# Nelly Belinga-Hill Mathematics Teacher Math Department Chair

## Presentation on theme: "Nelly Belinga-Hill Mathematics Teacher Math Department Chair"— Presentation transcript:

How To Differentiate Mathematics Instruction Using Math Stations Fulton County School System
Nelly Belinga-Hill Mathematics Teacher Math Department Chair Martin Luther King Jr High School June 28th, 2011

How To Differentiate Mathematics Instruction Using Math Stations
Essential Question How can I use Math Stations to differentiate instruction in my classroom? Agenda 1. Opening Activity: Choice Board (30 mins Thinking & 30 mins Sharing) 2. Morning Discussion: The Importance of Problem Solving in Mathematics (30 mins) 3. Connecting The Pieces: From Problem Solving to Station Teaching (30 mins) Morning Break (10:30 – 10:40 am) 4. Differentiating Instruction: How Math Stations Help Differentiate Instruction (2h) Lunch Break (12:40 – 1:40 pm) 5. Afternoon Session: Designing Your Own Differentiated Lesson (2h and 20 mins)

1. Opening Activity Choice Board

Problem solving Choice board
Choose 3 activities You have 30 mins You must go through the center Think – Group (optional) - Share 10 mins mins mins Draw Move Around Sing Write a Speech Math Challenge Questions Debate Journal Entry Describe the Learning environment Role-Play 1. Opening Activity: Choice Board

How many valentines? Solution To Math Challenge 1
Introduce yourself Share Some of Your Answers How many valentines? Solution To Math Challenge 1 There are five friends. For Valentine's Day, each friend gives each other friend a valentine. How many valentines are there altogether? Next, extend your reasoning to a larger number, what if you had 28 friends? Source: 1. Opening Activity: Choice Board

NCTM Standard 2 (1998) Sets the purpose of patterns, functions, and algebra in mathematics education at all grade levels. Mathematics instructional programs should include attention to patterns, functions, symbols, and models so that all students: understand various types of patterns and functional relationships; use symbolic forms to represent and analyze mathematical situations and structures; use mathematical models and analyze change in both real and abstract contexts. Source: NCTM Principles and Standards (1998) 1. Opening Activity: Choice Board

Types of solutions List Them All Do Addition Draw Points and Arrows
Make a Star Make a Grid Look for a Pattern Use a formula Just do it Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions List them all Do addition
Suppose the names of the friends are A, B, C, D, and E. Let's list the valentines that each friend gives, starting with A's valentines. A–B, A–C, A–D, A–E B–A, B–C, B–D, B–E C–A, C–B, C–D, C–E D–A, D–B, D–C, D–E E–A, E–B, E–C, E–D That's 20 valentines. Suppose the names of the friends are A, B, C, D, and E. A gives 4 valentines B gives 4 valentines C gives 4 valentines D gives 4 valentines E gives 4 valentines Add the numbers. The total is 20 valentines. Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions Draw points Make a star and arrows
This solution is a lot like "Draw Points and Arrows," except we arrange the points differently. Suppose the names of the friends are A, B, C, D, and E. Every arrow represents 2 valentines and there are 10 double-headed arrows. Again, that's 10 twice—a total of 20 valentines. Suppose the names of the friends are A, B, C, D, and E. Draw an arrow between each pair. Then count the arrows. There are 10 and each one represents 2 valentines. So that's 10 twice—a total of 20 valentines. Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions Make a grid
Suppose the names of the friends are A, B, C, D, and E. We make a grid of all the friends. Each pink square is a valentine. The gray squares show that each person does not send a valentine to himself or herself. Either count the pink squares (20), or notice that there are 5 x 5 = 25 squares in the whole grid, minus 5 gray squares. Thus = 20 valentines. Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions Look for a pattern
Here we look at even smaller numbers. What if there were only one person? Then no valentines are given. Zero. What if there were only two friends instead of five? Then there would be 2 valentines exchanged. Three friends, there would be 6 exchanged. Four friends, there would be 12. What's the pattern? 0, 2, 6, 12,...? Between the first and second numbers is a difference of 2. Between the second and third, a difference of 4. Between the third and fourth, a difference of 6. And so on. If the pattern were to continue, the next number would be a difference of 8—and 20 valentines would have been exchanged. Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions Use a formula
You know that if there are n people, each will send out (n - 1) valentines. So the total number of valentines V is V = n (n - 1) Since n = 5 in this situation, V = 5 x 4 = 20 Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Types of solutions Just do it
Get four friends. Now there are five of you. Give valentines to each other. Then collect all the valentines and count them. There are 20. Source: Annhenberg CPB/Math and Science Project 1. Opening Activity: Choice Board

