**THE CHALLENGE**

Adolescent learners vary widely in their physical, emotional, and cognitive development. For many teachers, the most challenging aspect of teaching middle school students is the constant problem solving energy required to meet their diverse needs. When diversity is at its peak, we are sometimes left feeling that short of super-human feats on the part of heroic teachers, it’s not possible to meet the varied needs of the children before us.

When varied learner readiness is the aspect of diversity confronting us, it can be a challenge to ensure academic growth for all. If students appear bored or overwhelmed, a common response is to track them into ability-based classes. Whether we isolate high achieving students into accelerated courses, learning disabled students into special education classes, students who have fallen behind into remedial classes, or English language learners into a stream of their own, we frequently do so at a cost to both the students themselves and to the mainstream population from which they’ve been separated. If we embrace full inclusion without applying effective differentiation strategies, we fail as well. Diverse classrooms where every learner makes significant progress are possible in part through tiered instruction and assessment.

For the most part, this blog details the journey of the middle school math department at Jakarta International School from 2006-2011, the years needed to institutionalize a tiered approach. The purpose here is to share the rationale, describe the process, provide examples, and a share some results.

**RATIONALE**

Consider this… You’re teaching a very heterogeneous class of learners. Planning with the end in mind, you design a course assessment encompassing all course learning goals. Meeting the standard indicates preparedness for future academic success. At the end of the course, all students perform well on the assessment. It’s time to reflect.

There’s reason to celebrate. All students have met the grade level proficiency standard. This is no small feat. Students are equipped with the knowledge and skills needed to work successfully in subsequent grade levels.

We might feel less enthusiastic while reflecting on our students’ growth. Depending on their initial readiness for success, different students have had different growth opportunities. Students at the beginning end of the readiness continuum have learned the most. Students in close proximity to the learning target have grown less. Some highly advanced students have experienced no growth at all. We feel pride that struggling students have made significant gains and disappointed that advanced learners have stagnated.

This scenario illustrates the most basic premise for a tiered approach. When we establish a single common learning destination for students in mixed-ability classrooms, one outcome seems inevitable – all students will not have equal growth possibilities.

Our guiding vision for student learning includes academic and personal development for all students.

Middle school math teachers around the world face the challenge of teaching students with varied readiness levels for success. The graph below shows a typically diverse breakdown of algebra readiness test results for JIS 7th graders at the beginning of a school year. The diversity reflected in the graph is pretty universal to heterogeneous, middle school math classrooms.

Some students are advanced, already capable of succeeding in a typical algebra class, while other students are far from ready, which isn’t too alarming since it is the *beginning* of 7th grade.

Lev Vygotsky’s “Zone of Proximal Development” and Mihaly Csikszentmihalyi’s concept of “Flow” offer guidance. The research from both of these psychologists, not to mention our common sense, suggests we should offer learning challenges suited to each child’s readiness level in order to create the optimal conditions for learning. Realizing that our students’ readiness levels differ so much, we offer varied challenges so every student can learn in a state of relaxed alertness.

I like the graph below, which Csikszentmihalyi uses in part to make the point that we can create the conditions for “Flow” by either increasing our skill level with a given activity or by boosting the challenges we face. Tiered instruction and assessment enhances a teacher’s ability to do both on behalf of students.

Bill and Ochan Powell’s framework for effective teaching supports the use of tiered instruction to work within a child’s ZPD and a challenge-by-choice approach to increasingly shift ownership for learning to students.

**OVERVIEW
**

That we should differentiate for varied readiness levels is not so controversial. The challenge lies in how to do so.

In a tiered class, students engage essential course content at varying levels of depth and breadth.

Students choose the challenge on homework assignments and assessments that will help them maximize their learning.

Three different levels of challenge are offered. We designate each by a color.

**DURING CLASS**

There are some steps we consistently follow when planning tiered lessons.

A lesson will have 1 or more learning goals. For example, the goal of a geometry lesson might be to have students apply equation solving skills while learning about triangle properties.

Following whole-group instruction, students are asked to select the challenge level that will help them maximize their learning. For example…

This learning cycle repeats itself as the unit proceeds. Click for more samples of…

***Tiered Problems for a Variety of Middle School Math Topics***

Tiered lessons share some general characteristics.

