Mathematics Education Newsletter
Mathematics Education Newsletter

Your Adviser

Dr. Peter Appelbaum Peter Appelbaum has office hours by appointment during the summer. Call him or e-mail because he will likely be in and out of the office most days.

Phone: 215-572-4476
E-mail: appelbaum@arcadia.edu

Let the Summer Games Begin ...

The National Council of Teachers of Mathematics has already posted its summer links. Check them out here.

Special Seminar this Fall:
Take Back the Mathematics Curriculum!

ED534 will be taught this fall by Josh Craven, who had much success with his class last fall on the teaching of Calculus. This fall he is taking on the Special Topics in Mathematics Curriculum Development course, which focuses on different issues and themes each time it is offered. In fall 2009, ED 534 will be examining mathematics curricula from the teacher's and student's perspective, including decision making processes for how school mathematics curricula should be created and improved, how they can be linked to current standards, and how math teachers can align them vertically and horizontally within schools. The course promises to be somewhat individualized based on the goals and experiences of those students who register. Mainly, though, the course is designed to create teacher leaders with insight into how their students can best have a cohesive math experience in their school system. Ed 534 is scheduled Wednesdays from 7:20-10 p.m.

Clinical Mathematics Education Goes Partially Online!

ED528B, Clinical Mathematics Education, is designed to follow a psychodynamic clinical training structure. Students pursue their own personal mathematics investigations, working on problem solving and posing, and the development of their own conjectures and mathematical arguments; at the same time, they facilitate such work for a small group of their own pupils. The dual nature of the work helps the group to explore issues of assessment, and finally come up with serious answers to questions about when and how teachers can believe they understand their own and their pupils' relationships with mathematics. How one comes to know, apply and understand mathematical skills and concepts is a complicated experience, as past students of ED528B can share! In Fall 2009, the course will use a partially online format, combining monthly on-campus Thursday evening meetings with weekly web-based communication and participation.

Check Out Summer & Fall Courses!

Summer II 2009 Courses in Mathematics Education

Fall 2009 Courses in Mathematics Education

Don’t forget the many other courses in education not specifically in mathematics that may be of interest! Check out course offerings at: www.arcadia.edu/courses, or on MyArcadia.

These courses are open to students pursuing a degree or certification, and also to folks interested in just taking a course or two. Spread the word! Tell friends and family about the opportunities here at Arcadia.

CIEAEM Meeting as Close as Montréal!

The International Commission for the Study and Improvement of Mathematics Education is holding its meeting in North America this year! Unbelievably close! July 26-31. Click here for the website. Since its foundation in 1950, the Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) intended to investigate the actual conditions and the possibilities for the development of mathematics education in order to improve the quality of teaching mathematics. The annual conferences which are the essential means for realizing this goal are characterized by exchange and discussion of the research work and its realization in practice and by the dialogue between researchers and educators in all domains of practice.This year's theme is MATHEMATICAL ACTIVITY IN CLASSROOM PRACTICE AND AS RESEARCH OBJECT IN DIDACTICS: TWO COMPLEMENTARY PERSPECTIVES.These meetings of teachers, scholars and policy-makers from all over the world are an amazing experience of international collaboration, not to be missed!

Mathematics Education Trust Grants - Something for you??

Established by the National Council of Teachers of Mathematics, the Mathematics Education Trust (MET) offers opportunities to expand your professional horizons! MET supports the improvement of mathematics teaching and learning at the classroom level through the funding of grants, awards, honors, and other projects by channeling the generosity of contributors into classroom-based efforts that benefit all students. MET provides funds to support classroom teachers in the areas of improving classroom practices and increasing teachers' mathematical knowledge. MET also sponsors activities for prospective teachers and NCTM's Affiliates, as well as recognizing the lifetime achievement of leaders in mathematics education. There may be a program that's just right for you! Click here for more info!

Arcadia Mathematics Education Seminar Takes on Social Justice Replacement Units

What's the hardest thing about introducing social justice mathematics into your curriculum? This year's ED 529 Mathematics and the Curriculum seminar took this on as part of its study of contemporary standards and recent trends in mathematics education. The course was co-taught by Professor Peter Appelbaum and Visiting International Professor Wolfram Meyerhöfer. Each member of the course designed a "replacement unit" for their current curriculum. The idea was to plan multi-day experiences for our students that could be justified according to traditional criteria, i.e., that the time allotted would accomplish the same learning objectives or more than were expected in the pre-existing curriculum. At the same time, we strove to make sure that these replacement units were far more valuable than the curricula to be replaced, in that they incorporated social justice mathematics themes at their core. In the development process it quickly becomes clear that we are anxious about making changes in our curriculum. Will this unit be worth it? Will it serve my students’ needs? Concerns bubble up. One way in which such concerns materialize is in the form of "Gatekeepers" (Appelbaum and Dávila 2007) - those individuals or groups of people who are perceived as potentially expressing dissatisfaction with our choices of social justice pedagogies, e.g., a principal or parents. For many pre-service and practicing teachers, the conversation regarding gatekeepers is more about perceptions they have regarding the struggles they will face when faced with gatekeepers within the structure of the school system than with actual realities. For others, this conversation is indeed about enlisting a potential doubter or adversary as a collaborator and supporter. In either case, the gatekeeper materials serve a unique psychoanalytic function. When a teacher imagines a potential gatekeeper – e.g., principal, parent, colleague, community member, student, themselves – he or she is projecting their own anxieties fears onto an imaginary construct. It is possible that any one of these real people may in fact display certain anticipated reactions. However, in the proactive process of working with gatekeepers, the teacher has an opportunity to interact with her or his own projections and concerns. Whether a teacher presents herself or her principal as worried about the lack of attention to the assigned content for the next month of the school year, the worry about not meeting obligations is the most important concern that the teacher must address. Whether explicitly addressing their own concern or not, the proactive composition of a letter to parents, or the preparation of a proposal for a meeting with an administrator, allows the teacher to work through any possible fears and worries that they may even be having trouble consciously articulating. For example, a letter that lists twenty standards that are being addressed by the forthcoming unit, along with specific suggestions for ways that skills can be practiced at home simultaneously helps a teacher recognize that the unit indeed addresses the twenty standards and indeed provides adequate coverage of particular skills. Furthermore, the composition of such a letter prepares a teacher to better accomplish these goals now that they are explicit, while also making clear to the teacher what must be assessed on an ongoing basis in order to meet the goals.