Checkpoint question: 5-mins discussions Discuss – Summarize - Share 2 mins 1 mins 2 mins
How do we build this type of reasoning across the grades (K – 12)? 1. Opening Activity: Choice Board

Across the grades The youngest children begin simply by counting. They count by 1s, then by 2s, 5s, and 10s. These patterns give students a natural strategy to understand addition and multiplication. When considering a number pattern such as 2, 4, 6..., a young student will ask herself, By what number can I count (add) to get to the next number in the pattern and the next and the next? As the student gets older, her knowledge of patterns advances from sums to products. When asked for the 50th number in the pattern, she will know to multiply 2 times 50. High school students can start to understand functions, such as f(x) = 2x + 2, where x is the numerical sequence 0, 1, 2, 3,…. They begin with simple in-out machines and gradually adapt their understanding to the abstractions of algebra. Source: NCTM Principles and Standards (2000) 1. Opening Activity: Choice Board

2. Morning Discussion The Importance of Problem Solving In Mathematics

Discussion Question Describe what is meant by “Problem Solving.” Why is this important? How is this different from the problem solving you see in most math books? 2. The Importance of Problem Solving In Mathematics

NCTM Standard (2000) Problem Solving
Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings. Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking. Source: NCTM Principles and Standards (2000) 2. The Importance of Problem Solving In Mathematics

Importance of Problem Solving
In everyday life and in the workplace, being a good problem solver can lead to great advantages. Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program. By learning problem solving in mathematics, students should acquire ways of thinking habits of persistence and curiosity confidence in unfamiliar situations Problem solving in mathematics should involve all the five content areas described in the NCTM Standard: build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. Source: NCTM Principles and Standards (2000) 2. The Importance of Problem Solving In Mathematics

Problem Solving Artifacts Found in Various Classrooms (Cont.)
What to do if you get stuck Read the problem again Look back at the lesson Look back at the previous work Look in the book Refer to the reference chart Ask your partner Ask the teacher 10 Steps to Success Just keep trying Try to determine what’s working Try to determine what’s not working Try to find someone who has done it Try and ask for help Try again tomorrow Try it a little differently Try one more time Try again Try 2. The Importance of Problem Solving In Mathematics

Problem Solving Artifacts Found in Various Classrooms (Cont.)

Checkpoint Question What type of Problem Solving Artifacts do you use in your classroom (or do you plan to modify and use)? 2. The Importance of Problem Solving In Mathematics

3. Connecting the Pieces From Problem Solving to Station Teaching

I Face Book through most of my classes. I do 49% of the reading
I spend two hours on my cell phone. I Face Book through most of my classes. I read 3 books a Year. I spend 3 ½ hours Online. I listen to music 2.5 hours a day. I do 49% of the reading assigned. MS HS 3. From Problem Solving to Station Teaching 24

I hear, and I forget I see, and I remember
I do, and I understand. Confucius As teachers, we recognize that we are teaching a different generation with different needs. It is therefore imperative to equip ourselves with tools that will help us address diverse learners, henceforth increase the engagement level. 3. From Problem Solving to Station Teaching

I Do and I Understand. What are Math Stations?
Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts. They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked. 3. From Problem Solving to Station Teaching

