1 Maximize ALL Students Mathematical Learning through the use of Powerful Instructional Strategies and Techniques Webinar Series Sponsored by the New Jersey Department of Education- Office of Special Education Programs Presented By Dr. Paul J. Riccomini
2 The Language of Mathematics Teach It! Learn It! Use It!
3 Language of Mathematics Introduction & Background Mathematical Proficiency Vocabulary and Assessments Language of Mathematics Strategies for Teaching Essential Vocabulary
4 Mathematical Proficiency Defined National Research Council (2002) defines proficiency as: 1. Understanding mathematics 2. Computing Fluently 3. Applying concepts to solve problems 4. Reasoning logically 5. Engaging and communicating with mathematics
5 CCSS for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important processes and proficiencies with longstanding importance in mathematics education. More information found here: (CCSS, 2010)
6 CCSS for Mathematical Practices 1. Make sense of complex problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. (CCSS, 2010) 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. (CCSS, 2010)
7 Common Core State Standards 6. Attend to precision. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
8 Learning Outcomes of CCSS-MP (McCallum, 2011)
9 Learning Outcomes of CCSS-MP These are BIG challenges for students with disabilities and those that are struggling. It will only happen if it is purposefully facilitated through teacher INSTRUCTION!
10 Mathematical Proficiency Mathematical vocabulary can have significant positive and/or negative impact on students mathematical performance
11 Mathematical Vocabulary Mathematics can be thought of as a language that must be meaningful if students are to communicate mathematically and apply mathematics productively. Vocabulary development is crucial to any experience involving language Vocabulary is central to mathematical literacy
12 How s OUR Vocabulary???? Define the following terms: Numerator Denominator
13 How s OUR Vocabulary???? Define the following terms: Numerator Denominator Top Number Bottom Number
14 How s OUR Vocabulary???? Define the following terms: Numerator Denominator That has nothing to do with what numerator and denominator mean! Top Number Bottom Number
15 Bonus Vocabulary Question Bonus: What is the name of this symbol? 1.29
16 Bonus Vocabulary Question Bonus: What is the name of this symbol? 1.29 vinculum
17 Teaching Vocabulary Students at-risk and/or with learning disabilities: often use short sentences with poor word pronunciations have limited receptive and expressive vocabularies are poor readers and do not tend to read on their own
18 General Vocabulary Instruction General Guidelines for Math Instruction 1. Establish a list of vocabulary for each subject area or unit 2. Evaluate comprehension of mathematics vocabulary on a periodic basis 3. Probe students previous knowledge and usage of important terms before it is introduced during instruction 4. Frame the context for new mathematics vocabulary Adams, 2003
19 General Vocabulary Instruction Guidelines for Math Instruction 5. Develop an environment where mathematics vocabulary is a normal part of instruction, curriculum, and assessment 6. Encourage students to ask about terms they don t know 7. Teach students how to find meanings of vocabulary words (e.g., dictionary, internet, notes, etc) Adams, 2003
20 Vocabulary Impacts Proficiency Clearly, an individual s vocabulary recognition and knowledge are vital components to become mathematically proficient When students struggle to learn important math vocabulary, teachers must employ evidenced-based instructional practices to help ALL students become successful.
21 Vocabulary Essential Questions Vocabulary Instruction 1. How are you teaching math vocabulary? 2. How are you facilitating the learning and remembering of math vocabulary? 3. Does each teacher have an established list of essential vocabulary for the year or per unit? 4. Are you testing math vocabulary regularly? 5. Are you practicing using math vocabulary throughout the course of the year?
22 Classroom Application Activity Identify 2-3 essential vocabulary words that seem to be challenging for students to learn in your upcoming math lessons and or unit. These words will be targeted for the application of vocabulary strategies we learn today.
23 Instructional Strategies 1. Writing about Mathematics Attribute Charts/Tables Venn Diagrams Word Banks 2. Explicitly Teach New Vocabulary 3. Concept Maps Frayer Model 4. Mnemonic Instruction Keyword Strategy
24 #1 Writing About Mathematics Attribution Charts or Tables Gives students opportunity to use mathematical terminology in written form Helps define and identify important attributes and/or characteristics Relates math terms to real world applications Increases engagement
25 #1 Attribution Chart Complete your chart for parallelogram
26 #1 Attribution Chart Completed by Student Rubenstein & Thompson (2002). p. 110 What are some misconceptions with this student s understanding of parallelogram?
