The elementary mathematics teacher is responsible for teaching students to think, talk, and write in the language of mathematics. All children have the capacity to learn mathematics and express themselves through numbers. The teacher’s job is to teach empirical thought and encourage them to use it. Van de Walle, Karp, and Bay-Williams state, "Children and adults alike need to think of themselves as mathematicians, in the same way as they think of themselves as readers." (Van de Walle, Karp, & Bay-Williams, 2010) Mathematics can be taught to all students. An effective elementary math teacher fully understands the information they are presenting and presents it with excitement and a positive attitude. Learning math is an essential like skill, just like reading. An educator’s job is to teach their students math, reduce their anxiety about learning math, and enable them to become lifelong learners of mathematics.
As a teacher of elementary mathematics, I aim to bring an open mind, positive attitude, enthusiasm, flexibility, high expectations, and an adaptable knowledge of mathematics content to my students. I will teach mathematics using multiple teaching strategies, adjusting to meet the needs of each of my students. I will accommodate all learners’ culture, language, and intellectual differences with the goal to make learning math enjoyable and meaningful. The math textbook will be used in the classroom, but it will be only one of many math resources. I will incorporate the use of manipulates, such as blocks, calculators, and computers into my instruction and encourage my students to use them when either working individually or in cooperative groups. Within reason, I will enlist the help of parents via meaningful activities to do at home. I hope to illustrate the importance and flexibility of math and also to build the confidence and self-esteem of the learners ability. I will also utilize multiple techniques to assess my students’ level of understanding of math: journals, class presentations, and one to one conversations. Finally, I will fully incorporate the Washington State Mathematics Learning Standards into my curriculum and instruction.
Knowledge is constructed. Oakes and Lipton state, Knowledge (or subject matter or content contained in the school curriculum) is not fixed, is not the same for everyone, and varies in different contexts over time." [Oak07] Children do not learn by merely "taking in" information. Students’ knowledge is built following a variety interactions they have with their environment: peers, teachers, and families. Learning is facilitated by discovery, experimentation, lectures, and meaningful exercises that develop both conceptual and procedural understanding. In mathematics, this can be accomplished using cooperative, self-guided, and direct instruction. No matter the teaching strategy, it is important that math is taught using both a conceptual and procedural approach. Students in my classroom will do more than just complete a set of prescribed problems or reiterating what I have just taught them. In math, they will learn multiple, flexible strategies to solve math problems. They will apply these approaches to problems developed in class and experiences outside of our classroom. They will also evaluate their conclusions, reflect about their processes, and what changes they can make the next time they encounter this type of problem. Students in my class will "do" math throughout the day, not for just a fifty minute period. Again, learning math is an essential life skill. I will demonstrate to my students many of the different examples of mathematics that we encounter on a daily basis, such as the calendar, telling time, and sharing with our friends.
In my cooperative classroom, during math, students will be encouraged to work with their peers for a variety of tasks or individually as it is necessary. For the majority of the time, they will work in groups of two, three, or four. As needed, our class will convene on the carpet for a mini-lesson. During these meetings, I can review what we worked on the previous day or activate their prior knowledge of a concept learned earlier. I can also introduce new information during our carpet time. However, it is important that students have time to explore, experiment, and test the information presented during our class conference. Therefore, during our conferences, we will meet for a small period of time, and sporadically as needed. Throughout our math time, I will encourage students to engage in meaningful conversations about math with me and with their peers. For example, when working on story problems, learners can demonstrate how they solved a problem. Another student can share how they illustrated the story problem. Again, math is more that doing problems. It is about understanding, applying, and analyzing the information that you are presented and supporting the solution that they discovered. Students can better come to these understandings while engaging in classroom talk.
To accommodate all of the learners in our classroom community, I will also differentiate instruction, as needed to help all learners accomplish the goal of the lesson. For example, to follow up on an activity about measurement, with one student or a small group, I can provide some direct instruction if they were not able to come to a complete understanding while with the cooperative group. Not all students learn effectively in cooperative environments and therefore, teachers should differentiate instruction as it is needed. Whether it is a student with learning or behavioral disabilities or a student whose native language is not English, I will work with them and collaborate with other teachers to understand how I can best meet their needs while teaching mathematics.
The curriculum based text book (standards based preferably) will be a part of the math instruction in my classroom. However, I will also incorporate other materials, such as story books, experiments, and real life problems that will complement the text and the Washington State Mathematics Learning Standards appropriate for the class. My goal is to teach students to look beyond the math text for their math experiences and examples. For example, in early fractions, I will ask my students to find multiple examples of fractions in and outside the classroom. They could use clocks, items in their lunches, or how books are divided amongst the library. The ability to know and do math is constructed. The more "real life" math situations I can provide my students, the more they will become stronger and confident in their ability in mathematics.