As they considered resources from Rethinking Mathematics (Gutstein and Petersen 2005) and www.radicalmath.org, the trajectory notion served to highlight both the importance of the social justice aspects of the unit/lesson and the ways that the social justice mathematics and the traditional Standards-based mathematics mutually support each other. Our trajectory designs required us to consider the potential of any social justice mathematics activity in terms of its purposes when used at the beginning, middle or end of a unit, and in this way they were really three different unit/lesson designs; the juxtaposition of each with the others helped to clarify our goals for the designs themselves. The consideration of how this placement would change the skills and concepts that would be developed through the designed curriculum helped the participants to determine what skills and concepts were possible in the first place, and in the process, helped the teachers to better understand the mathematics of the social justice experiences more deeply. Teachers rarely have the opportunity to reflect on the kind of mathematical thinking that they can spark for their students through the introduction of a specific experience. In this project, each teacher pursued the subtle differences that would be enacted by the choice that they needed to make about when and where to place a particular experience within the trajectory of the unit or lesson. They also were participant-consultants in the discussion of the other unit/lesson designs included here, which were also carefully analyzing these issues.

A maxim of psychoanalytic thought is that resistance is essential for critical learning to occur (Appelbaum 2008). In this assignment, the teachers’ resistance to new curriculum ideas became the explicit focus of the task. By labeling the fears and anxieties as external "gatekeepers", we were able to distance ourselves from our own resistance, objectify it, analyze it, and move through it to a new understanding of a social justice mathematics curriculum. Social justice mathematics was no longer set up as an alternative to "real" mathematics, and no longer positioned as oppositional to accepted practices. What was initially "othered" became an ally, a tool for accomplishing our own and others’ goals for school mathematics. A copy of the materials developed in this seminar is available at LINK.

Braitmayer Foundation K-12 Grants

Proposals are due November 1-15. This foundation is interested in K-12 education in the United States, with special interests in curricular and school reform initiative and preparation, as well as professional development opportunities for teachers. The foundation provides up to $10,000 for grants to be used anywhere in the US as seed money, challenge grants, or to match other grants to the recipient organizations. For more info, see www.braitmayerfoundation.org/guid.htm.

Book Reviews

Following up on the well-received review of Rethinking Mathematics: Teaching Social Justice by the Numbers, by Patricia Marnien Tresnan, Mathematics Teacher, Jenkintown Schools, Arcadia MAEd 2003, we welcome reviews of materials and resources that you have found more or less valuable in your work. Please contact Peter if you would like to have your ideas included in future issues of this newsletter.

Possible books to consider reviewing:

Mitch's Corner

Mitch BernsteinMitch's Corner is a regular feature of the Arcadia Mathematics Education Newsletter, sharing samples of resources from Mitch Bernstein, a high school math teacher in Philadelphia for 31 years. Mitch taught both traditional math and the reform Interactive Mathematics Program. He is now retired. He is a co-author of Algebra 1: An Integrated Approach.

Here is one of Mitch’s famous Problems of the Week:

The chart below illustrates how sales for an item has decreased as price of the article increased.

Price Number Sold Income (Price)*(Number Sold)
$1 85,000 $85,000
$2 80,000 $160,000
$3 75,000 $225,000

If the pattern shown continues,

1. What price should be charged in order to produce the greatest income?

2. What is the greatest income possible for this product?

Explain your answer. Solution.

Mitch’s collected resources are bound and available in the Landman Library Curriculum Materials collection. You may also pick up a free CD of the same resources from Peter Appelbaum in Taylor 312A.

 

 

Mitch’s Corner Solution

Continuing the pattern of the table, we can see:

$1 85,000 $85,000
$2 80,000 $160,000
$3 75,000 $225,000
$4 70,000 $280,000
$5 65,000 $325,000
$6 60,000 $360,000
$7 55,000 $385,000
$8 50,000 $400,000
$9 45,000 $405,000
$10 40,000 $400,000
$11 35,000 $385,000
$12 30,000 $360,000
$13 25,000 $325,000
$14 20,000 $280,000
$15 15,000 $225,000
$16 10,000 $160,000
$17 5,000 $85,000
$18 0 $0

1. To produce the greatest income, charge $9.
2. The greatest possible income is $405,000.