Martes,+Marissa+-+Inclusion+Strategies+in+Mathematics

=Martes, Marissa - Inclusion Strategies in Mathematics =

Introduction of Student
My name is Marissa Rae Martes. I had a lovely childhood growing up in Grants Pass, Oregon. I didn't know where I wanted to go to college after high school, because I never researched which school would be the best for me. Thus, I didn't really make the decision to go to Southern Oregon University (I joined a friend because she wanted me to room with her in the dorms and it was close to home), but attending SOU was one of the best non-decisions I have ever made.

A few years ago, if someone had asked me to explain my education and career goals, I would have told them that I was pursuing a degree in Mathematics and that I wanted to become a secondary school teacher of mathematics, because math was my favorite subject and I didn't know what else I wanted to do. Now, I can say that I graduated with a B.S. in Mathematics in only three years and that I will soon have a Master's, as well as, a teaching license in the state of Oregon! I hope to start my career as soon as possible in the Rogue Valley and possibly volunteer in the Peace Corps or Teach for America, or simply do some traveling during summer vacations. My goal is to also become fluent in Spanish someday.

My family brings me joy, especially my younger sister. I love to dance. I enjoy hiking, skiing, reading, playing tennis, and bowling (my highest score is 225)! You can also see my smiling face at the front desk of the Ashland Family YMCA! :)

My greatest fear is not having the ability to change students' attitudes about mathematics. I believe that I can inspire my students to learn mathematics and help them determine reasons for why it is important, but I hope to gain more resources and strategies that will help me change the attitudes of ALL of my students.

One of the hardest lessons I learned in high school was to ask for help and ask questions. I felt extremely powerless in some classes, because I didn't know how to improve my grade and was too prideful to ask for guidance. As a future teacher, it is important to teach my students how to be self-motivating, self-monitoring, and to ask for help when they need it. They have the ability to track their progress and learn what they need in order to be successful.

Introduction of Topic
I chose to research inclusion strategies in mathematics, because I will be licensed to teach middle and high school mathematics. Although we have looked at inclusion strategies more generally during class, I believe this research will benefit me personally, by relating inclusion strategies specifically to a mathematics classroom. Mathematics is a challenging subject that is not only difficult for students with disabilities, but can also be a struggle for students without disabilities. This assignment is the start of more extensive research and learning that I will continue throughout my career in order to benefit all of my students and create an inclusive classroom environment.

Top 5 Things I Learned

 * 1) Focus on “big ideas” - that is generalizable concepts rather than individual details.
 * 2) For all students, particularly those with cognitive or intellectual disabilities, development of mathematical understandings can be facilitated by progressing from concrete representations of quantity, to semi-concrete, and finally abstract representations.
 * 3) Even though students with disabilities have difficulty retaining facts, it is important to develop a conceptual understanding of the material, instead of focusing on memorization and procedural instruction.
 * 4) Different inclusion strategies may work for some students with disabilities, but not others. It is crucial that I use a variety of strategies in my classroom in order to increase the likelihood that my students are receiving the education and help that they need.
 * 5) Communication and planning is essential. Mathematics general education teachers should collaborate with special education teachers in order to support students outside of the general education classroom.

Top Resource
Cole, J., & Wasburn-Moses, L. (March/April 2010). Going Beyond “the Math Wars.” //Teaching Exceptional Children//, 42(4), 14 – 20. [|Going Beyond The Math Wars.pdf]

__Rating: 5 out of 5 stars__ This article was exceptionally informative, because I looked at inclusion strategies through the eyes of a special education teacher. It argued that through collaboration and communication, special education teachers can begin to teach students through inquiry-based teaching, instead of using direct instruction, traditionally thought of as belonging to special education. It described in more detail five strategies that promoted a conceptual understanding of the material from students. They include schema-based instruction, cognitive strategies, scaffolding, peer-mediated instruction, concrete-representational-abstract (CRA) sequence, and mnemonics.

