How do you adapt problem solving lessons so that they are accessible by all the students in your classes? Include a lesson idea and a reflection explaining how your adaptation will support the diverse needs of your students.
The CRAFT framework is for making math problem solving lessons accessible and engaging for diverse classrooms. CRAFT Framework
This is Aaron:
For this assignment I chose to use my “Learning Geometry through Billiards” (linked below) lesson to discuss how it is currently equitable or how it can be made more equitable. This lesson is one that I created the Math 506 class this summer. To summarize, the lesson called upon my students to take a picture (given to them) of a pool table with a cue ball and one other ball on it, and to figure out where they should aim the cue ball so that it bounces off a rail and send the other ball into one of the pockets. In this lesson, I asked students to go videotape themselves taking (and hopefully making) the actual shot, and then to take a screenshot of where on the rail that the cue ball bounced and to explain (with math) why this location worked.
First, let me discuss some of the positives in this lesson as it related to it be culturally equitable. The fact that this lesson is a little “out of the box” draws all students to an equal level of unknown. This lesson really requires students to enter into the math, which is something that is seldom asked of them. Another thing that is helpful for making this lesson more equitable is the picture that I have included for the students to see. This gives them a way of visualizing very easily what the problem is. Also, with this lesson, students are encouraged to help each other, and to even partner when videoing themselves taking the actual shot.
There are many things that could be done with this lesson to ensure that is even more equitable. The first that comes to mind is that there are many terms used that may be unknown to some students. I use billiard-related terms in my description of the lesson that I would want to make sure the students understood, such as: cue ball, rail, and pocket. Along the same lines I use terms like, screenshot and using Geometer’s Sketchpad. These are two things that I would need to make sure I modeled for all students.
There are also many things, in general, that can be done for a given lesson to make it more equitable for student learning. One method is to really focus on grouping students appropriately. Heterogeneous groups seem to ensure no group of students feels isolated. Another technique that I know I can improve in my own day-to-day practices is to call on more of a variety of students. It is so easy to unintentionally favor a group of students in this way. Lastly, for many of our students where we teach, the English language can be their biggest hurdle. There are things that we can do to help “equal the playing field” for them. We can consider giving them more time (as needed), work to vary our lesson instruction, and provide additional support or access to support.
Lesson Link: http://radmathteacher.edublogs.org/2011/07/04/mathematics-with-web-2-0-lesson/
Adapting a lesson can be as simple as including pictures with vocabulary or pictures that exemplify the main idea of the question being asked by the problem. I have decided to adapt a previous lesson, Dinner Plan.
The lesson idea is to create a dinner menu and cook the meal for at least four people at the cost of less than $5 per person.
http://birruetaf.edublogs.org/files/2011/07/Plan-a-Meal-Equity-issues-19e9mum.docx
From Suzanne:
I would use the same problem solving lesson plan as I previously posted, but I would alter it to make the lesson accessible to all my algebra students. 48.4% of the students at Prosser High School are Hispanic, many of whom have trouble with English and are financially challenged. To meet the needs of these students, I would make the following changes to my lesson.
Working in groups will help those students who struggle with the English language. Students would be asked to draw a picture of the situation and I would help those groups who couldn’t come up with a picture on their own. Using pictures, diagrams, and examples in my directions would also help not just the ELLs, but all my students. I would have the problem solving strategies double-sided with one side in English and the other side in Spanish. This way each child can privately decide which side to paste down in their math journal in order to be able to read the strategies in English or Spanish.
All my students would have access to graphing calculators while doing the work at school, but many of them may not have access to those tools at home. For that reason I would make sure there was plenty of time to do the work in class and the homework would not involve such tools. The homework would entail setting up of the problem and justifying the steps taken to solve the problem.
Here is my problem solving lesson with the changes necessary to make it fully accessible:
Lesson Plan – Standards-based Problem Solving & Euqitable
Title: Solving Systems of Equations
Outcomes: After doing this lesson, students will be able to solve an open-ended word problem involving systems of equations.
Standards addressed: “A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities” (OSPI, Washington State 6-12 Mathematics Standards, 2008).
Materials: Problem Solving Strategies that is already pasted in their math journals and posted on the wall of the classroom (in English and Spanish)
60 copies of Problem Solving worksheet (enough for 2 Algebra I classes)
Classroom copy of Holt text
Classroom set of graphing calculators
Procedures: The teacher will state her expectations of the students during group work. The teacher will remind the students to utilize the list of problem solving strategies that they have pasted in their math journals. The teacher will remind students drawing a picture of the situation first often helps. The students will be working collaboratively in their groups of four (the desks are already put together in groups of four) on the Problem Solving worksheet. As the groups are working, the teacher will walk around the room giving whatever assistance is necessary for the math to be pursued. Following their work on the problems, the teacher will guide the students in a whole-class discussion about solving systems of equations.
