Differentiated Math

by Jill Cook, Bissett Elementary
               

                I find differentiated instruction essential to the growth and performance of all students in my math class.  In order to effectively organize students in their groups for differentiation, there are many things that have to be done.  I first begin by looking at my students’ performance testing results.  I place each student into a quartile based on their assessment results; then I create my personal data wall.  After students are placed in the four quartiles, I group the students based on their achievement scores, which correlates with the inform series since it provides recommended skills for each student based on their score.  I have a large binder from which I look at the students’ scores and find something based on what they need to be able to do in order to move up another level by the next testing period.  Note:  These are skills that typically do not correlate with whatever mini-lesson I am focusing on that day. 

            Here is my current example of what has recently happened in my classroom:

            I teach a mini-lesson on division.  After modeling and practicing the strategy together, the students participate in guided practice with one another.  Usually, this is a game or cooperative learning activity in which they participate.  Then, the students complete their independent practice page.  This usually consists of no more than ten problems; however I typically assign 4-6 problems because I feel that students who can’t do 4-6 problems correctly don’t need the added stress of completing more problems when they may/may not be consistently successful.  Once the students are finished with their independent practice, they go to their differentiated instruction bin (I call them group activities).  While students are practicing independently, I start meeting with small groups on whatever strategy we are focusing on. 

            My group activity station consists of four shelves.  Each student’s differentiated activities are on those shelves.  I have my students grouped as the green triangles, orange squares, red trapezoids, and yellow hexagons.  The students are able to go to their shelf and choose an activity to participate in.  There is a large variety of skills they can practice, but they all focus on whatever our mini-lesson was or whatever skill I am working on in small group.  My green triangles have division problems to solve on their whiteboards and other activities that help them with our current small group focus, which is identifying landmarks of a data set.  My orange squares have the same division practice, but have games and activities that help them estimate products.  The red trapezoids are currently working on multiplying decimals, and my hexagons are reading and interpreting circle graphs with percents and fractions.  As you can see, there are a variety of activities the students get to choose from.  I include Everyday Math games, independent whiteboard practice from the math journal, use of manipulatives, and cooperative learning practice cards.  They also have inform questions in an envelope that they solve on the back with a pencil next to their initials.  They are in charge of solving 4-5 inform questions each day as well as checking other students’ work in their group to determine if they solved it correctly.  I have the EM Teacher's Guide to Games, so that is a great resource to use for my groups.  The students love playing landmark shark, factor captor, and multiplication top-it.  They use the Everyday Math fraction, decimal, and percent cards, as well as the telling time cards. 

            By integrating this differentiated instruction into math workshop, my students absolutely love it.  They get to work with one another and gain a sense of success because the students are learning and experiencing skills they are prepared to learn.  There is a high level of engagement, and my mid-year test scores show that this is an effective way to integrate differentiated instruction by using inform scores and recommended skills to help them make (and hopefully exceed) their expected growth.

Cooperative Learning: An End-of-Year Strategy

The end of the year is getting closer and the use of Cooperative Learning could be a strategy to help keep your students engaged.  Cooperative Learning has long been one of the best practices used by our district.  Here are some tips from SPS teachers that could facilitate the use of Kagan Cooperative Learning.

Follow the structure closely, having PIES embedded will provide:

·         Positive Interdependence: Is a gain for one, a gain for another? Is help necessary?

·         Individual Accountability:  Is individual public performance required?

·         Equal Participation: How equal is the participation?

·         Simultaneous Interaction: What percent are overtly active at once?

When introducing a new structure or one not used frequently, teach the structure using non -content material. Students can understand the structure directions then focus on the content material.

Think about how you would like to establish teams (heterogeneous teams, random teams, student selected teams, or homogenous teams).   

Keep in mind that all libraries in the SPS District have Kagan Cooperative Learning resources for teachers to check out.

Listed below is the homepage for Kagan Cooperative Learning. This site is primarily a resource for purchasing Kagan materials and training.  However, two features that could be really helpful for teachers are the Online Magazine and the Discussion board.

The Online Magazine has several departments to peruse, but some personal favorites are:

·         Featured Structures

·         Teacher and Training Tips

·         Tech Tips

·         Brain Matters

The Discussion Board is a blog that addresses questions about the use of Cooperative Learning.  There are responses from other educators as well as the Kagan staff.   Some examples of topics are given below.

How to support students with special needs during Kagan Cooperative Learning

Should middle and high school sit in teams?    

