ANNONTATED BIBLIOGRAPHY

Tomlinson, C. A., Brimijoin, K., Narvaez, L., & Association for Supervision and Curriculum

Development. (2009). The differentiated school: Making revolutionary changes in teaching and

           learning. Alexandria, VA: Association for Supervision and Curriculum Development.

Credentials 

• Carol Ann Tomlinson has more than 20 years experience in the field of education in the traditional public school system, as well as over 10 years experience as a Program Administrator for special services for students with specific challenges and gifted learners.  She is well versed in education illustrated in 200 articles, contirbutions in book chapters & books, and other professional development materials. Her accolades begin in 1974 when she accepted the award of Virginia's Teacher of the year and most recently named Outstanding Professor at Curry School of Education in 2004 and received an All University Teaching Award in 2008. Her special interests in education have always focused on curriculum & instruction for students with learning challenges and gifted students, effective heterogenous learning settings and instruction, and defining how creativity and critical thinking in the classroom
• Kay Brimijoin has spent over twenty years in the K-12 public school system teaching and administering school age students. Brimijoin has a PhD in educational psychology with concentrations in gifted education and curriculum and instruction obtained  at the University of Virginia. Brimijoin begin with her received awards in curriculum design, research and evaluation, and distinguished dissertation work from the National Association for Gifted Children. Kay Brimijoin continues to consult with schools across the country on differentiation, curriculum design, gifted education, and teacher education.
• Lane Narvaez was last known as the principal of Conway Elementary in St. Louis, Missouri. Lane Narzaez has over 15 years of educational experience which includes teaching and administering to school age students within the LaDue School district. Narvaez has a degree in include a bachelor of arts from Hunter College (New York), a masters in reading from Manhattan College (New York), and a doctorate in reading from Arizona State University. 

Commentary
One of the most critical and poignant statements Tomlinson and Brimijoin (2008) wrote in the book The Differentiated School: Making: Revolutionary Changes in Teaching and Learning, was, "It seems unrealistic to think that all those students will thrive in classrooms that disregard their learning differences." Chapter 1 fosters the concept of a teacher making necessary changes in the learning environment and to a teachers' thinking towards differentiation. Each chapter provides snapshots of various schools across the country taking great efforts in implementing differentiation in their school for the success of their students. The 'snapshots' are descriptions of each schools progress as the school team made such changes in the classroom environment and in their own pedagogies. For example in 'Snapshot 13: Keeping it Real!' a group of detractors were going around utilizing the acronym for differentiated instruction D.I. for 'dumb idea.' A prominent teacher on campus noted such commentary and used it for reverse psychology in his staff meeting on D.I. His overall goal was to ensure such detractors were informed about the benefits of differentiation. He states, "If you are an uniformed skeptic you'll sound ignorant because you'll sound like you're saying differentiation isn't what's best for teaching and learning." This teacher believes it is okay to be unsure of our methods and to disagree but it is in the best interest of the students to be informed and make every best effort so students are successful. It is important to find any means to ensure teachers meet students where they are in their leaning process and to get them as far as they decide to go. The overall goal of teachers is to create responsive classroom environments. 

Highlights

This chapter sets a tone illustrating what differentiation is and is not; Figure 1.1. What Differentiated Instruction Is and Is Not, provides some examples and explanations shown below:

This table really highlights and clarifies some of the challenges I have had while trying to implement in many of my classes over the years. I have clearly understood differentiation is beneficial for everyone, but I know when I am approaching lessons I have a hard time finding appropriate strategies to use for a particular lesson. This book is not a quick solution type of book, it really helps to better understand how your class environment is set up, know your students and their individual needs, and how differentiation can enrich the learning environment through the written observations of other schools and their journey towards differentiation. 

References:

Brimijoin, K. (2016). Sage Publications, Inc. Retrieved from https://us.sagepub.com/en-us/nam/author/kay-     brimijoin 

Narvaez, L. (2016). Sage Publications, Inc. Retrieved from https://us.sagepub.com/en-us/nam/author/m-lane-narvaez

Tomlinson, C. A., Brimijoin, K., Narvaez, L., & Association for Supervision and Curriculum Development. (2009).            The differentiated school: Making revolutionary changes in teaching and learning. Alexandria,  ] 

          VA Association for Supervision and Curriculum Development.

