How To Differentiate Mathematics Instruction Using Math StationsFulton County School System
Nelly Belinga-Hill
Mathematics Teacher
Math Department Chair
Martin Luther King Jr High School
June 28th, 2011
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
How To Differentiate Mathematics Instruction Using Math Stations
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)
Essential Question
How can I use Math Stations to differentiate instruction in my classroom?
1. Opening ActivityChoice Board
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Problem solvingChoice board
Choose 3 activities You have 30 mins You must go through the center Think – Group (optional) - Share 10 mins 10 mins 10 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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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?
Introduce yourself Share Some of Your Answers
1. Opening Activity: Choice BoardSource: http://www.learner.org/teacherslab/math/patterns/valentines/handshakes3_act.html?uid=0
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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.
1. Opening Activity: Choice BoardSource: NCTM Principles and Standards (1998)
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Types of solutions
1. List Them All
2. Do Addition
3. Draw Points and Arrows
4. Make a Star
5. Make a Grid
6. Look for a Pattern
7. Use a formula
8. Just do it
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Types of solutions List them all Do additionSuppose 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–EB–A, B–C, B–D, B–EC–A, C–B, C–D, C–ED–A, D–B, D–C, D–EE–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.
1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Types of solutions Draw points Make a starand arrows
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.
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.
1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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 25 - 5 = 20 valentines.
1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Types of solutions Look for a patternHere we look at even smaller numbers.
1. What if there were only one person? Then no valentines are given. Zero.
2. What if there were only two friends instead of five? Then there would be 2 valentines exchanged.
3. Three friends, there would be 6 exchanged.
4. Four friends, there would be 12.
5. 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.
1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Types of solutions Use a formulaYou 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
1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Checkpoint question:5-mins discussionsDiscuss – Summarize - Share2 mins 1 mins 2 mins
How do we build this type of reasoning across the grades (K – 12)?
1. Opening Activity: Choice Board
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How To Differentiate Mathematics Instruction Using Math Stations
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.
1. Opening Activity: Choice BoardSource: NCTM Principles and Standards (2000)
2. Morning DiscussionThe Importance of Problem Solving In Mathematics
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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
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How To Differentiate Mathematics Instruction Using Math Stations
NCTM Standard (2000)Problem SolvingProblem 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.
2. The Importance of Problem Solving
In Mathematics
Source: NCTM Principles and Standards (2000)
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Importance of Problem SolvingIn 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.
2. The Importance of Problem Solving
In Mathematics
Source: NCTM Principles and Standards (2000)
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Problem Solving ArtifactsFound in Various Classrooms (Cont.)What to do if you get stuck
1. Read the problem again2. Look back at the lesson 3. Look back at the previous
work4. Look in the book5. Refer to the reference chart6. Ask your partner7. Ask the teacher
10 Steps to Success
1. Just keep trying2. Try to determine what’s
working3. Try to determine what’s not
working4. Try to find someone who has
done it5. Try and ask for help6. Try again tomorrow7. Try it a little differently8. Try one more time9. Try again10. Try
2. The Importance of Problem Solving
In Mathematics
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Problem Solving ArtifactsFound in Various Classrooms (Cont.)7 Steps to Solving Math Problems
1. Identify the ProblemWhat is the question asking?
2. Define the ProblemWhat will the answer look like?
3. Formulate a StrategyHow should I tackle this problem (VANG)?
4. Organize the InformationWhat information is given?
5. Allocate ResourcesWhere can I read more or learn more about this?
6. Monitor ProgressHow much time do I have?What are my steps?Do I need to use a different strategy?
7. Evaluate the ResultsDoes my answer make sense? Is this the best possible solution?
5 Steps to Solving Math Problems
1. Identify Problem- What is the problem asking you for?
2. Indentify knowns/unknowns- Organize given information
3. Translate known/unknowns into math symbols/language- Assign variables, subscripts and formulas as necessary
4. Solve for unknown
5. Check answer
4 Steps to Solving Math Problems
1. Look for clues 2. Establish a Game Plan 3. Solve the Problem
4. Recheck and Reflect.
2. The Importance of Problem Solving
In Mathematics
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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 PiecesFrom Problem Solving to Station Teaching
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
I spend
3 ½ hours
Online.
I listen to
music 2.5
hours a day.
I do 49% of the reading assigned.
I spend two hours on my cell phone.
