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Good links to formative assessment

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As every teacher knows, students differ in their capabilities, their knowledge, and their interests.

In the early 1980s, the Cockcroft Report (1982) identified a "seven-year-gap" in student achievement in mathematics, motivated by the variation that the Assessment of Performance Unit had found in student response to the simple question: 6099 + 1 = ? They found that many seven year olds knew the answer was 6100, while many 14 year olds thought the answer was 7000. Subsequently, Shirley Simon and her colleagues found that the gap in the understanding of scientific concepts such as measurement was at least as great (Brown et al., 1995).

That is why the vast majority of teachers rightly reject the idea that "one size fits all" in education. Given the differences that demonstrably exist between individuals, the idea that the same teaching can be equally effective for all students is clearly absurd. However, once we accept this "brute fact" about the world, what we do about this is far from straightforward.

In some countries (eg France, Germany), the main way of dealing with the huge range of student achievement that we find in a group of (say) ten year olds is to require students to repeat a grade if they are not ready for the next grade. In others (eg Japan, Sweden, UK, USA) however much or however little they have learned, students move with their peers onto the next year's curriculum.

Of course, when countries employ such "social promotion" there will be a much greater range of achievement in the year cohort, and some way of dealing with this range of achievement has to be found. In England, especially in mathematics, but also, to a lesser extent, in modern languages and science, the most common way response is to group students on the basis of their current achievement, or on some basis of notion of "ability."

Grouping students by ability is attractive for many reasons. For teachers, the idea that one can assume a particular level of shared understanding within a class makes planning lessons more straightforward, and many parents appear to like the idea that teaching will somehow be pitched at a level that is more suitable for the specific strengths and weaknesses of their child. However, the empirical evidence-from across the world-is that grouping students by ability rarely achieves what it is claimed to do.

Firstly, students are almost always in the same ability group or "set" for the whole year, which means they are allocated to a group on their general ability in that subject, rather than on the basis of their understanding of a particular topic. For a particular unit, the range of achievement in a particular set is generally almost as great as the range in the whole year-group. And yet, teachers appear to narrow the range of teaching strategies they use when they are teaching groups they believe to be more homogenous (Boaler et al., 2000).

Secondly, ability-grouping tends to increase the achievement of those placed in the highest achieving groups and to reduce the achievement of those placed in the lower-achieving groups. The reasons for this are complex, and caused by a number of interacting factors.

For example, the best teachers are more often assigned to teach the highest achieving students, whereas the best teachers are most beneficial for the lowest achievers (Slater et al., 2008). Grouping students by ability therefore reduces average achievement by ensuring that the students who would benefit most from good teaching get less of it. When students are taught in sets, students in lower sets are promised that if they do well, they can move up to a higher set, but in general this rarely happens because of curriculum polarization (Boaler et al., 2000).

Within a few weeks of the beginning of the school year there is a large gap in curriculum coverage between the groups, so students who move up to a higher group will find it difficult, if not impossible, to cope because there is so much material they have not covered. It is important to note that these mechanisms are not inherent to the process of ability grouping, but rather are the result of the particular way that ability grouping is conducted in most countries (Venkatakrishnan & Wiliam, 2003).

However it is clear from research on international comparisons of mathematics and science achievement that these effects appear to be difficult to avoid. In general, the highest performing countries seem to have relatively broad range of achievement within groups, and smaller differences in achievement between groups of students of the same age in a school (Schmidt & Bursten, 1992). In other words, grouping students by ability is neither necessary, nor sufficient, for high achievement.

As the evidence of the shortcomings of ability grouping has accumulated over the last fifty years, there has been increasing interest in ways of teaching science and mathematics that recognize the differences in students. One idea that has been particularly popular in recent years is the idea that students have different learning styles-preferences in the way they like to learn-and if they are taught in the way that matches their preferences, they will learn more. Unfortunately, the available research evidence shows that this idea is just wrong.