Differentiating Content, Delivery and Assessment

Content Standard: 

CCSS.MATH.CONTENT.5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
CCSS.MATH.CONTENT.6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Lesson Goal: 
Students, by the end of the lesson, will be able to determine the Area of a square or rectangle demonstrating understanding of the definition and use of square units.

Engaging/Activating Activity: Students watch a Prezi presentation on Area & Perimeter 

https://prezi.com/8jp2fch6nmmq/real-world-perimeter-and-area-of-rectangles/

Differentiated Lesson Strategy I: Graduated Difficulty Activity

• Level I: Students demonstrate Depth of knowledge 1 and 2, demonstrate basic skills & knowledge, and proficiency of concept/skill.
• Level 1A: Using a ruler and graph paper students are to draw rectangles or squares specified in the provided descriptions, i.e. Draw a square 7 units long and 4 units wide. Students then find the Area of drawn rectangles or squares by counting the squares inside figures. Sizes will vary. Students will then define in their own words their learning process, describes steps taken to find the Area, then construct their informal definition of Area. 
• Level 1B: Students are given varied size squares and rectangles with square units provided inside the figures. Students need to identify the length and width of each figure and determine the Area of each figure, describes steps taken to find the Area, then construct their informal definition of Area. 
• Level II: Students demonstrate Depth of knowledge 3, apply their knowledge understanding of concept as they show mastery of Level 1 and extend strategic thinking. 
• Level 2A: Students are provided rectangular and square figures with minimum square units provided along the length and width inside figure; students are to problem-solve the Area of figures. Students must plan out their steps using the Graphic organizer, describing steps taken to find the Area, then construct their informal definition of Area. 
• Level 2B: Students are provided varied shaped composite squares and rectangles with specified dimensions identified. Students must use critical thinking and problem-solving skills to determine the Area of given composite figures. Students must plan out their steps using the Graphic organizer, describing steps taken to find the Area, then construct their informal definition of Area. 
• Level III: Students demonstrate Depth of knowledge 4, demonstrate and explain math reasoning within or beyond context of concept/skill; making connections with real-world or personal experiences. 
• Level 3A: Students are provided with illustrations of rectangles and squares which are connected in some manner. Dimensions are provided on various line segments of the figures. Students need to determine Area of of the shaded portion, then students must plan out their steps using the Graphic organizer, describing steps taken to find the Area, then construct their informal definition of Area. 
• Level 3B: Students are provided real-world word problems. Draw necessary diagrams to support their reasoning. Students must plan out their steps using the Graphic organizer, describing steps taken to find the Area, then construct their informal definition of Area.  

Differentiation Lesson Strategy II:

• Front-Load Vocabulary with all students: Use of Frayer model flash cards and/or coupled with a word search (read definition, then find vocabulary term)
• Provide Graphic Organizer for all Levels: Math Notes planner; helps students to identify important and necessary key ideas and highlights appropriate steps in problem-solving

Exit Ticket Assessment: Students are provide a three tiered worksheet. Students have the option to complete the level for which they believe is closely related to the types of problems they practiced during class time and/or complete any other level to assess their performance. 

LESSON PLAN: NEW-TRITIONAL INFO    

Content Standards: 

6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Mathematical Practices: 

MP.3 - Construct viable arguments and critique the reasoning of others.

MP.6 - Attend to precision.

Lesson End Product:  Poster

Lesson Objectives:

• Calculate the number of calories burned per minute for different types of exercise and body weights 
• Correctly write units (e.g. calories, cal/min, etc.) and simplify equations using them 
• Calculate how long it would take to burn off menu items from McDonald’s 

Lesson Plan Details

Students are to predict the objective of the project and create an essential question based off the initial article read and discussed in a fishbowl setting. Students, in groups, will investigate how long a person has to excercise in order to burn off calories. Students will work with unit rates, basic arithmetic skills, proportions, and numerical equations to effectively understand the task. There are three phases students will engage over a course of 5 days. The first phase is the launch activity where students watch a multimedia McDonald's video of a celebrity basketball player. They are presented with an open-ended question to activate brainstorming ideas of the various factors which may affect a person's ability to burn calories. As well as pay attention to various body types and weight which may also affect ability to burn calories faster or slower, which not directly pointed out to them at this time.  Students brainstorm in groups on more driving questions and create a poster of the factors their group believes affects the different body types. In phase two students are presented with varied body types, weights, and exercises; providing students an opportunity to practice calculating calories burned per minute. In this phase reflect upon their discussed factors and the results of their calculations. The goal is for them to discover the three main affecting factors: body type, body weight, and time spent doing the exercise. In phase three task widens the perspective of what may affect ability to burn calories, such as including varied exercises or different McDonald meals higher or lower in calories. Phase three is flexible providing students the opportunity to chose a particular person, three types of exercises, and four types of McDonald items (which vary in calorie, two on the high side and two on the low side). Students are then to add to their poster a compare & contrast chart illustrating their discoveries and any misconceptions in regards to food type, exercise, and body weight. Students are provided 'Deeper Understanding' driving questions to guide students in their discussion. 

