Context
The "Small Group Lesson" and the "Case Study" assignments were completed during the Spring 2007 Semester as a Block I requirement for Math 3030, Investigating Mathematics and Learning. It was created under the advisement of Tracie Salinas. Both assignments were completed at Moravian Falls Elementary School in Mrs. Heather Quessenberry's Kindergarten classroom, during our Block I internship.
The "Small Group Lesson" was co-taught with Molly Hartfelder and designed to reinforce the concept of graphing. It covers making a bar graph by using manipulatives, and was developed specifically for Mrs. Quessenberry's Kindergarten students. The "Case Study" was completed independently; however, I interviewed Molly Hartfelder on how she felt about the Addition Lesson I used, and her child was added into my report.
Impact on Student Learning
I have created the "Small Group Lesson" assignment in order to teach students about bar graphing, not necessarily to introduce the concept. Students will reinforce their previous knowledge about bar graphing, and make a bar graph using "Lucky Charms" cereal. During the lesson, students were encouraged to use the cereal as a manipulative to make their graph. There were a few other topics that students were learning through this lesson, such as working on counting skills, writing numbers, and using the right representation of colors for the marshmallows, along with learning how to make a bar graph. Students were in small groups rather than a whole class atmosphere, so students could benefit by receiving more direct teacher assistance. Not only did it benefit students, it benefited myself because I was given insight into the misconceptions students have about graphing.
I have created the "Case Study for Field Experience" assignment in order to investigate a child's learning abilities for mathematics. I will observe a student during the entirety of three different parts of a mathematics lesson, and write a case study on this child. I have changed the name of the student to protect his identity. I have named the child, "Mason". After I observed the student during the Mathematics Lesson, I interviewed Mason, and wrote a report to analyze his mathematical performance within the classroom.
Alignment
This assignment met the following North Carolina Instruction Standards for Elementary Education teachers:Standard 2: Elementary teachers have a broad knowledge and understanding of the major concepts in mathematics.
Indicator 1: Teachers have knowledge of number sense, numeration, and numeral operation. Teachers will illustrate, explain, and demonstrate prenumeration, numeration, fractions, decimals, rational numbers, integers, ratio, proportion, and percentages. Teachers will apply four basic operations with symbols and variables to solve problems and to model, explain, and develop computational algorithms.
Indicator 3: Teachers have knowledge of patterns, relationships, functions, symbols, and models. Teachers understand patterns, relationships, functions, systems, and models. Teachers recognize and use likeness and differences in defining patterns with actions, words, objects, numbers, and set. Teachers will construct tables to illustrate a relationship. Teachers will identify and apply variables, expressions, and relationships.
Indicator 4: Teachers have knowledge of data, probability, and statistics. Teachers demonstrate an understanding of the importance of formulating the proper question in order to obtain measurement and reliable answers through analysis. Teachers demonstrate an understanding of how to systematically collect, organize, analyze, and summarize data in order to predict outcomes, and various methods for reporting and representing data (graphs, charts, tables, and grids).
The "Small Group Lesson" assignment proves that I have shown how students must use their basic counting numbers; in order to show they can count the number of marshmallows for each section of the bar graph. I have provided examples of students' worksheets, asking students questions such as, "How many Horseshoes do you have?" By asking students' questions, I can see if they know how to count to the number 10. Students will also apply the basic ability of addition by telling how many they have in all. Not only do I know students have the basic counting knowledge, I know that their knowledge of relationships of patterns, functions, and models. In teaching our lesson about bar graphs, I provided examples of patterns that students could come up with in their graphs. By asking students questions like, "How many horseshoes do you have? How many balloons do you have? How many marshmallows do you have in total?" Students will be able to recognize the pattern of my questions and begin to answer by counting the number of marshmallows he/she has of that type.I also have the knowledge of data, probability, and statistics due to providing ample opportunities for students to systemically collect and organize their marshmallows for their Lucky Charms. I allowed my students to explain to me why the amount of squares they had matched the number of marshmallows of a certain type.
The "Case Study" assignment proves that I have a broad knowledge of mathematics, because I observed a child throughout an addition lesson. I was able to ask, Mason, questions throughout my interview, and help him if necessary. I was also able to hear him count correctly, and understand their task by just observing the lesson being taught. I was also able to use my knowledge of integers, algorithms, manipulatives, and models; and apply my knowledge when necessary.
Standard 7: Elementary teachers use developmentally appropriate strategies to design and deliver instruction in all areas of the elementary curriculum.
Indicator 2: Teachers understand and use an interdisplinary approach to teaching by connecting and integrating language arts, mathematics, science, social studies, healthful living, and arts concepts and processes, with appropriate technologies to enhance their teaching.