Assessment: The Problem Solving worksheet must be completed for the students to get half their daily homework points. The other half of their points comes from participating in the discussion. Solving systems of equations is a concept tested on their unit test, revealing mastery of this topic. Formative assessment will take place as the teacher walks around the room, making sure everyone is engaged and using the math on the worksheet and in the discussions.
Problem Solving Strategies
Draw a Diagram or Graph
Make a Model
Guess and Check
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
Resolución de problemas las estrategias
Bosquejarons una gráfica
Hacons uno modelo
Adivinons y verificez
Trabajons al revés
Hallons uno modelo
Hacons une mesa
Resolvons una problema simpla
Usons le argument el lógico
Usons uno modelo Venn
Hacons una lista organoleptico
The rest is the same, so I didn’t include it since it has already been posted.
From Geoff,
A Lesson in Geometry on Inductive Reasoning
http://gplb.edublogs.org/2011/07/17/equity-in-problem-solving-lesson/
Reflection
I chose this lesson to highlight equity in math teaching because I believe that this lesson encourages non-specific language skills, provides a level playing field for students when analyzing the diagrams, and relates to students who have ever opened a MySpace account or got online (even if never, the questions are not bizarre).
At this point in the trimester, students have explored volume and surface area; they have reviewed much of the algebraic calculations which they will need to be successful solvers for the rest of the year, but now students are primed to fulfill their real purpose for studying geometry: Logic. Since humans are inductive learners, and as deduction is a specialized skill derived after induction has occurred, I agree with how this book starts the learning, and I place it into something that I believe the students of all levels, languages, and abilities would find intriguing.
Since students are going to be progressing into proof structure in this chapter, and such terms as converse and syllogism are taught. I begin this first lesson with a foldable for notes: a cootie catcher. I do this to help language learners (as well as all students) have a place where they can store definitions and examples. I organized the contents of this unit into 4 main chunks, and as we go over each “chunk,” the students will be adding information to their cootie catcher to help further their understandings of geometric proof. Furthermore,
I aim to enhance problem-solving ability by approaching every example with Polya’s framework. As students become more and more attuned to problem-solving in a systematic approach, they can more quickly utilize options that frequent problem solving. One of the tools to problem-solving lies in understanding the data: make a table/list. This is equitable because it is a universal skill with applications reaching beyond the mathematics classroom. The knowledge of how to fill it out, how to choose the deviations, and where to make changes applies to making tables in this situation.
In this lesson, I seek for students to generalize their results and in so doing, to build skills in defining patterns or making connections. I chose to demonstrate equity in math teaching with this lesson because of the content of the examples. I chose to incorporate the cootie catcher foldable as a method to keep students organized throughout the unit and to provide a framework for developing language. Since students must be able to think logically about a proof, to see and make connections, I have the students practice their reasoning skills on questions that are not as involved geometrically but are more about creating counterexamples to disprove statements. Students must then go through the process of problem-solving in order to determine if they have truly identified the next term in a sequence. Since this lesson requires students to make predictions, test those predictions, and then adjust, I am of the opinion that this lesson provides equity and lends skill-building to problem-solving.
For an equitable problem solving assignment, I chose to use the activity that I planned for Math 506: Implementing Web2.0 into the classroom. The difficulty in implementing any type of activity involving the internet is that all students must have access to the internet. In my school district, nearly 40% of students are on free or reduced lunch. I imagine there are also a large number of students who do not have access to the internet after they leave school grounds. To make this activity equitable I would change it in the following way.
Originally, I had planned to have this activity be a homework assignment. I would give students the instructions on how to access the wiki once they received the e-mail invitation. And then there goal would be to upload a picture for the lesson. To ensure that all students are able to participate in the activity, rather than making it homework, I could make it an in class assignment and schedule time in the computer lab. I would still get student’s e-mails ahead of time so that the set-up process was easier. One thing that is great about my school district is that all students are able to log on to computers, and with that log-in they need to include an e-mail account. This ensures that all students are able to participate in the activity because they all have an e-mail address. Once students check their e-mail and click on the invitation link, we can walk through the set-up process together. This is great because students who are not computer savvy can follow along. I can also walk them through the steps of uploading a picture. Now that the activity is going to be completed in school instead of at home, students may not be able to access their own pictures, but they can still search the internet to find some really cool pictures that are of interest to them.
This lesson is easy to change into an equitable activity through the use of class time and a computer lab. This ensures that all students are receiving the same instruction, and because I can show them step-by-step, it will be easier for some students to complete. It also ensures that all students have the same access to the needed technology.