Kindergarten ideas

Kagan Publishing & Professional Development - KaganOnline.com

Learning is a "TEAM" effort

As teachers for Springfield Public Schools we know that we are immersed in numerous opportunities for professional development.  One of the most beneficial opportunities for me as a second year teacher was my cooperative learning training.  We all know how important cooperative learning is in the classroom and the results it has in engaging our students.    One key aspect that often gets overlooked is team formation.   I found forming teams according to the Kagan method of high, high-medium, low-medium, and low to be essential in managing differentiated instruction.   At first I was overwhelmed when forming my teams because I had so many behavioral issues.  I thought that I wouldn’t be able to put certain students with other students because of “behavioral problems.”  I was pleasantly surprised to realize that by grouping my students according to this structure, it minimized my behavioral problems due to that fact that I was better able to effectively engage my students.  I sorted my students based on writing/reading scores at the beginning of the year (high, high-medium, low-medium and low).  I used the student’s math scores as a way to differentiate separate math groups.  The students in my class are grouped by mixed-ability for their teams, and then when we break into math stations I group the students by like-ability.  I find it interesting that I have more behavioral problems in math stations when the students are working with like-ability partners, rather than when they are grouped in teams according to the Kagan Cooperative Learning team formation structure.   I am so thankful to have a better understanding of cooperative learning and love using it as a way to manage my classroom.

Lights, Camera, Action!

 When you stop to think about it, there are many similarities between Hollywood blockbusters and daily classroom activities—action and adventure, even comedy and suspense. As a teacher, you are both starring and directing, which makes it a challenge to see everything that unfolds. In the movie-making industry, directors review “dailies”, the most recent footage, and make decisions according to what is seen upon closer examination. You may find a similar process equally rewarding for your classroom work.

      It doesn’t require a professional film crew to capture your classroom on camera. It simply requires some intentional pre- and post-production planning by the director (i.e. YOU the teacher):

Film Focus: What are you curious about in your classroom? Perhaps you wonder what interactions are occurring among the other students while you are working with a small group. Perhaps you are wondering about the movement of students in the classroom during a class period.  Decide what will support your professional growth and is of interest to you.

Camera Crew: Find a trusted colleague who can operate the video camera (it could be an instructional coach or a peer whose schedule permits). It’s wise to let your administrator know your plans so he/she knows the purpose of filming is to support your professional growth and so he/she can provide help in securing a camera operator.

Setting the Scene: Make sure the classroom allows the camera operator to move around easily to capture exactly what you’re requesting. Prepare your cast members (aka your students) for the scene. Depending on the focus of your film, you may give them very specific guidelines, or you may intentionally remain vague. You may even choose to say nothing at all about the filming.

Roll Reality: Proceed with your classroom instruction and activities as if the camera is not present.

View Video: Choose a time and location where you are able to comfortably watch the footage. Many teachers find it helpful to do what directors do—watch the film in its entirety, then review specific clips in greater detail. Take notes of what stands out to you in relation to your driving focus and make a plan of action for future instruction.

     You may not find yourself walking the red carpet once you’ve completed this process, but you will find yourself on an even more prestigious path: knowing that your reflective practices will positively impact the learning of the “stars” in your classroom.

Differentiated Instruction: Working Wonders

After graduating from college and getting a position teaching art, I approached lesson planning with a one track mind.  What concepts and techniques did I want students to learn and what projects would we use to get there? Almost immediately I realized the art projects I had been assigning were too hard for some and way too easy for others, but I didn’t know there was another option.  How in the world could I give my students different projects to complete and still be fair? 

Three years later I learned about differentiated instruction.  The basic concept of DI is to deeply know your students and their needs and then to teach based on that knowledge. The concept intrigued me, and I was hooked from the start.  DI taught me that always giving all students the same assignment is what is not fair.  To be a great teacher means working to expand each and every student’s talents.  Kids come to you with different interests and different readiness levels. Once I realized that, I was ready to take the next steps in differentiating my instruction.

I am now in my seventh year of teaching art at the high school level and my lesson planning has changed drastically. The changes I have seen in my students’ learning, motivation, and confidence are unbelievable.  Right from the beginning of the year, students know that there will be several different projects happening at the same time.  I tell them that I will meet them at their level and challenge them accordingly.  They know that the main goal is for them to feel successful in their artwork.  Students are working harder than ever.

Along with the change in lessons, the physical environment of my classroom has evolved. We are constantly changing our seating groups, whether they are sitting in their “home base” seats or sitting with their groups based on the project they have been assigned.  In this learning community, that recognizes and respects differences, students are encouraged to share their artwork with peers and ask for feedback from them.

This has been such a positive change that the entire art department at Parkview is embracing the DI teaching philosophy.  We are working together to develop lessons that can be tiered based on student readiness or provide choice based on interest. We are comparing student work and determining what is successful and what areas need changed.  I was proud and excited when I happened upon a veteran art teacher from my department enthusiastically explaining to another teacher how we are collectively implementing DI and how successful it has been. DI is working wonders for our department and for our students. 

