The Summer of Our Discontent

Winds of Change

What does all the recent education research mean for middle school mathematics?

It seems like every week this summer, a new publication, article, or press release appears on the education horizon. Teachers are expected to read them, reflect on them, decide what is meaningful to the way they do their jobs, and implement change in their classroom. But its not that easy... broad generalization, vague language, and conflicting views cloud the issue. Teachers are screaming, Just tell us what to do! Well, heres one mans attempt to sort through the sea of words and give you some tangible ideas and suggestions for the upcoming school year.

Where We Are

In order to talk meaningfully about change in the middle school mathematics classroom, we must first take stock of where we are starting from.

For the last several years, many different influences have been changing the way teachers do their jobs. First and foremost, middle schools have been implementing various flavors of middle school reform. Middle school teachers have been pulled in every conceivable direction.

Progressive state and national assessments have pushed districts to raise middle school academic standards to higher levels. Attention has been focused on the middle school academic standards through studies such as TIMSS. TIMMS showed that typical middle school mathematics content is a rehashing of a wide variety of topics that were not learned in elementary school mathematics. The teaching of these topics was typically direct, and did not ask students to use higher-order thinking skills. It was widely believed that most middle school students were not capable of solving complex problems. Spurred by the disappointing results of these studies, districts have raised the bar on middle school academic standards. But by and large, they have not given teachers the direction, means, or professional development necessary to achieve these standards.

Raising academic standards in the classroom has led many districts to advocate differentiated instruction models. Differentiated instruction has asked middle school teachers to address the needs of all students, from gifted to special education, in the same classroom at the same time. The basis of differentiated instruction is building activities that allow for different levels of achievement. A basic level of achievement is expected in each activity. Students ready for more advanced topics have several opportunities to complete extensions based on the original activity. The philosophy is sound, but teachers have been given little professional development to help them design and manage such activities.

At the center of the academic standards debate for mathematics is the issue of Algebra. The National Council of Teacher of Mathematics has long advocated Algebra for All. Many districts are combining this vision with the needs for higher standards to push a traditional Algebra I course for all 8th graders. Does this meet the needs of all students? Is a high school course taught in a middle school setting effective? And if algebra is not taught at all in 8th grade, are we meeting the needs of our gifted population, who may be socially and academically prepared for algebra? Will this hold them back in their high school years, causing them to fall short of a Calculus course and a future in a top technological school?

Another key component to middle school reform has been social development. Research on adolescent development and psychology has put increasing attention on encouraging social development in the classroom. Middle schools, both formally and informally, changed their instructional delivery to support positive social development for middle school students. These changes have taken many forms; teaming strategies, common teacher planning, advisement programs, and re-evaluation of promotion standards and school climate.

Often, these changes place academic standards on the back burner. Social development and academic standards have bifurcated the middle school reform camps, sending conflicting messages to schools and teachers. The result can be a confused and disorganized implementation of change.

Whats Being Said Now

Over the last several months, many publications have attempted to address middle school reform in general, and the academic and social issues in particular. Within this sea of research, opinion, and directives are some salient points that can lead us to meaningful middle school change.

NCTM Principles and Standards for School Mathematics 2000

In April 2000, the National Council of Teachers of Mathematics released Principles and Standards for School Mathematics (PSSM), an update to the groundbreaking Curriculum and Evaluation Standards for School Mathematics (1989). While this update was largely viewed a clarification and tweak of the national mathematics standards, there were some substantive changes at the middle school level.

One of the most noticeable changes was in the grade band categories. Rather than K-4, 5-8, 9-12, PSSM was organized Pre-K-2, 3-5, 6-8, and 9-12. This follows more closely with the middle school concept, as well as many state testing programs. Thus, the content included in the 6-8 band was aimed squarely at middle schools and the middle school concept.

Another major change is the addition of a 5th process standard, Representation. Although implicit in the 1989 document, the idea that mathematical constructs can be represented in different ways is addressed specifically throughout the 2000 version. For example, a linear relationship can be represented through manipulatives, a drawn pattern, a numerical t-chart, a graph, or an equation. The Representation standard provides a very meaningful thread through which teachers can better connect content across grade levels.

PSSM lays out three main content foci at the middle school level. The first is the development of rational number concepts. This focus is the one that most closely echoes traditional middle school mathematics curricula on the surface, and takes it a few steps further. It discusses not only fluency with decimals, fractions, and percents, but also building a level of comfort where students recognize and utilize the relationship between the representations. Typically, moving between the representations and understanding their uses is a gap in the middle school math curriculum.

The second content focus is algebra and geometry. PSSM makes a bold statement, saying that there should be a substantial amount of both topics in the middle school curriculum, but they should be threaded throughout the grade levels and interconnected. The Standards fall short of making recommendations about when an Algebra I course should be taught. Some possibilities will follow in the closing sections of this article.

The third, and arguably the richest, content focus is proportional reasoning. Traditionally, proportion has been taught as a discrete topic, with a handful of real-world connections. But in reality, proportional reasoning pervades most every topic taught in middle school. Proportional reasoning can be used in probability, or any other topic involving ratios. It can be applied to geometry formulas, and used to analyze what happens to the area and perimeter of a rectangle when its dimensions are changed. It can be used in problem solving, and to extend or generalize patterns. And it can be used to quantify rates of change, slope, and linear relationships. Proportional reasoning has always been implicit in the middle school curriculum, and PSSM shows teachers that it can be used as a pervasive theme throughout grades 6-8.

Phi Delta Kappan Special Report: Middle-Grades Reform

In June 2000, the Kappan issued a special report on the state of middle school reform. The report is more of a summary of what previous programs have done in the past than it is a guide for continuing middle grades reform. But there is one key point made throughout the report that is important for all middle school educators to remember.