Connecting the Pieces Math Stations - Problem Solving
Students should acquire: Ways of thinking Habits of persistence and curiosity Confidence in unfamiliar situations Math Stations Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts. They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked. Math Stations Problem Solving Source: Carol Ann Tomlinson “How to Differentiate Instruction in Mixed-Ability Classrooms.” 3. From Problem Solving to Station Teaching

Example of a Math Station Lesson Math 1 Probability Lesson Video + Hands-On Experience
3. From Problem Solving to Station Teaching

4 Corner Picture Closing
….Math Stations Are Like….Because….. 4. How Math Stations Help Differentiate Instruction

Types of Math Stations Rotating Stations - rotate students through activities, or rotate activities through groups of students Individualized Stations - students/groups only use the stations they need or to which they are assigned Sequential Learning Stations - students must work through the activities in a particular order and proceed with mastery Thematic Stations - all activities set up to support a specific unit of study Enrichment Stations - stations that can be selected after assigned stations are completed 3. From Problem Solving to Station Teaching

What do stations look like in a math class?
Whole class warm-up Review station assignments made based on pre-assessment Pull a group to the teacher’s station for a structured focus lesson. Other students work at their stations. You move around to monitor their progress when students at the teacher’s station are working in pairs or independently. Whole class closure activity. Whole class warm-up On grade level focus lesson for most of the class Above grade level students work on an anchor After focus lesson, students refine their understanding at a specific station or through an anchor activity Above grade level students receive their focus lesson at the teacher’s station. Whole class closure activity. 4. How Math Stations Help Differentiate Instruction

Station Teaching Be Practical
Do Begin where students are, not where you think they should be. Pre-assess. Focus on the essentials so that struggling learners don’t drown in a pool of disjointed facts: Unpack the standard, explain the goal. Articulate your expectations and spend time modeling the type of work found at each station. Work diligently to ensure that struggling, advanced, and in-between students think and work harder than they meant to; achieve more than they thought they could; and come to believe that learning involves effort, risk, and personal triumph. Have a strong closing. Give students an opportunity to reflect on their problem solving skills: Math stations are not Math Games; they are learning centers. Don’t Do not ask Students to count off from 1 – 4 and form groups. Use your pre-assessment data. Students do not move from station to station in a round-robin style. You determine which station and when! Don’t just ask students to “Figure out the instructions.” Give clear instructions regarding material management, time management, direction of the movements, LOTS (Language of the Standard). Do not sit at your desk and miss out on scaffolding opportunities. Build in time for you to circulate and use your questioning techniques. Don’t work in isolation. Collaborate with your department to develop tasks for review, practice, and enrichment. 3. From Problem Solving to Station Teaching

4. Differentiating instruction How math stations help differentiate instruction

Connecting the Pieces Math Stations - Problem Solving - Differentiated Instruction
4. How Math Stations Help Differentiate Instruction

Differentiation is… GAPSS Instruction Standard 2.2 – All teachers make appropriate use of differentiation, including adjusting content, process, product, and learning environment based upon diagnosis of students’ readiness levels, learning styles, interests and personal goals. 4. How Math Stations Help Differentiate Instruction

Differentiation is not….
A class is not differentiated when assignments are the same for all learners and the adjustments consist of varying the level of difficulty of questions for certain students, grading some students harder than others, or letting students who finish early play games for enrichment. Source: Carol Ann Tomlinson, 1995 4. How Math Stations Help Differentiate Instruction

? Source: Carol Ann Tomlinson, 1995
4. How Math Stations Help Differentiate Instruction 37

Differentiate by… Product Content Process
What Students Learn Materials at varied ability or grade levels in one classroom; Varying the levels of complexity and abstractness Students may start at different places in the curriculum and/or proceed at different paces Product How Students Make Sense of Learning Use of diverse activities that are varied to meet student interests or preferences for learning Recognizes the many learning styles within any group of students. Process Students have some choice in how they will demonstrate what they have learned to the teacher, class, or other audience. Giving different assignments to different students increases motivation and results in an interesting variety of work products. Source: Calendra Brown, Fulton County Math Coach 4. How Math Stations Help Differentiate Instruction

