Mathematics Portfolio
Prepared By: Krystal Rodney
CRIN E07
Elementary Math Curriculum and Instruction
Fall 2008
College of William and Mary
Profession Margie Mason
Table of Contents:
Page #
Overview………………………………………………………. 3
Literature Connections ………………………………………. 5
Web Resources ………………………………………………… 8
Article Review …………………………………………………. 11
Problem Solving ……………………………………………….. 20
Lesson Planning ………………………………………………. 23
Reflections ……………………………………………………… 30
Overview – What Makes a Good Math Teacher?
A good math teacher must have many qualities. One must, of course, be able to do math, and compute mathematical problems fluently. But there are many other qualities that are necessary to become a successful math teacher. One must be able to plan well, create meaningful objectives, and using state standards. A math teacher must also be able to facilitate learning, and adjust instruction on the spot to accommodate students. A good math teacher must also accommodate students in terms of their diverse needs and backgrounds. The abilities to teach problem solving and use manipulatives are critical to successful math teaching. It is also necessary to be able to connect mathematics to core content and other subject areas. In this increasingly digital age, it is also important to incorporate technology into math instruction. Good math teachers must also be to include research - based techniques in order to increase student success. Most importantly, a good math teacher must be able to communicate effectively, so as to meet every student.
This portfolio consists of some of the work that I completed in my Elementary Math Curriculum and Instruction class in the fall of 2008. The work that I have included demonstrates my ability to be an effective mathematics instructor. The first piece of work that I included in this portfolio is called Literature Connections. This is a list of books that would be useful for teaching mathematical concepts. Web Resources is the next piece of work to be included. This is a list of websites that can be used in the classroom. During the course of the semester, I reviewed and critiqued recent research in the field of elementary math instruction. I have also included lesson plans and problem solving that I have done with my third grade classroom. As the last part of my portfolio, I have reflected on the work that I have done this semester.
Literature Connections
A good teacher is able to create interdisciplinary connections across content areas. It is also important for a math teacher to use different teaching strategies to enhance student learning. In this assignment, I compiled a list of books that can be used when teaching mathematics. Along with a short summary of each book, I have included a list of ways that each book can be used in the classroom. These books are very entertaining, and would be great resources for teaching certain mathematical concepts, or as a fun way to practice math. This Literature Connections assignment opened my eyes to the amount of literature based math resources that are available. I truly enjoyed reading these books, and I will definitely use math literature in my future classroom. Using books is a great way to get students excited and interested in math.
Chicka Chicka 123
Authors: Bill Martin, Jr., Michael Sampson, & Lois Elhert.
ISBN: 0-689-85881-7
Description of content: This is very similar to Chicka Chicka Boom Boom, but for numbers. In this rhyming book, 101 numbers try to climb to the top of an apple tree. Even though there never seems to be a place for zero, he saves the day when bees bother the other numbers.
How you can use the source:
· Help develop counting skills
Citation: Elhert, L., Martin Jr., B., & Sampson, M. (2004). Chicka Chicka 123. Simon & Schuster Books for Young Readers: New York City.
Arithmetickle: An even number of odd riddle-rhymes.
Author: J. Patrick Lewis
Illustrated by: Frank Remkiewicz
ISBN: 0-439-75535-2
Description of content: This is a book of addition and subtraction riddles.
How you can use this source:
· Help students pick out the pertinent information in word problems
· Help to develop problem solving strategies like drawing a picture.
· Students can create their own math riddles after reading this book.
Citation: Lewis, J.P. (2002). Arithmetickle: An even number of odd riddle-rhymes. Scholastic, Inc.: New York City.
Less Than Zero
Author: Stuart Murphy
Illustrated by: Frank Remkiewicz
ISBN: 0-06-000126-7
Description of content: This story is about a penguin that wants to save up to buy an ice scooter. However, he buys other things with his savings, and has to borrow money from other penguins, which gives him a negative amount of clams. Throughout the story, he tries to “get out of the hole” and save enough money for his scooter.