Additional Resources

 * Beatty, R., & Moss, J. (2007). Teaching the Meaning of the Equal Sign to Children with Learning Disabilities: Moving from Concrete to Abstractions. In W. Martin, M. Strutchens, & P, Elliot (Eds.), //The Learning of Mathematics: Sixty-ninth Yearbook// (pp. 27 – 41). Reston, VA: NCTM. [|Teaching the Meaning of the Equal Sign to Children with Learning Disabilities.pdf]

__Rating: 5 out of 5 stars__ I truly loved reading this article. The authors emphasized that since students with disabilities often having difficulty retaining facts, teachers use memorization as an instructional approach rather than developing conceptual understanding. During a study of 3rd grade students, the researchers wanted to see how these students would cope with an instructional approach that highlighted concepts rather than procedures. The students did exceptionally well, even after a period of three months. The researchers were able to correct students' misconception of the equal sign, which they retained even after a short-term intervention using manipulatives. This article inspired me to incorporate more worthwhile activities in the classroom.


 * Huetinck, L., & Munshin, S. (2008). //Teaching Mathematics for the 21////st// //Century: Methods and Activities for Grades 6-12// (3rd ed.). Upper Saddle River, NJ: Pearson.

__Rating: 3 out of 5 stars__ This resource has been one of my favorites through this program in general. We read the first few chapters in my special methods course, which offered knowledge about teaching mathematics and included activities that I could use in the classroom. More specifically, I found a section about special education that described specific strategies that would help increase the effectiveness of my instruction for students with learning disabilities. However, since it is somewhat brief I rated it a three. I would write down the material in this section as a daily reminder of what I should constantly be thinking about as I teach to all of my students. I might also use some of the activities provided by the authors to promote a conceptual understanding of mathematics.


 * Keller, Ed. (2006). //Disabilities, Teaching Strategies, and Resources.// Retrieved February 28, 2012, from [|http://www.as.wvu.edu/~acad/sitemapm.html].

__Rating: 4 out of 5 stars__ This website is a collection of inclusion strategies from teachers who have taught students with disabilities in a mathematics classroom. Resources are organized based on how they will benefit students with certain disabilities. The author includes strategies, resources, books, videos, and organizations as categories of inclusion. He also notes that the strategies have been successful for some students with disabilities, but they may not be successful for all students with disabilities. This site was helpful, because of how the author categorized the different strategies. I will definitely use this website as a resource in the future.


 * Mancil, R., & Maynard, K. (2007). Mathematics Instruction and Behavior Problems: Making the Connection. //Beyond Behavior//, 16(3), 24 – 28. [|Mathematics Instructin and Behavior Problems.pdf]

__Rating: 4 out of 5 stars__ This resource argued that the same instructional strategies used to teach students with mathematical deficits can also help prevent behavioral problems from occurring in class. A task that was new to me was the idea of “chaining.” Chaining is where students complete part of a problem until they have mastered it, and then move on to another part until they can complete the whole problem on their own. I want to try this technique in my classroom. More general instructional modifications include: modifying content, modifying teacher behavior, modifying task demands, and modifying delivery.


 * Mastropieri, M., & Scruggs, T. (2010). //The Inclusive Classroom: Strategies for Effective Differentiated Instruction// (4th ed.) Upper Saddle River, NJ: Merrill.

__Rating: 4 out of 5 stars__ This resource served as a foundation for my research. Although it focused on mathematics concepts taught at the elementary level, the section on problem solving was helpful because I can relate it to all grade levels. Montague's seven-step strategy for solving word problems was especially interesting, because the cooperating teacher that I am currently placed with has a similar strategy for helping her students solve problems. I also plan on furthering my research and using resources such as Pro-Ed //Guideline Math Paper// and the National Library of Virtual Manipulatives recommended by the authors.


 * Michaelson, M. (2007). An Overview of Dyscalculia. //Australian Mathematics Teacher,// 63(3), 17 – 22. [|An Overview of Dyscalculia.pdf]

__Rating: 3 out of 5 stars__ Math is a difficult subject for most students, but it can be especially difficult for students with a cognitive deficiency in numeracy, or dyscalculia. It is important for teachers to recognize the signs and be informed about the disability so that they can better assist students with this disorder and implement strategies. The authors of this article included a list of instructional modifications designed to accommodate learners with dyscalculia.