Lesson Differentiation

ELL - Partner with a fluent English and native Spanish speaking student; front-load and provide initial article - translated in Spanish - the day before actual activity with tier 2 and 3 vocabulary defined

GIFTED - Provide multiple opportunities to respond to open-ended questions relative to the task, inclusive of the 'Deeper Understanding' questions provided with lesson

SPECIAL NEEDS - Front-load by pulling students at the end of the day prior to activity and work on fractions, multiplication & division facts, and setting up unit rate problems to prepare creating a resource page; provide a partner who has a high math fluency; provide a multiplication chart or calculator 

Differentiation provided for ELL and Special Needs students are chosen to alleviate anxiety and frustration during the task with peers. Partnering such students with more fluent students provides an opportunity to practice English Language structures, academic vocabulary, reading & writing skills. Differentiation for Gifted students allows them to extend their thinking beyond investigating for the 'Best' answer. The 'Deeper Understanding' questions are more broad and real-world connected. Each group defined has differentiation that is most appropriate for them to increase their higher order thinking and problem-solving skills.

Reference: 

Mathalicious, (n.d.). New-Tritional Info. PBLU, Buck Institute for Education (BIE). Retrieved from http://pblu.org/projects/new-tritional-info 

GROUPING PATTERNS

Writing in MathematicsPresently students are using annotative skills in all core courses (ELA, Mathematics, & Science). Students are being trained to utilize Ethos, Pathos, and Logos using color coding as they write. The color codes are as following: green-claim, blue-evidence, orange-reasoning, and purple-transitions. In math teachers are focusing on identifying students' claim and evidence with the colors as they answer a word problem, 'stop n jot,' or an open-ended question. Teachers are to provide as many writing opportunities within groups, as well as on an individual basis. Before group interaction students will practice writing in answering provided Cornell note questions and then summarizing their learning provided through the note-taking. Both in answering the question and summarizing students must clearly write their claim in green and providence from the notes in blue. Teachers are to encourage students to close read what they wrote and make any reflective corrections. When in groups students collaborate in brainstorming ideas and mapping out their thoughts for the final product. Use of roles helps to manage the learning task so they can have not only a visually creative output but an output that clearly communicates their learning and mastery of objective. Providing a 'quality of evidence' rubric also provides the appropriate criteria to allow them to asses their overall work, including the writing portion. Annotation methods can be applied in learning any and all math content standards.

Heterogenous/Homogeneous Grouping

Heterogeneous groups are obtained through the understanding the individual students will benefit from each other. Heterogeneous grouping is most often implemented when there is a concept students are are finding a degree of challenge, with at least two of the four students having a much higher capability to accomplish such focus skill or concept. Varying perspectives are shared and those that are struggling the most are provided an opportunity to grasp connections their peers are sharing. "The richness of ideas and perspectives...the shared learning help to benefit each student... Students in these groups can work together on a variety of tasks, including reading to each other...cooperative learning structures or group projects, as well as working independently," (Herrmann, 2014). Homogeneous groups are obtained through the understanding students are having challenges on a focus skill, gifted students who need extension work, or ELL students who may need front loading for any successive lessons, for example. 

Grouping Patterns

• Small-group instruction: can allow teachers to engage with students who have challenges and need concept or skill reinforcement or enrichment. This can be an opportunity to implement kinesthetic (body smart) and intrapersonal (self smart) teaching behaviors. The kinesthetic aspect can be mainuplative tools and/or moving activities which will have students physically engage with the learning and help them scaffold the learning. The intrapersonal aspect could have students set goals, writing in a journal, or possibly providing options for them to demonstrate their understanding. 