After developing tiered assessments and assignments, we started thinking more and more about how to manage our tiered classrooms. Essentially, any strategy that develops cooperative learning skills and/or promotes self-reliance is worthwhile. Similarly, planning lessons with big ideas in mind promotes a sense of cohesiveness between all challenge levels.

At the end of a unit, students select the assessment challenge level that will enable them to best demonstrate the extent of their learning. The following graph shows the breakdown of color choices for all middle school students at JIS on all summative assessments during the 2006-10 school years.

Following a unit’s assessment(s), students reflect on their learning experience during the unit.

Reflections generally reveal students feeling appropriately challenged. In the majority of cases, students felt that they had selected a level of challenge that was an appropriate learning target towards the goal of maximizing their learning. Sometimes students believed they could have made a better decision. In few cases did they perceive that all targets were outside their zones of proximal development (situations where students who selected green felt the assessment was too difficult or students selected black and felt the assessment was too simple).

**RESULTS**

The psychological benefits of feeling appropriately challenged seemed to translate into improved learning outcomes. Compared to the difficulty level of assessments in previous years (prior to offering choices), green level assessments are the most similar. With the introduction of the blue and black level challenges, it’s clear that students are now tackling greater challenges, on average, than in the past. The graph below shows that grades held steady at the same time, suggesting an overall increase in student achievement.

Before introducing tiered assessments, students at the beginning end of the readiness spectrum tended to bring average test scores down. After, students at the beginning end of the readiness spectrum (those who selected green level assessments) performed at an accuracy level comparable to students taking blue and black level assessments. The performance of students working at a “green level of readiness” seemed to improve following the implementation of a tiered approach.

During the 2009-10 school year, JIS began giving students the MAP (Measure of Academic Progress) assessment. Students were tested at the beginning and end of the school year. Results indicate the tiered approach is having its intended effect: students across the readiness spectrum are meeting or exceeding expected growth rates.

Each student has a RIT, a number that represents their current skill level in mathematics. Over the course of the year, students are expected to grow by different amounts depending on their starting points. The horizontal axis represents student subgroups across the readiness continuum. The Blue bars represent JIS 7th graders’ mean growth. The Red bar represents the mean target growth set by NWEA, the organization that administers the MAP, based on historical growth rates.

We believe these consistently strong results from year to year (with 2 out of 3 teachers being different) speak to the power and importance of systematically implementing a tiered approach. An articulated tiered curriculum (the learning goals we have for students across the readiness continuum in addition to the materials that support the attainment of these goals) is a critical component of effective differentiation. Each teacher has been able to focus their energy on helping students be successful towards reaching tiered learning goals, rather than focused on developing a tiered curriculum, which while intellectually stimulating and fun, is also quite challenging.

The JIS 7th grade results are particularly dramatic examples of the power of Challenge by Choice. 7th grade math classes tend to have an enormous range of readiness levels because the breadth of topics covered is so wide and these topics extend learning from previous years.

Differentiation in 7th grade also exemplifies the importance of supporting advanced learners through a balanced offering of acceleration and enrichment. Rather than moving on to a relatively narrow set of 8th grade algebra learning goals via a traditional tracking system, advanced kids get the chance to grapple with rich problem solving challenges for a variety of important math topics like probability and statistics; ratio, proportion and percentages; and measurement. When topics lend themselves to acceleration, like equation solving, advanced kids are accelerated through above grade level learning goals like solving systems of equations as an example.

Remember the algebra readiness test results from the beginning of the year. A similar test at the end of 7th grade yields dramatically improved results.

Another positive development has been the decreasing need for a remedial 8th grade math course. For years, the math department felt that a remedial course was needed to serve the needs of our most vulnerable students. Teachers never felt very satisfied with the effectiveness of the course, but we didn’t know what to do. Having previously tracked students, it didn’t feel possible to have all students successfully complete the same 8th grade math course. Over time, it’s been wonderful to see our 8th grade math teachers feeling more comfortable with differentiation and our students feeling more confident in their skills. Both developments have led to the elimination of our remedial 8th grade math course, and a single math course has now been offered at each grade level (with no remedial 8th grade option) since 2009.