 * O'Neil, M. (March 2006). Multiplying Polynomials. //Mathematics Teacher//, 99(7), 508 – 510. [|Multiplying Polynomials.pdf]

__Rating: 4 out of 5 stars__ Although this resource is very specific, I found it extremely helpful. The author of this article describes how you can multiply polynomials without using the FOIL method. I liked this article, because his students responded positively to this alternative method for multiplying polynomials and it can also be used to multiply numbers with two or more digits. I think this model would be visually appealing to students with learning disabilities.


 * Wadlington, E., & Wadlington, P. (2008). Helping Students with Mathematical Disabilities to Succeed. //Preventing School Failure//, 53(1), 2 – 7. [|Helping Students with Mathematical Diabilities to Succeed.pdf]

__Rating: 5 out of 5 starts__ This resource was extremely helpful and applicable. Although it doesn't mention a specific disability protected under IDEA, it does discuss dyscalculia as a mathematical disability. It listed practical intervention strategies that I can use in the classroom, such as writing in journals, using manipulatives, and a variety of different approaches to thinking about mathematics. I thought it was especially interesting how the authors categorized students into quantitative and qualitative learners. I also want to reference this source in the future, because of its emphasis on math anxiety and how it can affect students' performance.

__**Lesson Title:**__ Finding Probabilities with a Coin
Time/Duration of Lesson: 60 minutes

Materials:
 * Daily Work notebooks
 * pencils
 * coins (pennies) or two-sided chips

Part I – Rationale

a) Focus & Purpose: The purpose of this lesson is to start developing the concept of probability through a coin-tossing experiment. Students may have an idea that the probability or chance of a coin coming up heads is one half or fifty percent. If they don't, they will have the opportunity to analyze the results of flipping a coin thirty times in a row and then combine the results of the whole class in order to draw conclusions.

b) Objectives:
 * Students will form a hypothesis about how many days in June Kalvin will eat Cocoa Blast cereal and conduct an experiment in order to test their prediction.
 * Students will compute the fraction of heads after any number of trials by dividing the number of heads so far by the number of trial days.
 * Students will convert fractions into percent using calculators if necessary.

c) Oregon Content Standards: 6.2 Number and Operations and Probability: Connect ratio, rate, and percent to multiplication and division.
 * 6.2.2 Determine decimal and percent equivalents for common fractions, including approximations.
 * 6.2.3 Understand the meaning of probability and represent probabilities as ratios, decimals, and percent.
 * 6.2.4 Determine simple probabilities, both experimental and theoretical.

d) Instructional Strategy: The instructional strategy for this lesson is “inquiry.” This strategy is appropriate because it introduces the concept of probability in a setting students may have seen before. By having students gather data and forming hypotheses, I can more easily guide their learning and understanding about finding probabilities with a coin.

e) Teaching to Diverse Learners:
 * 1) Logical-mathematical and tactile intelligences will be activated during the use of manipulatives. Verbal-linguistic and auditory intelligences will benefit from clarifying their generalized process with a partner. Also, kinesthetic/tactile learners will benefit from physically flipping the coin.
 * 2) This lesson addresses the “comprehension,” “analysis,” and “synthesis” levels of Bloom's taxonomy. By explaining their ideas with a partner, students will be thinking at the comprehension level. The analysis level is addressed by determining and illustrating their methods. Finally, by making hypotheses about how many days Kalvin will eat Cocoa Blast cereal, students will be synthesizing.
 * 3) Some students might need more guidance, such as students with IEPs. I will be walking around and making sure that everyone is on the right track. TS will need frequent positive feedback for being on task. Students will have to answer questions throughout the lesson with partners, in small groups, and with the entire class. TS will have the opportunity to type his homework at home and include it with his Daily Work notebook.