Throughout the middle school reform process in the late 1980s and early 1990s, there have been two main schools of thought. One advocates the need for higher academic standards in the middle school. The other raises the need to address the social development of middle school students.

In most cases, these two schools of thought were seen as opposing viewpoints. But recent talks between middle school reform advocates have yielded an important result. Addressing both academic standards and social development in a middle school reform model is possible. Moreover, well-implemented programs that help a student develop socially are very compatible with achieving high academic standards. A well-adjusted, happier student tends to be open to learning more in the classroom setting.

The Kappan report has extensive anecdotal records of reform efforts over the last several years all over the country. Every middle school teacher would be well-served to browse the report for ideas. But the most important point to take from the article is that social development and academic programs can and should coexist.

Maryland Math Task Force

Assembled by Maryland State Superintendent Nancy Grasmick, the Maryland Math Task Force was changed with the task of addressing the states drooping math scores. In June 2000, they previewed their recommendations at the June state board meeting. Two of these recommendations could have an enormous impact on middle school mathematics in Maryland and beyond.

The group will discourage local districts from mandating high school algebra in 8th grade. Many school systems in the state have been considering making this change for all students to try to increase calculus enrollment numbers in 12th grade. The group does not advocate no algebra in the middle school at all, but they are opposed to using the high school algebra curriculum in the middle grades. The task force is prepared to recommend that algebraic concepts be taught throughout all grade levels.

The second recommendation that the group will present is that middle school math teachers have their own content-based certification rather than general K-8 certification. Statistics show that a large number of teachers nationwide, and within the state of Maryland, are elementary certified. The teacher shortage is reaching critical levels. What will this mean to the future of middle school math staff? Some conjectures will be presented in the final section of this article.

What To Do

Research is great, but what does it mean to middle school math teachers in the classroom? Some conclusions and recommendations for action are presented below.

In Your Classroom

1. Read, understand, and support Principles and Standards for School Mathematics 2000. Support it in your classroom. PSSM provides significant elaboration and many examples of the content that was touched upon earlier in the article. It addresses expectations and goals for each of the 10 standards in the middle grades. This document will guide a teacher towards better classroom practices and richer content for their students.

2. Focus on the new Representation standard, and use the Communication standard to get to it. For example, there are many different representations for rational numbers; fractions, decimals, and percents are the ones most commonly addressed in the middle grades. But students rarely see the interconnected nature of the three representations. Manipulatives and meaningful discussion about the forms would help draw out the connection between these representations. Easing requirements and allowing students to represent a rational number in a way theyre most comfortable with would also go a long way towards building that understanding.The Representation standard can be used in many other ways than just with rational numbers. PSSM provides many more examples. These are things that teachers have been doing in their classroom to a certain point. A small amount of adjustment would make the activities much more rich.

3. Advocate for algebra and geometry to be threaded in the middle school, not taught as high school courses in the middle school. There are many arguments for this the Principles and Standards, the Task Force findings, and countless other studies. But the most compelling argument is equity. By teaching Algebra I to a select few, a school system denies the rest of their population to the rich mathematics of algebra. Conversely, by teaching a high school Algebra I to all students, districts do a disservice to students who are not developmentally ready for a traditional algebra class. By threading the concepts throughout and building them gradually, teachers can encourage developmental readiness for Algebra I, and still teach the rich, meaningful mathematics contained in algebra and geometry.

Outside Class

1. Keep your ear to the ground. Theres lots of research out there, and no teacher has time to read it all. But teachers should keep abreast of large-scale reform issues, task force findings, and independent reports. One to watch for this fall is Turning Points 2000, a sequel to the groundbreaking Turning Points produced by the Carnegie Foundation. The Internet can be a powerful tool for keeping informed, and most teachers have access either at home, at the workplace, or both. The NCTM and MCTM websites sort through the publications and give teachers access to only the best and most important articles.

2. Collaborate and share ideas with your colleagues. Discuss articles and debate opinions on middle school reform. Share successes from your classroom. Elicit suggestions from master teachers. Request support from your administration for common planning time to achieve these goals.

3. Get math certified. If you love math, and love teaching math, take the time outside of the classroom to begin work on secondary certification. The Maryland Math Task Force has recommended that the state move in that direction. Although change will be a long time coming, there is no harm in planning ahead. Ultimately, learning more will translate to better teaching practices in your classroom.

4. Learn and implement differentiated instruction. Nobody debates the fact that middle school students have differing needs. Differentiated instruction, implemented and supported properly, is a great way of addressing these needs without sacrificing the pacing for all students.

Support from Below, Support from Above

Solicit support from feeder elementary schools. A key statement in the Maryland Math Task Force report is that algebraic concepts should be taught at all grade levels. Fill in the blank problems, patterns, and tables can help build algebraic skills at the early grades.

Form partnerships with local elementary schools to discuss and promote good mathematics teaching practices in your classroom and theirs. Share successes, and discuss ways to enact meaningful change.

With high-stakes exams implemented or on the horizon in 30 states nationwide, high school teachers need to be aware and supportive of initiatives in their feeder middle schools. They also have a responsibility to communicate their needs to middle school teachers so that incoming high school students can be better prepared.

The formation of a vertical team from grades K-12 within a district is an excellent way to achieve this articulation and share mathematical ideas. Many districts have implemented such teams and have increased communication across grade levels about mathematics.

A Season of Change

Middle school is a time of great change for adolescents. The first decade of the 21st century will be a time of great change for middle school education. Documents like the Kappan Reports, Principles and Standards for School Mathematics, and Turning Points 2000 will help guide middle school reform in the next several years.

Great teachers remember that their students are the top priority. For the sake of improving their education, heed the winds of change.