Besides academic development, adolescents also need and want opportunities to struggle, opportunities to make decisions, and teachers who guide them with a broad view of their development.

Achievement test scores and enrollment figures are easy to report as measures of success, but they only tell (a relatively insignificant) part of the story. Tiering’s impact on class culture and other aspects of our vision for student learning has been even more significant. Listen to some teacher, student, and parent reflections on the **“Perspectives”** page to develop a sense for how people feel.

Beyond achievement gains and encouraging stakeholder sentiments, research on effective teaching and learning consistently supports a tiered approach. The following are some recommendations for supporting learners of different readiness levels. Tiering makes it possible to support all students in the way that’s consistent with how they learn best.

An added benefit of the tiered approach is that heterogeneous student groupings can be preserved. The advantages of effective differentiation vs. ability based tracking are numerous. Here are some benefits brainstormed by the JIS Math department.

The challenge of meeting diverse needs is universal. A wonderful aspect of the work at JIS is that it’s been done by an extremely diverse math faculty.

It would be irresponsible not to mention certain “dangers” or downsides that accompany this work. The upfront workload is significant. I’ve developed tiered learning materials on my own, and I’ve also done it alongside colleagues. Both approaches can work but it goes without saying that the more you divide the work between team members, the easier, more effective, and FUN the work will be.

Another caution relates to the green challenge level. In our experience, it’s critical that green level expectations be rigorous and respectful. Using a tiered approach can have an incredibly positive impact on the sense of community in a classroom. On the flip side, class culture can deteriorate quickly if students perceive that green problems are for the “dumbies” or beneath the mainstream expectation (for more on this point, see “Finding Tiered Problems.”)

I hope this brief introduction leaves you feeling more interested to think about using a tiered approach with your students.

Ginny(23:21:36) :Following whole-group instruction, students are empowered to select the level of challenge that will help them maximize their learning. For example, after a lesson on triangle properties, students might be presented with problem solving tasks similar to the following.

Hello Dave, from North Carolina. One aspect of tiered instruction we seventh grade teachers struggle with is not the assessment but the differentiated ‘instruction’ itself. Could you share how you structure your class period (how much time do you have?) to teach the three color groups and the differences in how you deal with kids who need some more concrete work vs the abstract-ers. I would imagine: general lesson followed by working with the green, blue, blacks?

David Suarez(08:28:35) :Thanks for the question, Ginny. Know that we similarly struggle on the question of how to differentiate the instruction itself. Our philosophy is built on the premise that we should start with the end in mind, identify tiered learning goals that allow all of our students to experience growth given that they arrive to us at very different starting points, and then work from there to facilitate the growth. We’ve spent much of the last two years focused on creating tiered learning goals. We’re excited that the obvious (or at least what seems obvious to us at the moment) next step is to really think about how to make this differentiated learning happen in the classroom. Right now, there are 10 middle school math teachers at Jakarta International School who are working to address this challenge. I assure you that all of our approaches are unique, so whatever I write is just one of many approaches.

We teach 90 minute blocks that meet every other day. Having taught math with daily 50 minute periods, my personal preference is to have less frequent, larger blocks of time to work with. It’s easier to structure blocks so that I can address the three different tiers in one way or another during a single session.

What you imagine is definitely a popular approach. So, after the whole group part of the triangle lesson, for example, that might last 20-30 minutes, I’d let students know what the three practice assignments are. What happens from there is really dependent on the particular topic and difficulty of the assignments offered. I want students working at tables so that there is at least one other student who is working on the same color level they’re working on. Whether or not the whole table is working on the same color or not depends on my mood and the dynamics/culture of a given class. The one constant is that seating must be flexible. I like to have a seating chart that groups students heterogeneously to begin class. What happens when students begin independent work varies from class to class.