Part II – Procedure

a) Anticipatory Set: I will ask students if they have ever flipped a coin in order to make a decision. Maybe they have flipped a coin to see who goes first in a game, race, or performance. Why did you use a coin in order to make an important decision? Was it a fair way to decide who goes first? What are the chances of getting heads? Of tails? If you toss seven heads in a row, are you more likely to get heads or tails on the next toss?

b) Forming Hypotheses: Students will read Problem 1.1, concerning Kalvin's choice of cereal, together and out loud. The last line says, “Predict how many days in June Kalvin will eat Cocoa Blast.” I will have students write their answers in their notebooks, along with why they think their hypothesis is true. I will also give students the opportunity to ask their partner for help or clarification. This will benefit TS and other students with IEP's.

c) Data Gathering: First, we will discuss bias and how it might affect the results of our experiment.


 * How should you toss a coin to be sure you have a fair trial?
 * What if you always start with tails facing up when tossing a coin? Do you think this introduces bias?
 * Collecting data in a random way can help us predict what to expect when a coin is tossed. What does random mean?

I will help students draw a table that will help them record their data. They will test their prediction by flipping a coin 30 times (one for each day in June) and recording the results in their table. In order to check for understanding, I will walk around and make sure that students are performing the experiment correctly. TS will have a chance to work with a partner or students at his table. We will discuss as a class how to fill in the 2nd, 3rd, and 4th columns in the table. I will call on TS to answer questions that will tell me whether or not he is understanding the material.

d) Revising Hypotheses: As a class, we will discuss the question “As you add more data, what happens to the percent of tosses that are heads?” Then, we will move on to Question B and discuss the results of the entire class. I will make a table on the board displaying each group's results and another one displaying the total number of heads flipped for all groups.

e) Analyzing the Process: Students will write in their notebooks whether their initial hypothesis was correct and explain why or why not. Then they will write an answer to Question C in order to be excused from class.

Homework: ACE 47, pgs. 13-19, # 1, 3-5, 19, Bonus #31

__**Reflection:**__

T.S. is a 6th grade male student in my cooperating teacher's Homeroom and Core 1 classes. He has an IEP concerning a specific learning disability. However, the “IEP Confidential Information Sheet” my cooperating teacher gave me, did not specify a certain one. The IEP contained information regarding “specially designed instruction” and “supplementary aides/services, modifications, and accommodations.” Even though my cooperating teacher explained to me that his IEP was for reading and writing, I applied the accommodations T.S. needed in order to succeed during the mathematics lesson. Since T.S. has an IEP for reading and writing, he would benefit in class from having someone read items and response choices aloud to him.

When I first wrote this lesson, it was based on a lot of individual work. Although they had some, students did not have a lot of time to converse with classmates. In order for T.S. to succeed, it is important for him to be given the chance to work with a partner or ask them for help. The classroom setting easily allows for this accommodation, because of how the tables/desks are arranged. However, I inserted moments within the lesson where I would specifically ask students to talk with their partner, check each others' answers, and make sure they agree on an answer, because it is important for T.S. to ask for help when reading a problem or question.

It was also important to include more “checks for understanding” within the lesson. The instructional strategy I used did not utilize many checks for understanding to begin with. In order for T.S. and many other students to succeed, it was important to include checks with understanding among classmates, as a group, and possibly individually with me as I walk around the classroom.

It is especially important that I give T.S. frequent positive feedback for simply being on task. I have noticed that he gets easily distracted when he is allowed to converse with classmates. Although he needs to be able to ask for help, it is important that I constantly give him positive feedback when he is using his time wisely and doing his work. T.S. is able to work hard on a task for an extended period of time, when he feels successful and confident.

The IEP form also mentioned that T.S. should be given the opportunity to type assignments and homework. Although there is a computer in the classroom, I did not give T.S. time to type homework assignments during class. I believe this is something his parents can help him with at home. Therefore, I included a few resources they could possibly use at home in order to type his mathematics homework.

**__Resources__:**
http://illuminations.nctm.org/Activities.aspx?grade=3 This website from the National Council of Teachers of Mathematics has many online activities that promote mathematical learning and conceptual understanding.

http://www.mathtype.com/en/ This website will allow you to download a free software that will help students type math equations. It could help T.S. type his math homework.

I also found the book //Teaching Mathematics for the 21st Century: Methods and Activities for Grades 6-12// by Linda Huetinck and Sara N Munshin to be very helpful.