27 #1 Venn Diagrams
28 Classroom Application Activity Develop an attribution chart and/or Venn Diagram that you can use to accentuate/highlight the critical attributes of the vocabulary word(s) that you selected. Use the next time!
29 Writing About Mathematics Support writing through focused & targeted writing tasks. Write about the term FRACTION using the following terms: Number, whole, numerator, and denominator Describe the term CIRCLE using the terms: chord, diameter, radius, center Develop on for one of your selected vocabulary words
30 Teaching Mathematical Vocabulary 1. Concept maps a. Frayer Model 2. Mnemonic Instruction a. Keyword Mnemonic Strategy
31 Concept Maps/Graphic Organizers Concepts maps are visuals (sometimes called graphic organizers) that assist students in remembering information Use to help students learn important attributes, remember steps in a problem and important formulas
32 Frayer Model The Frayer Model is a graphical organizer with 4 sections Helps students with word analysis and vocabulary building. Helps students create and organized visual reference for vocabulary Produces a paper product that can be revisited easily and quickly throughout the year using a variety of activities
33 Frayer Model The framework of the model prompts students to think about and describe the meaning of a word or concept in four parts Defining the term, Describing its essential characteristics, Providing examples of the idea, and Offering non-examples of the idea.
34 Example Frayer Model
35 Example Frayer Model
36 Using the Frayer Model Four Steps : 1. Explain the Frayer model graphical organizer to the class. Provide a model using a familiar term/concept. 2. Select a list of key concepts from a math Chapter you just taught. 3. Divide the class into student pairs. Assign each pair one of the key concepts and have complete the four-square organizer for this concept. 4. Ask the student pairs to share their conclusions with the entire class. Use these presentations to review the entire list of key concepts.
37 Classroom Application Activity Using one of the essential vocabulary words that you identified during the first breakout activity, develop a Frayer Model Using the Frayer Model Learning Sheet provided. As you are developing the Frayer model, think about the ways in which you might use it in your lessons. Use it in your next lesson!
38 Mnemonic Strategies Are devices, such as formulas or rhymes, used as aids in remembering. Mnemonics are instructional strategies suited for students who have difficulties focusing attention and exhibit poor motivation. Mnemonics are enjoyable, engaging, and highly successful.
39 Mnemonics are most effective when They are used to reinforce objectives to remember specific content. They are directly & explicitly taught and practiced (e.g., I DO We DO Two Do You DO) They are combined with comprehension instruction. They are included with application activities. It is an effective strategy for ALL Students!!!!!
40 Types of Mnemonic Strategies Pegword Method Letter Strategies Keyword Method
41 Example of Keyword Mnemonic Testing your Disney character knowledge. Identify which one is Chip and which one is Dale from the picture below.
42 Keyword Mnemonic Strategy Used to strengthen the connection between a new word and its associated information. Three ways to put information into a more meaningful and memorable forms (Reconstructive Elaborations) 1. Keyword method (acoustic reconstructions)-using similar-sounding keywords. 2. Symbolic Reconstructions- abstract information is reconstructed into a symbolic picture. 3. Pictorial or mimetic reconstructions- used to remember familiar or concrete information.
43 Perpendicular (purple dictionary)
44 Perpendicular (purple dictionary)
45 Parallel Lines (Pair of Elves)
46 Ray (run away)
47 Ray (run away)
48 Classroom Application Activity Using one of the essential vocabulary words that you identified during the first breakout activity, develop a Keyword Mnemonic using the learning sheet provided. As you are developing the Frayer model, think about the ways in which you might use it in your lessons.
49 Summary Keyword Recode unfamiliar word to an acoustically similar but familiar word or keyword. Relate the the keyword in an interactive picture with the to-be-remembered information Retrieve the new definition by thinking of the keyword and what was happening in the interactive picture
50 Summary Math Vocabulary Understanding of essential mathematical vocabulary is essential for students to become proficient Some students will struggle with learning vocabulary; therefore, teachers must use evidenced-based practices to teach vocabulary Attribution Charts and Venn Diagrams The Frayer Model and the Keyword strategy offer teachers an instructional practice that is effective for all students
51 Vocabulary Essential Questions Vocabulary Instruction Essential Questions 1. How are you teaching math vocabulary? 2. How are you facilitating the learning and remembering of math vocabulary? 3. Does each teacher have an established list of essential vocabulary for the year or per unit? 4. Are you testing math vocabulary regularly? 5. Are you practicing using math vocabulary throughout the course of the year?
52 Contact Information Paul J. Questions?