Essentially, I want everyone problem solving, asking questions, and finding help when difficulties arise. When students get stuck, they tend to first seek help from those closest to them. If that fails, students might seek out a classmate at another table grouping. If that option isn’t available or doesn’t work for some reason, students call on me. When I’m helping students, I’ll frequently try to make it known to the rest of the class what I’m helping out with so that students who are interested can join the conversation. This plays out for the remainder of the period. Ideally, all students would get their questions answered. Inevitably, students take work home and end up with more questions. So, what I left out is that before the main lesson topic of a day, I’ll typically take requests from students for problems they need help with. I try to always assignment homework problems that have answers available so that students are able to immediately self-assess their understanding. Occasionally, I need to spend a few minutes giving answers to problems which didn’t have solutions offered. Either way, students end up making their misunderstandings known, and I’ll leave these requests on the board until I’ve been able to address them. In this process, I try to gauge the severity of the misunderstanding. Given the request, what are the chances that the student’s misunderstanding is of a severe nature? How many other students had issues with the same problem? Would the whole class, or a large group, benefit from a discussion of the problem? As a teacher, this gets pretty exciting because it involves a lot of problem solving on the fly. I must be flexible about how to proceed depending on what I find out from students as they make their difficulties known. As long as no individual student has an overwhelming lack of understanding (which would likely require more intensive one-on-one support outside of class), most students are able to function while waiting for support on the problems they requested help with. Most often, I’m able to get to student requests on the day requests are made. Infrequently, though it does happen, some requests will not be addressed until the next class. Requests that can afford to wait are usually of the higher difficulty variety. Because of the foundational nature of green level challenges, it’s usually far more disadvantageous to allow a student who struggled with a green level problem to linger without the quickest intervention possible.

Another favorite approach of mine is to already have prepared key problems at the different levels of difficulty for the “guided instruction” phase of the lesson. These green, blue, and black level problems are posted, and students are told how to proceed. Frequently, I’ll ask students to start with green and move up in difficulty. Occasionally, it’ll be appropriate to let students go directly to their color level of preference without regard to the others. I’ll monitor progress as students work together. When I feel like the green problem(s) has gotten as much productive attention as it’s likely to get, I’ll discuss the problem with students (sometimes not worrying if students aren’t listening who feel confident with the challenge offered). At some point, I’ll post individual practice problems. Students realize that they should work out problems during the guided instruction up to and including the difficulty level they plan to shoot for. In this way, students might proceed to green level individual practice after they’ve achieved success with the guided green level problems. While this is happening, other students might still be engaged with the guided instruction phase, working with peers and/or waiting for the problem to get discussed. Deciding when to post the individual practice assignment takes some creative thinking. Depending on a variety of factors, sometimes I’ll post the individual practice assignment quickly. Other times, I’ll withhold it if I want students to stick with the guided practice assignment for longer than they might if the individual practice was already offered.

I’ve gone on for a while… hopefully this spurs some thoughts about how to possibly approach the challenges you face. If it raises more questions, keep shooting.

Kevin(04:00:33) :David,

I have one other teacher with me in this operation. We have been doing only different levels of homework, but the same tests and quizzes. After doing this for a couple of months, we are going to start giving leveled tests.

With the homework, the most interesting result was that some of the kids were getting help from their parents to do the blue or black levels. That is cool. There were a lot who were happy doing the green level – which is fine as that’s grade level work.

Tomorrow, I am giving the first test where they can choose their level. I gave them a glance at the different tests today so they could have as idea of what they need to study. It will be interesting to see how it goes.

I must say that the kids seem to really like the fact that they can choose their level of challenge – they feel a little in control of their learning.

Cheers,

-Kevin

David Suarez(04:14:55) :Kevin, what you’re seeing is consistent with what we’ve experienced. I like seeing kids getting extra help on the blue and black level problems. It’s nice that all students have the opportunity to experience the challenge on homework problems that results in them seeking extra help instead of just the earliest readiness students who frequently see themselves as the only ones who ever need extra help on homework when one assignment is offered to all.

Rochelle V. Gray(08:41:17) :Does the program have a Language Arts or Social Studies pieve.

David Suarez(09:13:01) :Hi Rochelle,

I’ve worked with CbC in science and math classes, but the strategy is a general one applicable in any subject area. I just don’t have any specific guidance to offer for language arts and social studies. Sorry!

pitriawati(00:41:18) :Hi,

I am interesting on writing about tiered task for my thesis proposal. i found it difficult to find some literature discussing this particular topic. i wonder if anybody can suggest me any website, books, and journal discussing about this topic. I live in Indonesia by the way, and in my country it is difficult to find some books or journals written in english.