Indicator 3: Teachers promote new learning by using students' prior knowledge, misconceptions, and interests when designing lessons.
Indicator 4: Teachers implement a variety of teaching and communication strategies for instruction.
Indicator 5: Teachers assist students in developing multiple learning strategies to address discipline specific content, critical thinking, and problem solving skills.
Indicator 6: Teachers modify instruction and assessments to meet the needs of individual students.
Indicator 7: Teachers develop and use a variety of formal and alternative assessment strategies as an integral part of instruction and learning appropriate for assessing individual, peer, team, and collaborative skills.
"The Small Group Lesson" assignment proves that I understand how to integrate language arts and mathematics by changing my lesson plan to include an opportunity to read a children’s book about graphing. As a class activity, I could read the book, Alfie Gets in First, and have students help me graph the number of emotions Alfie goes through. I also made adaptations for students to include art, by coloring their graph. Students could also use technology to make their graph by using an online website. Our main focus was to promote new learning by using students’ prior knowledge.This artifact proves that we did this by showing we taught something that students’ have already learned by providing an ample opportunity for us to re-teach bar graphing, and clear up any misconceptions for students. We tried to focus on students interests by providing students with something they enjoyed to eat, cereal. We included a variety of teaching and communicating strategies for instruction because we provided questions for students to answer, instructions for students to follow, and allowing students to come up with their own name for their graph.
We allowed students to use their problem-solving skills because they had to collectively come up with a name for their graph. Students thought critically when they had to answer a question such as, “How many ‘Green Hat’ marshmallows do you have?” or “How many ‘Blue Balloon’ marshmallows do you have?” or “How many marshmallows do you have total?” Students would have to explain to me their answer and how they came up with their answer, allowing me to see how students logically came up with their answers. I have shown how to modify instruction to meet the needs of the students by providing a separate page for Accommodations as an Attachment. I have provided examples of how a teacher could modify the Revised Lesson Plan to meet the needs of an older, Elementary student's curriculum, and the needs of an ESL Learner. I have also shown how teachers can develop a alternative assessment to assessing student's just by written tests. By looking at the student's graphs for correction, I can tell whether a student has learned what I want him to learn or not.
The "Case Study Assignment" has proven that I can design and deliver instruction by connecting mathematics to language arts by having students write their algorithms. It has promoted new learning by using the student's prior knowledge to understand their answers for the misconceptions among the individual work. I have implemented a variety of communication strageties by interviewing Mason separately from the entire class, and asking different kinds of questions to find out what he has learned. I have modified his instruction based on the assessment of his learning on the addition worksheet, and found new ways to get him to think differently about a question
Standard 9: Elementary teachers understand and use the process of problem solving, reasoning and proof, communication, and representation as a foundation for the teaching and learning of mathematics.
Indicator 3: Teachers develop instruction in communication that enable all students to organize and consolidate their mathematical thinking through communication.
Indicator 4: Teachers develop instruction in making connections that enables all students to recognize and use connections among mathematical ideas, understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and to recognize and apply mathematics in contexts outside of mathematics.
Indicator 5: Teachers develop instruction in representation that enables all students to create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena.
The "Small Group Lesson" shows that I understand how to use the mathematical concepts in order to help my students think through communication. I continually asked my students questions, and repeated myself to get answers. I made connections among mathematical ideas by interconnecting the concepts of counting, and making a colored pattern. I applied mathematical concepts to children's books by making a bar graph of Alfie's emotions. I enabled all of my students to organize, record, and communicate mathematical ideas by first reteaching what a bar graph was, and then having them complete one of their own and giving it a title.
The "Case Study" assignment shows that I understand how to use the mathematical concepts in order to help my students communicate their representations of the algorithms. I asked questions to Mason, and continually asked him how he had done something. I tried to explain how counting one set of disks, and counting the other set, related to counting them all together. I used the language of mathematics, "Addition, Equals to, and All together," to get my student to understand how to add the disks together.
Standard 15: Elementary teachers encourage under represented groups to engage in the schooling process, especially mathematics and science.
Indicator 1: Teachers utilize community resources, give personal attention and encouragement to under represented groups of students, use relevant and real-world applications that interest a diverse population, and encourage under represented groups to assume leadership roles.
During our "Small Group Lesson", I tried to desperately encourage our lower achieving students to speak up more throughout the lesson, and asked them questions such as, "What should we name our Graph?" to get them to take ownership of their graph.
I continually asked Mason questions during the "Case Study Interview" about why he was doing something, and provided support when he needed to ask a question, or simply did not understand a concept, or responded with the words, "I'm lost". I provided Mason with personal attention and encouragement for when he did get the answer correct, and made sure to provide slight criticism or a different way to do the problem if he did not understand.
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