The use of manipulatives will be encouraged for most of the math experiences my students will encounter in my classroom. "Manipulatives such as blocks and scales and technology such as calculators and computers are useful tools, and students should be learning how and when to use them." (Center, 2008) Manipulatives can represent another approach to thinking about math. Manipulates, such as pattern blocks, Unifix Cubes, Base Ten Blocks, Cuisenaire Rods, recycled items to count and sort, geometric blocks and shapes will be available in clearly labeled clear bins in an area that is easily accessible for students in the classroom. Students will be encouraged to explore, experiment, and "flex" their understandings about math concepts with these tools. When introducing a new topic or reviewing prior knowledge, I will incorporate manipulatives to illustrate what we are learning. When working independently or in small groups, students will be encouraged to illustrate their understanding with these tools. I will also use them as a way to assess a learners understanding of a concept or procedure. Manipulatives are also a great resource for teaching children who are not confident in their math abilities, have a learning disability, or are non-English speaking. Manipulatives too can accommodate most teaching strategies, such as cooperative learning, learner-centered investigations, and direct instruction.
Technology such as calculators and computers provide another type of manipulative or resource in the classroom that can help students grow and flex their understanding about mathematics. Van de Wall, Karp, and Bay-Williams state, "Virtual manipulatives are a good addition to physical models, as some students will prefer the electronic version; moreover, they may have access to these tools outside of the classroom." (Van de Walle, Karp, & Bay-Williams, 2010) Calculators, for example, can easily demonstrate relationships between numbers. Students can easily explore small and large numbers on a calculator and what different operations have on those numbers. Manipulatives, both physical and technological are essential to teaching children the flexibility of math and how you can use multiple approaches to any given problem. The more experiences learners can have to think, construct, and explore a mathematical concept, the more likely they will be to develop an effective, rich understanding about the concept.
Enlisting parents as partners in the education of their child, benefits the students' learning. "All students achieve more when their families support their learning." (Van de Walle, Karp, & Bay-Williams, 2010) Parent partnerships are a useful strategy for building a students' self-esteem and confidence about mathematics. Parents can participate in a variety of activities that can be done at home to deepen a child's mathematical understanding. Before sending an assignment home, directions and goals for the assignment must clearly be laid out (for the student and the parent). Parents’ time is valuable and time spent on fruitless exercises will diminish the effectiveness of the assignment. Many fun, enriching math activities can be done at home. For example, parents and students can estimate measurements around their house, they can find multiple examples of fractions, or together they can develop and solve a math problem based on an experience that occurred at home. They can even cook a meal together incorporating their favorite recipes for their family or invite another family to join them and double the recipes. Incorporating parents into the study of mathematics can benefit student achievement and boost self-esteem. This partnership will also be valuable during the formal assessment of student development throughout the school year.
Assessment is an important part of my teaching of mathematics. Integrating assessment throughout lessons and activities allows more informed instructional decisions about what to teach and when information should be taught. It will allow me to make progress checks on students' development in mathematics in relation to their learning goals and evaluate student achievement. The National Council of Teachers of Mathematics states, "Assessment should be more than merely a test at the end of instruction to gauge learning. It should be an integral part of instruction that guides teachers and enhances students' learning." ((NCTM), 2010) In my learning community, assessment, formally or informally, will take place daily. It will help guide my instruction and the strategies I am using to teach my learning community.
In mathematics, assessment should incorporate a multiple of concepts, procedures, mathematical processes (problem solving, reasoning, and communication), and even students' confidence and beliefs about mathematics. (Van de Walle, Karp, & Bay-Williams, 2010) For example, when students provide answers to problems, I will ask for them to justify their conclusions, either orally, written, or using illustrations. Some assessments will not include an answer to a set of problems. In order for students think, talk, and write effectively about mathematics, I need to confirm that students are able to do more than just provide an answer. They need to be able to explain, test, and defend their conclusions.
Assessments in my classroom will take shape in multiple ways. For example, I will incorporate math journals for students to reflect about a class lesson, explain a method they used to solve a problem, develop questions that they may have about a concept or procedure, or defend or evaluate their solution to a contextual problem. The journal will be a collection of their work and assessments throughout the school year. I can use their journals as tool make decisions about instruction, evaluate the effectiveness of the math curriculum, and monitor their progress towards their learning goals. Journals will promote learning in my classroom. They are also a great opportunity to students to continue their practice of writing math.
Another type of assessment I will use in my elementary classroom are rubrics and performance indicators. Van de Walle, Karp, & Bay-Williams define rubric as, "A framework that can be designed or adapted by the teacher for a particular group of students or a particular mathematical task (Klum, 1994)" (Van de Walle, Karp, & Bay-Williams, 2010) A rubric is a rating scale that evaluates performance level on a task rather than a series of problems graded right or wrong. The more specific the task the rubric is assessing, the better the feedback. "Performance indicators are task-specific statements that describe what performance looks like at each level of the rubric and in so doing establish criteria for acceptable performance." (Van de Walle, Karp, & Bay-Williams, 2010) Meaning, based on the rubric, the student will be assessed on what is acceptable achievement. Both rubrics and performance indicators should focus on learning objectives and not the grading scale.
All children can learn math. As a teacher, it is my job to teach and encourage my students to think, talk, and write about mathematics in an environment that is rich with mathematical experiences and encourages their development as lifelong learners of math. Daily, I will bring to my students a positive attitude about math, an excitement about learning math, and my high expectations for them to develop a rich understanding about math. I too will continue to develop my own knowledge about mathematics and be able to present to my students.