Teaching Mathematics from a Problem Solving Approach

I enjoy teaching mathematics, but in kindergarten it always seems to be a struggle to find a curriculum that is hands-on, standards based, rigorous and developmentally appropriate--all at the same time. In addition, most curriculum programs take the same approach to instruction: The teacher models a mathematical principle, the students engage in practice of the principle; either with a partner or alone, and then the students do a worksheet to show their understanding of the principle.

This model did not feel right to me and I was not convinced that the students were achieving a deep understanding of the mathematical principles they were being taught. I began to do some research and came upon a book called Teaching Student-Centered Mathematics.

This book completely changed the way I thought about the teaching of mathematics. Finally, I understood the underlying foundation behind the different mathematical strands of our curriculum. To say it was eye-opening would be an understatement!

However, this didn't solve the problem of the curriculum we currently had. I decided to approach our ACP committee for permission to rewrite our current curriculum from a problem solving approach, which is the approach recommended in this book. 

Once I received permission, I spent the summer creating units that presented the curriculum in a different format: First, the teacher poses a problem to the students. Then, the students grapple with the problem; either in a large group, small group, with a partner or alone. After that, the students come together to discuss how they approached and solved the problem. Finally, the teacher clarifies any misconceptions, introduces pertinent vocabulary, makes anchor charts to support concepts and wraps things up by stating the essential understanding that should be taken away from the lesson.

The rest of my team agreed to try this approach with me, and we meet once a week to discuss how things are going, share student successes and struggles, preview upcoming lessons and discuss assessments. This collaboration is a vital part of teaching in this manner, as it ensures fidelity, provides a means for us to think about mathematics in a deeper way and allows to to make meaningful changes to the curriculum.

The one take-away from all of our meetings is that the students enjoy learning mathematics in this way. It is not always easy, and there is still the struggle of finding a way to reach all learners, but all in all, it is a win-win for us so far. I think the biggest challenge for me has been to teach students how to talk about their thinking, especially this early in the year. Often, it is a few students who carry the conversation, but I am hopeful that will continue to change as the students mature and become comfortable with the process.

Here are some pictures from our journey thus far:

Sorting and Classifying

Finding things that are the same

The Great School Supply Sort: How can we organize all our supplies?

A work in progress

"I have all the glue sticks. Bring me your glue sticks!"

The finished product

Position and Location

Representing positional words on the playground

Finding hidden treasure by using positional words to follow a map

Creating our own maps

Patterns

Creating placemats using pattern blocks to form a pattern

Having Fun With Our Five Senses

Meet Mr. Broom. Mr. Broom joined us as a special guest the first two weeks of school. He didn't talk much, but he did assist us as we learned about our five senses. 

We began our study of the five senses by reading the book Me and My Senses by Joan Sweeney. This book was a wonderful introduction to our five senses. The language was simple and easy to understand and the illustrations captured the attention of young learners.

Once we had established some common background knowledge, we created a chart to capture our questions about the five senses. We started by discussing what it means to wonder and what it means to ask a question. Slowly, the questions began to emerge and we soon had enough to inspire us to do some research and learn more about our five senses.

Sense of Hearing

After reading the book Hearing, from the Acorn series of books, the students played a game of Sound Bingo. In this game, they listened to a CD of different sounds, such as a dog barking or a plane taking off. Then, they had to find a picture that matched that sound. We also read the book A Listening Walk by Paul Showers and went on a listening walk around our school. We were amazed to discover how many things we could hear when we closed our mouths and focused on listening to the world around us.

Sense of Sight

We began our study of the sense of sight by reading the book Seeing. Then, we went into our cubby area, turned off the lights and conducted a seeing experiment. We sat knee to knee with a partner and looked into their eyes. Without the students knowing, I turned on the light. The room was filled with gasps as the students saw their partner's pupils shrink dramatically. They were even more amazed when I turned the light back off and they saw their partner's pupil double in size. This led to a lively discussion about the purpose of the pupil in our eye. The students were able to determine that the pupil got bigger because "There wasn't enough light." Likewise, they deducted that the pupil got smaller when "There was too much light." The next day, we tested our sense of sight along with our powers of observation while we played a game of "I Spy."

Sense of Smell

After reading another book in the Acorn series, titled Smelling, the students tested their sense of smell by sniffing a variety of mystery bottles. We learned that unless the brain has experienced a smell before and put a name with it, it will not be able to recognize it. The students were able to identify vanilla and cinnamon out of the five mystery scents.

Sense of Touch

We had fun finding things around the classroom and hiding them in our "Feel Box" for others to touch and guess. Some were definitely easier than others to identify! We read the book Touching and learned that the nerves in our bodies send messages to the brain and then the brain tells us what we are feeling.

Sense of Taste

In what was probably the most dramatic day of our five senses study, the students participated in a taste test after reading the book Tasting. They were each given a plate with four items on it: A lemon wedge, Tootsie Roll, Pringles chip and a piece of Baker's chocolate. They were told they could eat the items in whichever order they chose, but in the end, they had to try to determine which items were salty, sweet, sour and bitter. Suffice it to say, Baker's chocolate was an unwelcome surprise for their young taste buds!

Popcorn: An Experience for Every Sense

We culminated our study of the five senses with a multi-sensory experience...popcorn! Each student received a plate of popcorn and they explored it one sense at a time. We created a chart of words which described the way the popcorn looked, felt, smelled, sounded and tasted. It made "sense" to add some special seasonings to our popcorn to enhance the tasting experience!

Teacher as Facilitator

On Monday, my students decided we should have a party. After a full school year of learning and growing together, who was I to say no? 

I truly believe that the role of the teacher is to be a facilitator of learning. This can be a challenge when working with young students, but the rewards far outweigh the challenges. Planning a party seemed like the perfect opportunity to hone my facilitation skills.

On Tuesday, we created a list called, "Things Found at a Party." 

On Wednesday, the students were placed into groups and each group was given a large sheet of chart paper with a category from Tuesday's list written at the top. They worked with their group to brainstorm ideas. I was impressed with their ideas and amused by some of their spelling choices. My personal favorite was the entertainment group's idea to "roll around on the floor."

On Thursday and Friday, the students and I used voting and tally marks to narrow down the lists and come up with an official party plan. This week, we will set a date and time and work on gathering supplies for the big event.

What was my biggest take away from the process? I realized that with a little bit of facilitation, young children are capable of planning and organizing a big event like a classroom party. I am not going to lie, I cringed a little inside when they chose to have pancakes as their main food choice and blue Gatorade as their main beverage, but they owned the process and I have yet to hear of anyone perishing from this odd pairing.

Discovery Time 3.0

As the year winds down, I find myself reflecting on my favorite moments in kindergarten from the past nine months. Invariably, my thoughts return to Discovery Time. I am continually amazed by what I see and hear from students during this time. Because the activities are open-ended, the results are never the same and I have witnessed creativity, social awareness and problem solving skills flourish throughout the year. 

So, without further ado, here are pictures of some of our Discovery Time activities from the past few months.