• Collaborative Groups: can allow students to engage with each other and share their thought processes and ideas in a social setting, which incorporates Gardner's multiple intelligence 'interpersonal' skills. Such groups reinforces, extends their thinking, and increases their creativity while working together. Students are allowed to explore, make and reflect on mistakes, and learn to come to a consensus in solving the given task. Depending on the end product expected such groups can incorporate several intelligences such as, visual spatial (picture smart), verbal-linguistic (word smart), and logical-mathematical (logic smart).

• Ability Grouping: can be done as heterogeneous or as homogeneous groups. Such groups allow students to get provided with work which will absolutely fit their needs. Multiple intelligences incorporated in these groups verbal-linguistic and logical-mathematical (word/logic smart). 

Group Reinforcement
Small group instruction can be used to reinforce writing in Mathematics. In such groups teacher can work on some skills and then allow students to complete open-ended questions relative to the skills practiced in the groups. Collaborative groups can reinforce writing by having students contribute the written portion and use varied colors to indicate which portion they contributed. All peers can use their color to edit another peers work before finalizing their overall writing for the end product. Ability grouping can reinforce writing quite similar as in small group instruction, provided open-ended questions or to complete an exit ticket. In each group the specified writing activity will immediately indicate to teacher what misconceptions, skill gaps, and thought processes which may need reinforcement and enrichment. The writing is an anonymous way for students to express their needs without anxiety and a sense of judgment. Writing samples will visibly identify those needs and students can immediately guided to appropriate scaffolds to further guide them in meeting the content standard being addressed. 

Me, Myself, and My Teaching

Introduction

Hello all, my name is Nakia Edwards and I am working on my Single-Subject credential in Mathematics. I have had the greatest opportunities to work in three different districts over 17 years with students in 6th through 12th grade. My goal as a teacher is to be able to help students, who like myself struggled in math class, to become less anxious and more confident in their learning experiences. As well as becoming an effective teacher who knows their students' needs and how to appropriately provide scaffolds to help them learn at their highest potential. I struggled in math because I grew up in the era of 'one size fits all' and if you don't fit in a particular mold then you get overlooked and dismissed as having potential to be successful. My teachers lacked in the area of differentiating instruction and providing enriching activities. I worked hard and understand the struggles many students feel. I want to make huge efforts to be reflective and conscientious of the diverse learning styles and needs of my students.

Work in Progress (WIP)

Currently I am positioning myself in a professional environment which fosters the growth of not only their students but their teachers as well. Using my reflective nature and strategies I have seen over my National University journey I will take every measure to incorporate those beliefs and strategies into my pedagogy. I want to make a difference, encouraging and empowering students to find the value in education and the worth of having a solid math foundation can have in their futures. 

DIFFERENTIATED INSTRUCTION & LEARNING ACTIVITIES

I am a math teacher, who also as a student struggled with learning math in the classroom, and so in my remembered experience I realized what caused most of my challenges. Instruction was not being differentiated to meet the needs of all students but for those students for which learning through lectures and other linguistic manners made learning easy. I, on the other hand, needed to be taught math and any other subject through kinesthetics, use of graphic organizers, peer collaboration, and from something simple as using different colors to illustrate connections between concepts. So now as I engage with students I know how to differentiate for my students, but first getting to know them makes differentiating more effective. 

From what I gathered from my experience most students are pretty similar to me and want to learn by doing hands-on activities, becoming more organized and using graphic organizers, engaging in activities like drawing or using colors to help them make connections. I am always researching and looking for appropriate strategies to utilize in the classroom. Here is one that is a great scaffold for teachers to refer to on a regular basis http://www.fortheteachers.org/differentiation_framework/#Diff_Skills or even http://www.beesburg.com/edtools/glossary.html. The latter website I have been using for the last 7 years of my teaching career, it is one my bookmark websites. It provides an explanation and sometimes it will have a link with examples.  

Use of peer cooperative or collaborative groups is one strategy I use most often in my classroom. Students have a the capability to communicate the learning to other students who may find challenges sometimes more effectively than teachers. Such groups also can alleviate anxiety for students who are not used to talking to the whole group but are capable of doing the work. I also provide many variations of visuals with lots of varying colors to keep the attention of our students. Visuals could include Powerpoints which have the appropriate amount of animations and color so as to not hide the necessary content.