Differentiating by Learning Profile Choice Board Revisited
Group 3 Group 2 Group 1 Visual Spatial Intelligence Draw Tactile Bodily Kinesthetic Move Around Auditory Musical Sing Linguistic Write a Speech Logical Math Challenge Questions Debate Intrapersonal Journal Entry Naturalist Describe the Learning environment Interpersonal Role-Play Group 4

What type of differentiation are we implementing
What type of differentiation are we implementing? Send a Reporter in 5 mins to the other group. Group 1 Breakout Activity Handout #10a Circumference Problem Group 3 Error Analysis Group 4 Vocabulary in Math Group 2 Develop Sensitivity For Struggling Learners 1 Min Challenges Anchor Scaffolding Problem Solving: Focus on the Process rather than Arithmetic Source: Dr. Riccomini “RTI in Math” 4. How Math Stations Help Differentiate Instruction

Differentiating by Interest Questions to ask yourself
How will students use this topic in their worlds? How will the topic help students explain their own experiences? How will the topic contribute to or deepen students/ current interests? How can the topic help students fulfill their aspirations? How can the topic help alleviate students’ fears and concerns? What will students gain if they learn this topic or lose if they do not? What will happen if students use this new skill or knowledge well and what will happen if they do not? Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 47 4. How Math Stations Help Differentiate Instruction

Drain the Pool Learning Task Question: If tasks at stations are the same for all students, are all students needs being met? 4. How Math Stations Help Differentiate Instruction

Lunch Break (1h)

5. Designing Your Own Differentiated Lesson
Afternoon Session

This Morning We learned that…
…and they DEFINITELY don’t learn alike! Source: Calendra Brown, Fulton County Math Coach 5. Designing Your Own Differentiated Lesson

Designing Your Own Differentiated Lesson Unpacking the Standard
Content Goal Emphasize content knowledge. The main focus is on what students need to know or understand. Example: Knowing the Meaning of Rate of Change within a real life context. Key Verbs: “know, understand,…” Process Goal Emphasize students’ learning or developing a skill. “Do it, and do know how and why!” Example: Knowing how to compute the rate of change given 2 points, a linear or non-linear function. Key Verbs: “Analyze, conduct, write…” Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 59 5. Designing Your Own Differentiated Lesson

Include the 5Cs Curiosity Collaboration Creativity Choice Take a minute to think about the activities on your list. Apply 5 C’s to both lists. To what degree are they present in the things you love to do and absent in those things that you would rather not do? Call on participants to share I would try to add hand motions to help them recall the 5 C’s quickly. Curiosity: touch brain Collaboration: Motion with hands “come here motion” Creativity: swirl hand Choice: hands showing either/ or Competence: Hands across heart These same 5 factors are important to remember as we design instruction that promotes understanding, interest, and excellence through a high level of student engagement. According to Harvey Silver and Richard Strong, our level of interest in and engagement with anything depends on 5 factors. Competence I said so Source: Hanson, Silver, Strong “The 5 C’s of Interest and Engagement” 5. Designing Your Own Differentiated Lesson 47

Which Standard? How will you differentiate the lesson using station teaching?
5. Designing Your Own Differentiated Lesson

Remember: Station teaching should produce “strategic learners”…
Able to analyze a problem and develop a plan. Able to organize multiple goals and switch flexibly from simple to more complicated goals. Access their background knowledge and apply it to novel problem. Develop new organizational or procedural strategies as the assignment becomes more complex. Use effective self-regulated strategies while completing a assignment. Attribute high grades to their hard work and good study habits. Review the goals and determine whether they have been met. Source: 5. Designing Your Own Differentiated Lesson