Uncle Roy will not take leftovers with him
after dinner.
• Sam’s family likes leftovers, but not too many.

How big a turkey should Sam recommend to feed the ten people (Sam,
Mom, Dad, two teenage siblings, Judy, Uncle Roy, and Uncle Roy’s three
kids) who will be eating Thanksgiving dinner? Explain your reasoning

To ensure all my students in both grades would have success with this, I manipulated the problem by making the numbers easier to think about and work with (depending on the ability level of the groups) and reduced the number of people in the family and changed some of the conditions. Here is an example of the question modified to meet the needs of one of my groups in Grade 5:

Sam loves to help around the kitchen. With Thanksgiving approaching, there is plenty to do! Sam offers to help determine how big a turkey the family should buy for the dinner.

He finds some “rules of thumb” for buying turkeys. The suggested weight range is from:

• 1 kilogram to 1 ½ kilograms per adult,
• ½ of a kilogram per child,


• The two teenagers in Sam’s family, including Sam eat more than most of the adults
• Uncle Roy eats more than anybody else.
• Sam’s younger sister Judy does not really like turkey, so she will fill up on dinner rolls and just eat a little to be polite.
• Sam’s family likes leftovers, but not too many.

How big a turkey should Sam recommend to feed the six people (Sam,
Mom, Dad, one teenage sibling, Uncle Roy, 1 child sibling) who will be eating Thanksgiving dinner? Explain your reasoning

Here, I have modified the problem without losing the integrity of the process in solving the problem.

I have grouped my classes by ability and then let them go. I introduced the problem and made sure they knew what I expected (answers with pictures, numbers and words)and set them on their way! Throughout the class, I went around listening in on their conversations. What I heard was nothing but rich mathematical discourse. These students, even those that proclaimed they hated math began to come alive and was engaged in the activity!!

Post IGOR

We are back! Hurricane IGOR has certainly torn away September month and now it is time to get back on track. Students have been back to school since Monday and I have stepped it into high gear with the problem solving.

In the beginning of the school year my goal was to establish a respectful, relaxed classroom environment where students became more comfortable with themselves as well as with their peers. I wanted them to see that math could be interesting and that it was ok to make mistakes. Teaching Grade 5 from last year, I knew I would have a little more work ahead of me before I could go full steam ahead with them. I needed to get them comfortable with the unknown (not using a text book, no tests, different expectations) and ready for working more independently. I needed to start with getting the math discourse going and having students begin talking about math and how they were thinking about it. I did simple problems with them getting them used to how the class runs. I also needed to get a feel for their personality, strengths and needs. One of the key ingredients to teaching this way is to know your students; to be able to give them problems at their level that will challenge them but yet give them success. During the classes I would have students work together and allow as much freedom as they needed. I would sometimes interject their conversations and refocus them by asking a question to get them back on track.

My goal for my Grade 6 class was a little different because I had those same students last year. I was able to mold them and get them to a place at the end of the school year where they could just jump right in this year and begin learning math through problem solving. Already knowing their strengths, weakness and areas of need really jump started the year for me. I knew what groups worked the best and who to call upon for help when it was needed.

Due to the Hurricane that blew through here 2 weeks ago, students are only just returning from a 2 week absence from school. So, it is the first week of October and I am only beginning my first attempts of seeing my kids in action.

September 13, 2010

So school has started and here I am diving into the year. What have I done in math class so far? Nothing! Well, that is probably what my students would say, but in reality I have spent the last week starting and working on the most important ingredient of my classroom; having students respect and appreciate each others differences and begin to have them work as a team.

I did not teach the Grade 5's last year like I did my now Grade 6's. So I needed to know more about these individuals. I talked about how important it was for me to get to know them and their feelings toward math. I explained how you think about math and feel about it really makes a difference in how you do it. I had them then write their math autobiography where I told them to be completely honest with me about their feelings towards math, why they liked it or not, what they think they are good at in math and things they have trouble with. Well, they took off. I was a little worried they would kind of not tell the truth to make me happy in saying they all loved math. But they were genuinely honest. Most said they did not hate math, but that it was not their most favorite subject. They felt it got boring on times, especially when they would use the book. They all said they felt they would like math this year and that they hoped I would make it fun for them. I was pleased!!