Thank you in advance for your help

Pitriawati

David Suarez(07:33:05) :Hi Pitriawati,

As a starting point, Rick Wormeli discusses tiering in “Fair Isn’t Always Equal,” and it’s also mentioned in Tomlinson and McTighe’s “Integrating Differentiated Instruction and UBD.”

I’d love to hear back from you as you discover additional resources and complete your thesis.

David

Dan(06:39:32) :Hello David

I have watched your videos on differentiated instruction within the maths classroom with much interest. It seems you have developed an excellent way of differentiating effectively at this level. I was wondering if you yourself teach in this manner with high school students in Grades 9 and 10, or if your colleagues do, in preparation for AP/IB Diploma mathematics.

Many Thanks

Dan

David Suarez(11:33:27) :Hi Dan,

I’m thrilled to know you’re interested. My classroom experience is limited to middle school. I’ve recently been in touch with an advanced algebra teacher who has begun tiering with two challenge levels in his classroom. Thus far, he’s seen results similar to what I experienced early on in middle school classes. He’s happy. I’m confident CbC with Tiered Instruction and Assessment can be effectively applied in grade 9 and 10 classes. If I’m lucky, I’ll have the chance to work with some grade 9/10 teachers interested in tiering. Anyway, if you have any inclination whatsoever, you should give it a shot. The approach works really well. Your students will appreciate it. Please keep in touch.

David

heather(11:05:09) :Please clarify some concerns of mine.

When I read about tiering, many sites tier by starting at the standard, then below grade, and above grade. ‘…based on your choices above, determine how many tiers you will need and develop the lesson. When tiering according to readiness, you may have three tiers: below grade level, at grade level, and above grade level…’ So if a student is placed in a below grade group, how can you give them a passing grade? I’m confused.

Another example recently presented to me was in drama. The assignment was to present a scene. The tiering had speech as the standard and below standard was miming. If the standard must include speech, then anyone who does not speak must fail? Why would you include miming as an option if it does not allow the student to meet standard? I pointed this out, but was told that it allowed the student to participate at their current level of readiness and therefore it was tiering and valid. What am I missing?

Another point that troubles me is when teachers give the students’ choice in the 50%, 60% and so on ranges. Shouldn’t we rather give them the standard as the goal and scaffold to get them there? Doesn’t this model reinforce that the student isn’t capable? How does that help them see themselves as a successful learner?

Another scenario that confuses me is this- A math teacher gives out practice sheets with varying levels of support (tips and some key answers already in). If a student completes the sheet with a high degree of accuracy, but it was more heavily supported, could they feasibly get a higher grade than a student who takes the sheet with less support and who is less successful?

I understand that grading “assessment as learning” and “assessment for learning” is frowned upon, but realistically we required marks to justify the reporting grade and cannot base it on one or two end unit grades. So, how do I come to terms with this dilemma?

I can “wrap my head” around the lesson presented on the website above that starts with the standard and “goes up” in level of difficulty. The blue and black levels would translate to 80 and 90s, correct? But I see other lessons that people tell me are tiered and I just don’t see how they can be what was intended, how they can translate into a grade or how they can truly motivate a student.

Please help!

David Suarez(14:47:46) :1. when curriculum is modified below grade level expectations, such modification needs to be noted on a report card, or a passing grade should not be granted.

2. i agree that miming isn’t an appropriate tier if the learning goal involves speaking.

3. yes, we should scaffold to help kids reach rigorous learning goals.

4. on the math example, one would need to closely look at what students successfully completed to evaluate their learning.

5. about grading with few assessments… very, very good question. to benefit students, only the most recent evidence of learning should be included in a grade that’s intended to reflect mastery – add that piece of complexity to your puzzle. i feel comfortable with grades being based on very few quality assessments.

6. i’m really not clear on your reference to point values (60s, 70s, 80s, 90s). i wonder if you’re asking about what grades are possible at the different levels of complexity. in our school, kids can earn A grades on any level of complexity. we report both the level of complexity attempted and the achievement towards that level.

Summary – tiering curriculum can be done well and it can be done poorly. it’s an intellectually challenging exercise to effectively plan tiered lessons that maximize student learning.

hope some of this is helpful. sorry for the slow reply… good luck!

