When I first stepped into the kindergarten classroom that would become the setting for my final Student Teaching placement, I was struck by how cozy and sweet the room was. Many people who have never been inside a kindergarten classroom are struck by a kind of Alice in Wonderland effect: everything seems smaller, more whimsical, more brightly colored.
This was especially true of my classroom, where the classroom's calendar is flanked an elaborate kitchen set, and where math manipulatives are stored next to a huge wooden box filled with toy cars.
This was especially true of my classroom, where the classroom's calendar is flanked an elaborate kitchen set, and where math manipulatives are stored next to a huge wooden box filled with toy cars.
My Students
I first met many of my students during the school's Orientation Open House. They entered the room cautiously with their parents, craning their necks and roaming with curious eyes towards the desks. When I tried to introduce myself, many of them hid behind their parents' legs, or just regarded me shyly.
The first day of kindergarten is, naturally, very emotional for both children and parents. I had helped my master teacher prepare our opening activity, and I'd been given some crucial pieces of advice from both my master teachers, who share the classroom teaching responsibilities.
The beginning of the semester was overwhelming. My master teachers were teaching a combination Kindergarten/First Grade class for the first time in six years. Our classroom would be made up of six first graders and eighteen kindergarteners, fourteen of whom were boys. I quickly realized that though five and six year-old boys can be lively and funny, they are also active, talkative, and somewhat slower to settle into a routine compared to their female peers. How could we channel so much energy effectively, I wondered? How could we teach such a diverse group of students to become independent learners?
I first met many of my students during the school's Orientation Open House. They entered the room cautiously with their parents, craning their necks and roaming with curious eyes towards the desks. When I tried to introduce myself, many of them hid behind their parents' legs, or just regarded me shyly.
The first day of kindergarten is, naturally, very emotional for both children and parents. I had helped my master teacher prepare our opening activity, and I'd been given some crucial pieces of advice from both my master teachers, who share the classroom teaching responsibilities.
The beginning of the semester was overwhelming. My master teachers were teaching a combination Kindergarten/First Grade class for the first time in six years. Our classroom would be made up of six first graders and eighteen kindergarteners, fourteen of whom were boys. I quickly realized that though five and six year-old boys can be lively and funny, they are also active, talkative, and somewhat slower to settle into a routine compared to their female peers. How could we channel so much energy effectively, I wondered? How could we teach such a diverse group of students to become independent learners?
The School
The school my cozy classroom is tucked into is situated in an upper-middle class neighborhood in the beachside city of Encinitas, California. The school boasts a successful Dual Language Immersion program for each grade, kindergarten through sixth. Two-thirds of the students are white, and the majority of the school's English Learners are enrolled in the bilingual program. Nevertheless, the population is culturally and economically diverse.
Often, the school's social and economic diversity is visible in the neighborhood's contrasts. Less than a half mile inland from a sprawling cliff-top mansion, there is a block of apartments not-so-affectionately known as "Tortilla Flats." My students are the sons and daughters of surfers, executives, migrant workers, artists, and small business owners. It was my job to try to appeal to as many of them as possible as they transitioned into elementary school.
The school my cozy classroom is tucked into is situated in an upper-middle class neighborhood in the beachside city of Encinitas, California. The school boasts a successful Dual Language Immersion program for each grade, kindergarten through sixth. Two-thirds of the students are white, and the majority of the school's English Learners are enrolled in the bilingual program. Nevertheless, the population is culturally and economically diverse.
Often, the school's social and economic diversity is visible in the neighborhood's contrasts. Less than a half mile inland from a sprawling cliff-top mansion, there is a block of apartments not-so-affectionately known as "Tortilla Flats." My students are the sons and daughters of surfers, executives, migrant workers, artists, and small business owners. It was my job to try to appeal to as many of them as possible as they transitioned into elementary school.
The Curriculum
Math instruction within our classroom was varied, and fell within the California State Standards. A half hour of each day was devoted to Calendar Time, which provided the whole class with practice in tracking the days of the month, tallying the number of days we had been in school, and counting by 2's, 5's, and 10's. The math curriculum also utilized the workbooks designed by enVision, a core curriculum for students in grades K through 6. Each day, students completed pages from the workbooks as an entire class. Students completed the worksheets step-by-step, and were encouraged to erase and correct any mistakes. I observed that highly directed math instruction worked well to channel the bubbling energy of our students, and the first few weeks of school I watched as they transformed into more and more focused young learners.
Students in our classroom were happy and engaged. Our math instruction was rich and content-driven, but students seldom participated in independent or small group math activities. I wanted to learn more about the benefits of small-group instruction, as well as developmentally appropriate practices for younger students. Furthermore, as my master teachers and I learned about the rigors of the Common Core, I wanted to investigate instructional methods which promote creativity in the face of academic challenges.