To bring this classes together more, I decided to proceed with one of my favourite team building activities of all time. I challenged them to build the tallest tower using only plastic drinking straws, paper clips, modeling clay, and tape. I put them into groups of 4-5, gave them the materials and stepped back. I wanted to watch the dynamic of each group and identify the team players and those that think there is an "I" in team. It didn't take long for the leaders to emerge and the followers to follow. I quickly stepped in and got them on track and asked them to start thinking like a team. I was pleasantly surprised to see that after some time, all groups realized they could work faster as a team rather than individuals. All was good.
At the end of the activity we had a great conversation about all the ways they used math. They could not believe how much math was involved such as planning, designing, communicating, knowing how shapes affect the design, predicting how much tape they would need to hold the straws together and so on. I felt this activity was a great way to begin my inquiry based math class and it gave students a chance to dive in and have fun with math, even if they did not realize it!!

Assessment the third time around

Before I begin to talk about how I am assessing my students in math this year, I feel I have to first explain how I am planning to structure my math classroom and learning environment.

In taking on a Problem Based / Inquiry Based approach to teaching mathematics, one can appreciate the importance of providing rich, authentic and thought provoking problems and tasks where children learn the intended math by solving the problems. Over the last two years I have collected and combined many good questions and tasks. I have also discovered the wealth of problems on the NCTM website under "Teaching Children Mathematics Problem Solvers". It is here that I will base my entire year of math on.

To help keep me organized, I have read through all of the tasks that I intend to introduce this year in both Grade 5 and Grade 6 math. I have identified the big ideas, or the main mathematical concept that each of the problems will deal with. In a chart form listing all of the specific outcomes for each grade, I have listed the name of the problem under the corresponding outcome that students would be working on by completing the problem or task. This way I can tell by a glance what outcomes are being assessed for each problem, or what problem I can give a student who needs to work on a particular outcome.

This leads me to the assessment piece. As students are working on individual problems/tasks, I will identify which specific outcomes they have been dealing with and determine the level of achievement they have attained. If I feel for certain they have successfully achieved an outcome, I will use a checklist of outcomes and check off that particular outcome for that particular student. This will give me a quick way of telling which students have achieved which outcomes.

To qualify the level of achievement of these outcomes, I will continue to use my chart where each outcome that students were working on will be identified and a comment about student success of the outcome will be made. I am thinking I will try and do this for each individual problem that students complete, but I think this may get really busy and for little gain. I need to at some point communicate with parents their child's successes in math and share with them the work they have completed. I am thinking I may continue to do the chart making comments on each outcome, but will do so electronically and then once three or four activities or tasks are completed, print off the completed chart and then send it home.

For my purposes, this will solidify my own knowledge about student thinking in mathematics and more importantly provide me with evidence about students' needs.

Does this make sense?

Assessment

One of the biggest challenges for me was getting my head around assessment. If I were to implement this Problem Solving approach in my class, how was I to assess student learning? I found from the last two years organization and thinking ahead are two essential ingredients to getting assessment done right. I found that I needed a way to track student achievement of individual outcomes as each student was at a different place at different times. I needed someway to monitor their progress as they worked through concepts and I needed some way to communicate all this to home.

The first year I collected every piece of work students completed and assessed each and every one. At that time I was still in a unit base mind set where I would have students solve problems based on a set unit of work. For example, students may for a month work on problems concentrating on measurement or fraction. I would then list all the outcomes completed in chart form and report on each one individually and identify what level of achievement the student accomplished. This was very time consuming and I found I was reporting on a lot of the same outcomes more than was needed. I also found that I was not communicating with home very often as it was taking a over a month, if not more to complete the unit of work.

Last year, I tried a similar approach but decided to not collect every piece of work. Instead, I gave students specific questions and tasks that would assess their understanding of the work they were completing. I used these one page tasks for their assessment of the unit work and found it less time consuming. However, I still had to complete the chart of outcomes and report on each one individually. During this year, I found by keeping on top of this work and reporting on the outcomes when I was sure a student had achieved instead of waiting for the unit of work to be completed, saved me a lot of time and torment. I like the chart form which lists the outcomes as it gives me and the parents an in-depth look at where their child is in terms of the curriculum. More importantly, it lets me see without a doubt where a child's needs are and guides me to providing them with the help they need.

This year, I am doing it differently again!

On My Way!

Welcome to my Blog!
I really hope you enjoy reading about my journey into teaching mathematics in a Grade 5 and Grade 6 classroom through an inquiry based approach. I have been playing with the idea for the last two years now and I have finally come to a place where I think I am ready to fully implement this into my math classroom.

So why a blog? I felt I needed a place where I could communicate my findings as I go and more importantly a place where I could reflect on the days/weeks activities. I also needed an informal avenue where others could make suggestions as to what went wrong in the lesson and/or what went right! I would also like to see the conversation about teaching this way open up where more teachers and educators start talking about the possibilities of going outside the box and daring to be different.

So let's begin!