How you can use this source:
· Introduction to negative numbers
· Drawing a number line, or a graph with negative numbers to keep track of Perry’s clams
Citation: Murphy, S. (2003). Less than Zero. Harper Collins Publishers: New York City.
A Place for Zero: A Math Adventure
Author: Angeline Sparanga LoPresti
Illustrated by: Phyllis Hornung
ISBN: 1-57091-602-0
Description of content: This is a story about the number Zero. He lives in the land of Digitaria with other numbers. Their favorite game is Addemup, which he can’t play because he has nothing to add. He goes on a journey to find his place in among the numbers. He meets people like Count Infinity, who help him learn how valuable he really is.
How you can use this source:
· This can help students learn more about the concept of zero.
· Can provide an introduction to multiplication.
Citation: LoPresti, A.S. (2003). A Place for Zero: A math adventure. Charlesbridge: Watertown, MA.
One Grain of Rice: A Mathematical Adventure.
Author: Demi
ISBN: 0-590-93998-X
Description of content: This is a story about a girl named Rani. She lives in India in a village ruled by a raja. The raja hoards all of the village’s rice. As a reward for a good deed, Rani can choose a reward from the raja. She asks for 1 grain of rice, to be doubled every day for 30 days.
How you can use this source:
· This can help students learn about multiplication by 2. You could also work backwards in the book, and talk about division by 2.
Citation: Demi (1997). One Grain of Rice: A mathematical folktale. Scholastic Press: New York City.
Web Resources
Students are becoming technologically savvy at a younger age. Many students spend lots of time playing video games, and using the computer. As a math teacher, it is important to use strategies that incorporate students’ interests and abilities. If students are not comfortable with technology, teachers can introduce technology into the classroom in a fun and non-threatening way.
In this assignment, I had the opportunity to collaborate with one of my classmates to create a list of websites. These websites can be used in many ways. We found websites that can be used to teach mathematical concepts, problem solving, and reinforce what it learned in the classroom using games. When compiling this group of websites, we explored each site. We then wrote short description of each site, and how it could be used in the classroom.
I decided to include this assignment in my portfolio because it shows my ability to use different resources in lessons. These resources can be incorporated in a lesson that introduces a topic, or provides practice and reinforcement for students.
The Future’s Channel
Address: http://www.thefutureschennel.org/hands-on_math.php
Description of contents:
Under “Teaching and Learning,” click the “Mathematics” link. Under “Activities,” you will find links for Geometry, Measurement, Fractions, and more. There are even mathematics movies children can watch movies with activities. Most of the activities are simple and easy to for the students to do.
How you can use this source
· You can give the students this address and they can work on problems in groups or even at home
· It is a more interactive site than others I have seen
The Future’s Channel. (2008). The Future’s Channel. Retrieved from September 6, 2008, from http://www.thefutureschennel.org/hands-on_math.php
Math Playground
Address: www.mathplayground.com
Description of contents:
Students can practice math skills, play games, and have fun with math with this interactive, kid friendly web site. It is easy to navigate and has fun games for every level. It is colorful and bright and will hold the child’s attention.
How you can use this source:
· Have students go on to watch videos and play games
· Another resource students can use at home to practice their math skills
Math Playground. (2008). Math Playground. Retrieved September 6, 2008, from www.mathplayground.com
Animal Math Page
Address: http://bingostreet.com/animal-math-bingo.html
Description of contents:
This is a fun site for the lower grades. It is a game children can play that has pictures of different animals. Children can pick from a number of levels and practice their multiplication and division skills. Children type in their name and the site is “personalized” for them!
How you can use this source:
· This is a great site to have children practice with multiplication and division because it gives instant feedback
· It is very easy and kid friendly, so children might revisit it time and time again
Animal Math Page. (2008). Animal Math Page. Retrieved September 6, 2008, from http://bingostreet.com/animal-math-bingo.html
Math for Kids: A Medieval Adventure in Problem-Solving
Address: http://library.thinkquest.org/4471/
Description of contents: This website was designed for and by 4th graders. Students can solve word problems, or design their own word problems. Students can also learn how to solve word problems through multiple strategies listed on the site.