The Challenges of ST Math
One of the first professional development events that I attended as a new Student Teacher was a training event for a new software program called ST Math. ST Math is a program developed over the span of more than ten years by the MIND Research Institute, a nonprofit neuroscience and education research program based at the University of California Irvine. I was impressed by how simple and straightforward the program seemed, and yet how challenging the problems turned out to be.
When I returned home after my training, I was inspired to do more reading about the design of ST Math. I was amazed by what I read, and for good reason. ST Math teaches mathematical concepts and spatial awareness through the use of bright, clean visuals that are completely language independent. Furthermore, the program aligns perfectly with State and Common Core standards. The fact that the program is language independent is a boon to school districts across the country who serve an ever-growing number of English Learners. In an article published in 2010, the principal of one such school stated the following:
"The students are able to fully understand a concept visually before they ever have put a label on it. That's the opposite of how we traditionally teach math, which is to tell students--in a language they may not even fully understand--what they are going to learn before they experience it."
Two weeks later, we introduced ST Math to our students. One of our first grade students, an English Learner who has struggled with language, became so excited by his progress with the program that he jumped out of his seat and shouted, "Miss Berger! I get it!"
Many students showed a wonderful enthusiasm for the new program and its mascot, JiJi the Penguin. It also became clear that the students struggled with one of the central components of the program: they became anxious when they could not successfully solve a problem after the first try.
Over the next three weeks, I observed as some students began to feel confident enough to click around the screen until things began to happen. However, others constantly sought my help in order to guide them through the tasks associated with each game. I observed that with only one or two exceptions, the students who needed the most help with the new program were students who were, according to kindergarten academic standards, among the lowest-achieving in math in the class. I began to wonder if the problem-solving abilities of these same students was impacted by the emphasis on teacher-led instruction in our classroom.
The next question seemed obvious, but was a very challenging one to answer. How might I address the need for more open-ended, problem-based instruction in my classroom?
Conducting My Needs Assessment
Based on my observations of the students and their work with ST Math, they very much enjoyed the program, with its emphasis on play-based learning. Most students seemed eager to negotiate each game by applying methods of trial-and-error. I was motivated to learn more about how we could integrate informal, problem-based instruction into our classroom.
In an effort to learn more about developmentally appropriate math instruction, as well as the benefits of problem-based instruction, I began to read different books and articles about these subjects. In the book Integrated Curriculum and Developmentally Appropriate Practice: Birth to Age Eight, education researchers Hart, Burts, and Charlesworth write that "Classroom activities that build [learning] connections are characterized by using a variety of materials and situations and by the presence of a great deal of social interaction." They also describe the three ways young children acquire mathematics concepts, according to educational research. (I discuss the relevance and importance of this in greater depth in my Literature Review.)
Cognitively Guided Instruction
As I was researching math instruction and developmentally-appropriate practices, as well as reading more about the goals of problem-based instruction, I was invited to a school inservice about Cognitively Guided Instruction that was being led by one of the school's recently retired teachers. Cognitively Guided Instruction, I learned, is a research-based philosophy for teaching mathematics. Within Cognitively Guided Instruction, or CGI, teachers provide word problems and guide their students toward understanding how they might implement multiple strategies in order to answer the question for themselves (Knapp, 1995, p. 40). The emphasis is not on the correct answer, but on the independent problem-solving strategies of the students. As researcher Debra Viadero states,
"If teachers understand those strategies and understand how children think mathematically...they can teach in ways that help their students build on what they already know and learn from each other."
A classroom that uses CGI is one that encourages an experimental attitude towards problem solving. Teachers and students share and discuss strategies, and students are driven by their own problem-solving skills. When students do not learn based on understanding, they are simply learning a series of isolated skills that can only cover a limited subject area (Schmidt, 2006, p. 93). Franke and Kazemi summarize the benefits of CGI nicely, stating:
"When individuals learn with understanding, they can apply their knowledge to learn new topics and solve new and unfamiliar problems."
I resolved to implement a new classroom routine using CGI math problems. As I began to research the possibilities, I began to structure my own thinking around a central question:
How does open-ended, problem-based learning affect student achievement and attitudes towards math?
I hoped to answer this question by gathering evidence on a number of sub-questions.
A classroom that uses CGI is one that encourages an experimental attitude towards problem solving. Teachers and students share and discuss strategies, and students are driven by their own problem-solving skills. When students do not learn based on understanding, they are simply learning a series of isolated skills that can only cover a limited subject area (Schmidt, 2006, p. 93). Franke and Kazemi summarize the benefits of CGI nicely, stating:
"When individuals learn with understanding, they can apply their knowledge to learn new topics and solve new and unfamiliar problems."
I resolved to implement a new classroom routine using CGI math problems. As I began to research the possibilities, I began to structure my own thinking around a central question:
How does open-ended, problem-based learning affect student achievement and attitudes towards math?
I hoped to answer this question by gathering evidence on a number of sub-questions.
- How will problem-based learning assist students in learning problem-solving strategies?
- How will students' understanding of their own strategies evolve?
- Will students' attitudes toward the new method improve as they gain confidence in their ability to problem-solve?