Reviewing the research on learning styles is difficult, not least because of the huge variety of learning styles classifications that have been proposed-in one research review, Frank Coffield and his colleagues identified 71 different learning styles classifications (Coffield et al., 2004). However, when a group of leading psychologists were asked to review the research on learning styles, their conclusion was clear:

"If classification of students' learning styles has practical utility, it remains to be demonstrated." (Pashler et al., 2008 p. 117).

Moreover, it may be that teaching students in their preferred learning styles actually reduces the amount students learn (Wiliam, 2016).

As an alternative, some writers have suggested that what students learn should be based on what they are interested in (Tomlinson, 2004), but the problem with such an approach is that students would then not learn a lot of mathematics and science that they need to learn to make progress. Others have argued that some things may be "developmentally inappropriate" for students to learn, but such arguments seem to rest on the now largely discredited "stage" theories of learning (Willingham, 2013). The most important difference between students is simply what they already know. Of course, we have known this for a long time. Almost fifty years ago David Ausubel said:

"If I had to reduce all of educational psychology to just one principle, I would say this: The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly" (Ausubel, 1968 p. vi).

This, of course, is why formative assessment is so important. We need to find out what our students know before we teach them anything new. But finding out where our students are is just the first step. We also need to decide what to do with this information, once we find out that the students are at different places in their learning, and that is why differentiation is so important.

Differentiation is simply an approach to teaching that recognises the varying levels of achievement in a group of students. In the past, teachers have been encouraged to prepare different lessons for different students in the same class, for example by having one set of activities for the low achievers, one set for the average students, and one set for the high achievers. As well a requiring an unrealistically large amount of preparation time for the teacher, such teaching is often inefficient, because teachers spend much of their time moving from group to group checking the groups are on task. Given the class sizes typically found in schools, the only practical approach to dealing with the range of achievement found in a class is a process of inclusive differentiation.

Of course, this is challenging, and unfamiliar to many teachers, which is why the National STEM Learning Centre developed a new online course, 'Differentiating for Learning in STEM Teaching', to support teachers in developing their practice of differentiation.

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Differentiation: getting the balance right

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As every teacher knows, students differ in their capabilities, their knowledge, and their interests. In the early 1980s, the Cockcroft Report (1982) identified a "seven-year-gap" in student achievement in mathematics, motivated by the variation that the Assessment of Performance Unit had found in student response to the simple question: 6099 + 1 = ?

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Short video on an innovative concept. More primary related

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Math.6.NS.A.1

Common core State Standards

Math: Math

6: Grade 6

NS: The Number System

A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions

1:
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. How do learning menus enable Ms. Morey to provide differentiated instruction?

2. Why does Ms. Morey allow students to sometimes choose which tasks she assesses?

3. What resources does Ms. Morey use to design her menu tasks?

School Details

Enumclaw Middle School
550 Semanski St
Enumclaw WA 98022

Data Provided By:

Teachers

Math / Kindergarten 1 2 3 4 6 / Coach

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Learning Menus: Giving Options & Independence

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Crystal Morey uses learning menus to provide students with independent exploration of concepts in her sixth grade math class. Each of her menus has options for an appetizer, main course and dessert task. While students work on their menu tasks, Crystal is able to pull aside a small group to work with on targeted math skills.

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Strategies grouped again:
Outcome, product, response, etc.

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Three categories of differentiation:
Task, Support, Outcome

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NQT: advice and support for newly qualified teachers | Tes

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Find a range of support, advice and guidance for NQTs. From your first day as an newly qualified teacher through to completing your induction, Tes is here to help. Find tips from industry experts and columns from teachers who have been in your shoes. Visit the page now for the latest advice.

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Some good ideas for strategies as word docs at bottom

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London Gifted & Talented creates high quality learning programmes and e-resources to stretch students and support their teachers at Key Stages 1-5 across the curriculum. Our online resources are free to use and accessible from all over the UK and worldwide.

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Good start point - 7 strategies