Managing by Multiplying

Do you manage your classroom as a multiplier or a diminisher?  In their book Multipliers: How the Best Leaders Make Everyone Smarter Liz Wiseman and Greg McKeown explain how to bring out the best in people by multiplying each person’s intelligence.  A multiplier sees smarts as dynamic, something that can grow and change based on effort, experience and encouragement.  This attitude differs from the diminisher who sees smarts as static, either you have it or you don’t and not very many people have it. 

Diminishers fall into one of five categories, empire builders, tyrants, know-it-alls, decision makers or micro-managers.  Multipliers, on the other hand, are talent magnets, liberators, challengers, debate makers or investors. (1)

How does this research transfer to the classroom setting? Let’s consider elements of just two types of multipliers, the liberator and the challenger.  According to Wiseman and McKeown, being a liberator begins with classroom environment.  “It’s a professional and serious environment, which gets lighter and more fun as the students work harder.”  This duality is the key; the teacher who is a multiplier will provide a safe place for thinking and contributing yet demand a high level of engagement.  “I give you space; you give me back your best work.”  The trick is to generate pressure without generating stress.

Here are two important strategies for accomplishing this trick.  First of all, be consistent.  When a teacher is consistent students know what to expect and will become comfortable with voicing ideas and making mistakes.  Being consistent also creates safety.  This is required if we want students to learn from mistakes.  By distinguishing best work from outcomes, teachers provide a positive pressure rather than unproductive stress.

Secondly, shift the ratio of listening and talking.  Liberators hone the skills of listening, paraphrasing, and probing.  This creates space for students to share what they know and are thinking.

This leads to one of the characteristics of the challenger who asks questions effectively.  “Diminishers give answers.  Good leaders ask questions.  Multipliers ask the really hard questions.”  Wiseman and McKeown dare us to stop answering questions and begin asking them. Ask questions that go beyond what students currently know and require them to research, problem-solve, investigate and grapple with ideas – questions that require them to learn.  Finally, combine these two attributes of a multiplier by creating an environment in which students are encouraged to create the hard questions themselves.  Give equal weight to asking a good question as to answering a teacher’s question.

As the leader in the classroom, a teacher who chooses to be a multiplier must develop a complex set of skills, but the payoff is tremendous.  By liberating and challenging your students they will walk away smarter, more capable, and more likely to become multipliers themselves.

For a summary of Wiseman and McKeown’s research see Harvard Business Review:  http://hbr.org/2010/05/managing-yourself-bringing-out-the-best-in-your-people/ar/1.

M & M's: A Terrific Treat

When it comes to delightful combinations, the makers of M&Ms ™offer a variety of options--chocolate and peanut butter, chocolate and pretzels, chocolate and peanuts, chocolate and chocolate....it seemingly never ends! Each combination is designed to suit the consumer's unique taste.

When it comes to delightful combinations of our M&Ms (Mentors/Mentees), there are certain ingredients that must come together as well. Who better to offer insight than those actively involved in the process? In the words of a building principal, a mentor teacher, and a first year teacher:  

An effective mentor is someone who works to develop a relationship with the mentee so that the mentee feels comfortable discussing the ins and outs of being an educator, who takes time to foster the relationship with the mentee by checking in formally and informally to ensure that his/her needs are being met, and who builds up the mentee. (Principal)

An effective mentor demonstrates active listening, models a positive example, and is adaptable to the needs of their mentee. An effective mentor provides encouragement and support (and is a cheerleader for their mentee when necessary). (Mentor)

My mentor is most effective when she's helping me with the everyday aspects of running my classroom--helping me learn the "hidden rules" and procedures that may not be in writing anywhere but are important that I know. (Mentee) 

Combining the ingredients effectively requires attention to specific details:

When pairing mentors and mentees together, it is important to look at the positions the individuals are currently teaching in.  Additionally, it is critical to consider the personalities of both the mentor and mentee. (Principal)

When pairing mentors and mentees, it is important to consider their teaching and learning styles. There is great benefit to observing and collaborating with those who do things differently. Once paired, mentors and mentees must practice and work toward establishing a safe relationship, where growth can occur in a comfortable environment. (Mentor)

I appreciate the fact that my mentor supports me in developing my own teaching style. (Mentee)

The makers of M & Ms™ know that some combinations just wouldn't be a hit. Tofu M&Ms™ are not likely to be hitting retail shelves in the future, for instance. When creating Mentor/Mentee relationships, there are certain things to avoid as well:

An effective mentor is not an evaluator and should not be demeaning to the mentee. (Principal) 

Mentors should not come across as controlling and/or cause the mentee to feel insufficient or stressed.  (Mentor)

Having a mentor share too much information at one time does not support a new teacher in learning what’s important. (Mentee)

When all the right ingredients come together in the mentor/mentee relationship, there are satisfying results for everyone!