Shashi Krishna(11:49:35) :Hey David,

I teach IB Computer Science and have, from this year, started implementing the tiered approach for students to solve Java programs in so that they choose the kind of challenge they want to work with. Now, I am not sure how familiar you are with the IB program but the kids are graded from a score of 1 (lowest) to 7 (highest). My understanding is that in tiered assessments the basic curriculum content would be a 5, perhaps, and any advanced and higher order thinking strategies that kids apply will get them a 7? So that is to say – kids who choose level 1 task consistently will probably keep getting solid 5s or the occasional 5/6 but not higher. Those who challenge themselves and solve more complex problems will get 6 and advanced programmers get 6/7 or 7. Is this the right way to approach this?

Thanks.

Shashi

David Suarez(16:40:17) :Hi Shashi,

I’m thrilled to hear you’re applying this approach in your computer science classes. It seems like an entirely appropriate fit. I haven’t used the IB grading scales before, but I’m familiar and attempted last year to incorporate some its spirit into a rubric used for evaluating students in math (as we moved away from points and percents). Here’s what our department came up with after a few iterations over the course of a year.

A

- All learning goals are met within the topic of study

- Accurate and attentive to detail at all times

- Sophisticated understanding shown through application, analysis, synthesis, and/or evaluation

- Consistently presents work in a clear, logical and organized way

A top score was earned by students satisfying all of these requirements. Whether students completed a Standard, Advanced, or Highly Advanced assessment, they were expected to satisfy these criteria to earn a top score (A). This forced us to include opportunities for students to demonstrate higher order thinking skills on all levels of challenge. Standard level assessments had less opportunities as a percentage of the entire assessment than Advanced and Highly advanced tasks, but some were included, and students who earned A’s on standard assessments really were working to a very high standard. Students earning A’s on Advanced or Highly Advanced tasks were working to an insanely high standard. When another school I worked with offered lower possible grades for standard level work, some of the power of the tiered approach was lost as students and parents saw the work as being of a substandard (not standard) rigor level. The school raised the level of rigor on their standard assessments, adjusted their grading approach so all students could earn top marks, and the results were positive.

In the case of my school, students working at any level of challenge were able to earn an A (or whatever), and this grade was accompanied by a challenge level descriptor. In this way, a Highly Advanced A was a higher achievement than a Standard A, but any student could earn an A. This approach was used in middle school, though, and I understand the implications for high school may be different (especially if GPA’s are calculated). The different IB math tracks come to mind, though, as I think about how the middle school approach I’m describing is possibly still justified. I believe all students who take IB Studies, IB Standard, or IB Higher math courses can earn 7′s in their respective courses. I’d like to think the tiered approach is analogous to offering all three tracks in a single classroom. What I don’t know about the IB grading scales is how 5′s are perceived. If 5′s are a significant achievement, then it may not matter. If 5′s are perceived the way C’s are perceived in a traditional system, I believe it will.

Hope this is somehow helpful. I’d love to hear how you end up going forward and how things turn out!

David

David Suarez(16:57:46) :I just thought of one more thing, Shashi. Offering a top score of 5 for your basic level of challenge seems consistent with the Layered Approach advocated by Kathie Nunley. Maybe checking out her site will help you:

http://www.help4teachers.com/

Elena Sentevska(05:12:03) :David,

I am an educator from Belgrade. We are currently getting ready to organize a CEESA learning institute in Belgrade, with a relatively small group of learning support specialists and counselors from the region. My presentation is on alternative math strategies. Can I use your differentiation model when I talk about differentiation in math? Also, last year Bill and Ochan Powell showed a video of your class, but I cannot locate the link (if you don’t mind sharing that as well)?

Greetings from Belgrade,

Elena

David Suarez(11:02:28) :Hi Elena,

Wonderful to hear you’re talking math differentiation in Belgrade! I would love for you to share this strategy with your colleagues. Bill and Ochan Powell use parts of the clips contained on the Classroom Video’s link (located at the side of this page); you should be able to find what you’re looking for there. My guess is that the clip you viewed came from one of the first videos. Do you see it? Good luck!

David

AppliedMan(13:35:16) :What a bunch of bullshit.

IB students are such good students that they probably don’t even need the help of ANY teacher, they are self – motivated students already because of the high influenced backgrounds of their parents.