How can you use this source: Students can have a challenge by designing their own math word problems to post on the website.
ThinkQuest Jr. Team 4471. (1998). Math for Kids: A Medieval Adventure in Problem-Solving. Retrieved September 6, 2008, from http://library.thinkquest.org/4471/Default.htm
Cool Math 4 Kids
Address: http://www.coolmath4kids.com/
Description of Content: Students can learn math and solve problems on a colorful website. If you click on the ‘teachers’ link at the top of the page, it will take you to strategies for teachers to use in their classrooms to teach a variety of subjects. One thing that struck us was “Survivor Algebra,” which can be used for middle school. Students are divided into groups and are taught a mini-lesson on algebra. Then they are given problems to solve within their group.
How you can use this source: Survivor Algebra would be a good way to allow for problem solving in the classroom. There are also other resources for teachers. Students can play math games and learn math (the games actually are challenging). There are also lessons on certain math subjects, and a math dictionary that students can use.
CoolMath.com, Inc. (2007) Cool Math 4 Kids. Retrieved September 6, 2008, from http://www.coolmath4kids.com/
Article Review
In this article review, I read and critiqued four articles in the field of elementary math instruction. These articles were published after 2001. The articles cover teaching math in special education settings, incorporation of technology, National Council of Teachers of Mathematics (NCTM) standards, and the views of United States teachers on effective math teaching strategies. In the critiques of these articles, I addressed the articles’ connections to the NCTM standards, connection to the Virginia Standards of Learning, and how they can relate to my future experiences in teaching mathematics. This is very important to my development as a math teacher. I must be aware of current research that may improve my students’ success. It is also important to know the National and state standards, so that the lesson plans I create will be aligned with them. While it is always good to go beyond the standards if possible, the standards are a good starting point for the creation of quality lesson plans.
Article #1 – Integrating Reform-Oriented Math Instruction in Special Education Settings
In this article, the effect of Enhanced Anchored Instruction on the performance of students with learning disabilities was explored. Enhanced Anchored Instruction (EAI) is rooted in problem-based learning. It allows students to do problem solving using multimedia and hands-on activities. The study sought to find out if this method was more effective for students with math learning disabilities (MLD), and what practices teachers used that provides positive results for students with MLD.
In the study, 4 math teachers were chosen. These teachers all had a background in special education. The teachers were randomly assigned to teach 100 middle school students. The teachers were also randomly assigned to teach one of two instructional sequences. All students took a pretest before the beginning of the study (the Iowa Basic Skills Test). Teachers assigned sequence A did problem solving with their classes, while teachers with sequence B worked with the typical curriculum (which emphasized very basic “survival” math skills). After a few weeks, students took a post-test (Kim’s Komet Problem Solving Test). After this, sequence B teachers did problem solving, while sequence A teachers went back to the normal curriculum. Students again took a post-test after a while.
The results of the study showed that students benefited from the use of EAI in the classroom. They also found that students’ problem solving skills deteriorated slightly after not being used for a while. However, the students were still able to use much of what they learned. Students improved in their problem solving skills, but had did not improve very much in computation.
I think that this article was very good. It seems like a legitimate study, and they documented the experiment very well. They also compared it to another study that they did earlier with EAI, and analyzed their findings. However, the study does not tell us whether they are in an urban or suburban setting. It also does not tell us about the type of population that we are dealing with. Multimedia problem solving might not be feasible in some areas where money is an issue.
This aligns very well with NCTM standards. NCTM’s goal is to have problem solving be a primary form of math instruction in the classroom, and this type of instruction strives to do just that for all students. I think that it is also important for my future teaching. I would have never thought of using multimedia software to help learning disabled students with problem solving. However, considering that it seems to be successful, I think that I might use it.