I Face Book through most of my classes.
I read 3 books a Year.
3. From Problem Solving to Station Teaching
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
I hear, and I forgetI see, and I rememberI 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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Connecting the PiecesMath Stations - Problem Solving
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.
Problem Solving
Math Stations
3. From Problem Solving to Station Teaching
Source: Carol Ann Tomlinson “How to Differentiate Instruction in Mixed-Ability Classrooms.”
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Example of a Math Station LessonMath 1 Probability Lesson Video + Hands-On Experience
3. From Problem Solving to Station Teaching
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
4 Corner Picture Closing
4. How Math Stations Help Differentiate Instruction
….Math Stations Are Like….Because…..
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How To Differentiate Mathematics Instruction Using Math Stations
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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
• 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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Station Teaching Be PracticalDo
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 instructionHow math stations help differentiate instruction
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Connecting the PiecesMath Stations - Problem Solving - Differentiated Instruction
Problem Solving
Math StationsDifferentiated Instruction
4. How Math Stations Help Differentiate Instruction
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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.
4. How Math Stations Help Differentiate Instruction
Source: Carol Ann Tomlinson, 1995
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
4. How Math Stations Help Differentiate Instruction
?
Source: Carol Ann Tomlinson, 1995
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Source: Calendra Brown, Fulton County Math Coach
4. How Math Stations Help Differentiate Instruction
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Differentiating by Learning ProfileChoice Board RevisitedVisual
Spatial Intelligence
Draw
Tactile
Bodily Kinesthetic
Move Around
Auditory
Musical
Sing
Linguistic
Write a SpeechLogical
Math Challenge Questions
Linguistic
Debate
Intrapersonal
Journal EntryNaturalist
Describe the Learning environment
Interpersonal
Role-Play
Group 1Group 2Group 3
Group 4
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How To Differentiate Mathematics Instruction Using Math Stations
What type of differentiation are we implementing?Send a Reporter in 5 mins to the other group.
Group 2
Develop Sensitivity For
Struggling Learners
1 Min Challenges
Group 2
Develop Sensitivity For
Struggling Learners
1 Min Challenges
Group 1
Breakout Activity
Handout #10a
Circumference Problem
Group 1
Breakout Activity
Handout #10a
Circumference Problem
AnchorScaffolding ProblemSolving: Focus on theProcess rather thanArithmetic
AnchorScaffolding ProblemSolving: Focus on theProcess rather thanArithmetic
Group 3Error AnalysisGroup 3Error Analysis
Group 4Vocabulary in MathGroup 4Vocabulary in Math
4. How Math Stations Help Differentiate Instruction
Source: Dr. Riccomini “RTI in Math”
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Differentiating by InterestQuestions 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?
4. How Math Stations Help Differentiate Instruction
Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 47
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Differentiating by Readiness LevelDrain 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 LessonAfternoon Session
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Source: Calendra Brown, Fulton County Math Coach
This MorningWe learned that…
5. Designing Your Own Differentiated Lesson
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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,…”
Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 59
5. Designing Your Own Differentiated Lesson
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…”
Designing Your Own Differentiated LessonUnpacking the Standard
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Competence
Choice
Creativity
Collaboration
Curiosity
I said so
Designing Your Own Differentiated LessonInclude the 5Cs
5. Designing Your Own Differentiated Lesson
Source: Hanson, Silver, Strong “The 5 C’s of Interest and Engagement”
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
5. Designing Your Own Differentiated Lesson
Which Standard? How will you differentiate the lesson using station
teaching?
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
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:
http://iris.peabody.vanderbilt.edu/ 5. Designing Your Own
Differentiated Lesson
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
1. Please explain ________2. EQ: What are several ways that math stations can be used to differentiate
instruction in your math classroom?
Closing Activity
5. Designing Your Own Differentiated Lesson
1
Very low
2
low
3
medium
4
high
My understanding of math stations
before the presentation
My understanding of math stations
after the presentation
Nelly Belinga-Hill
How To Differentiate Mathematics Instruction Using Math Stations
Make and Take…
To Create 1 Folder Game, you will need:
1 folder 4 pockets 1 folder game hand-out Scissors Glue sticks
5. Designing Your Own Differentiated Lesson
Nelly Belinga-Hill
Math Stations Website:
Employees > Instruction > Math > Documents > Secondary Mathematics > Professional Development > Math Stations
Thank You Fulton County.