Some other general ideas for making lessons equitable include:
• Make lessons that involve options for a final product. This gives students the opportunity to pick an option that they feel they would be able to accomplish given what materials are accessible to them.
• Design lessons that are very open-ended, that way students of all skill levels can participate. Those with lower skills can complete the activity at their level of knowledge, and students that are advanced can complete the activity at their level.
Link to Action Plan for Incorporating Web 2.0: Determining the Slope of a Line
http://jcoulson.edublogs.org/2011/07/18/incorporating-web2-0/
For the equity lesson, I chose to reflect upon a lesson I created for Math 506. The link below has both information about the lesson and how it is equitable for students.
http://pierckat.edublogs.org/2011/07/19/equity-issues-in-a-problem-solving-lesson/
Josh here.
My lesson involving Technological Media presents a minor equity issue since it requires students to know how to use a laptop to navigate Excel and work with a spreadsheet. I’ve required home-based computer assignments in the past, and I am sometimes surprised how one-dimensional students are when working with computers. They know how to do what they need to, but that’s about it. The same with us all, I suppose.
Anyway, I’ll be teaching 7th graders next year, so I imagine that they probably will be unfamiliar with Excel. Consequently, I would like to modify the lesson referred to above to include a period of whole-group practice before moving in to the assignment. This will allow me to assess students’ abilities in addition to preventing students unfamiliar with Excel or spreadsheets from being at a disadvantage. It would be better for them to make mistakes before the assignment. Also, a whole-group practice session may make doing the assignment more timely and efficient by working out wrinkles before hand.
Lesson Reflection/Overview
This lesson is a great way to meet state standards because making each origami fold requires the students to visualize different geometric figures and the follow up activity they do requires them to analyze the properties of these figures. What makes the lesson even better is that it is equitable and allows students to enjoy the mathematics they are doing.
Students of different cultures tend to have different learning styles and this activity stimulates many different styles of learners. Another thing incorporated in the lesson is the art of a culture different then the dominant American culture in the classroom (Japanese/Chinese). Diverse cultures value group work which is also involved in the activity.
For a lesson to have equity, it must address many different types of learners. 7 of the 8 intelligences included in Gardner’s Multiple Intelligences are addressed in this lesson:
Linguistic- Groups will be listening to my explanation on how to make each fold, then discussing with each other on how to do it. The cultural story telling I give them will also benefit the linguistic students.
Body Kinesthetic- The students will be physically moving and making the folds, not just sitting in a desk watching me lecture.
Interpersonal- The students will be working together in a group and communicating with each other.
Spatial- As the folds of the triangle are being made the students will be able to use they’re visual skills to recognize what type of triangle they are making.
Logical-Mathematical- Students will be working with numbers and have set, step-by-step instructions to work with. This is also a very concrete activity that they can think about logically.
Musical- There will be noise and sound as all the groups chat and work together.
Naturalist- As they identify more and more triangles the students will recognize the pattern in the types that there are.
I think this lesson is such a good thing to include in a classroom because it does address several important issues. The lesson is equitable, and addresses many types of learners. It is also fun and different from a traditional math lesson. From my experience, doing this lesson in the classroom draws in the learners and brings motivation to them. Students are also able to get a hands on, visual representation of the material. By doing this they are able to obtain a deeper understanding of the content.
The link below will take you to this lesson plan.
http://jacobsod.edublogs.org/2011/07/26/frog-origami/
My lesson for problem solving presents a minor equity issue since it requires students to know certain vocabulary terms (ratios, proportions, equivalent fractions), and how these are used to solve problems. I will need to adjust my lesson to review all of this information so that everyone understands these terms and processes. I could also add in having different students come up and explain their methods to solve the problem during the discussion part of the lesson. This would allow for varied visuals of how to represent the problem and its solution.
For my lessons to have equity I have to be careful when writing word problems, specially if I have ELL students in the classroom. I try to take special care of the words that I use when talking and the ones used in problems as they could have different meanings. For example when using Will as a name the students could get confuse with the form of the verb. Also I try to make the word problems and activities relevant to them choosing setting which they are familiar with. I don’t plan too many activities on computers because they are not available to them; when I do I make sure that I sign up in the computer lab at school so they can use them. When using worksheets I also have them translated into Spanish as it is the main language spoken by our ELL students. There are also alternatives problems for students with IEP’s so they can have access to the same education.
In my lesson plan, I did not put anything about equity problems because I was thinking of my students, who are not from different cultures. It is usually only one. When we have students from other cultures, students and teachers come together to help him or her. But we usually no write about that, we just do it. Nevertheless, I thinks that implicitly i did it, because i did a survey about their opinion about winplot, class and feeling there. But I would like to write about respect and tolerance.