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September 1, 2000
Vol. 58
No. 1

Reworking the Workshop for Math and Science

Kayla eyed the table of potted dandelions that had been pulled from the schoolyard. The 1st grader's task was to put the plants into the correct life cycle order—sprout, plant, flower, and seed head—to show what she'd learned from our science unit on life cycles. Kayla looked at me suspiciously. "Those are weeds!" she announced.
"Well, you're right," I replied. "But weeds are plants. Can you put them into the plant life cycle order?"
"I could if they were plants," she responded. "But they're not. They're weeds."
I panicked. How could the brightest child in my class not understand something so simple? I drew a diagram; I argued; I reasoned. Finally, sensing my frustration, she gave me a reassuring smile and in a soft, soothing voice said, "OK, Mr. Heuser. Weeds are plants."
It wasn't until later that I realized that the problem wasn't Kayla's, but my own. Classification, like ordering, is a developmental cognitive structure. These structures are what humans use to organize data and make sense of the world. Like many 6-year-olds, Kayla was still developing her classification structures. She still saw plants and weeds as separate entities. My failure to differentiate instruction for Kayla led to her incomplete understanding of life cycles.
  • how to differentiate instruction so that children with varying cognitive structure development can learn science and math content, and
  • how to develop the structures necessary to understand that content.
Fortunately, teachers can address both challenges through one teaching technique: the math and science workshop (Heuser, 2000).

One Workshop

During a science unit on the states of matter, one workshop minilesson began with a question: What happens when different solids and liquids are mixed? The teacher held up two vials, one filled with vegetable oil, the other with colored water. After soliciting a few predictions, she combined the two and drew the results on the board. Students shared ideas about why the oil would rise to the top. The teacher concluded the minilesson by setting a few safety and cleanliness rules and outlining the expectations for the activity period: "At your tables are containers of many different solids and liquids. Decide which two of them you want to mix together, discuss with a neighbor what you think will happen, then mix them. Record your results with pictures and labels."
The students were excited to begin the activity period. For the next 40 minutes, each student worked actively to answer the initial question. Students made decisions about what to mix; they predicted, measured, observed, recorded, and discussed. Exactly what they learned depended on their levels of readiness. When the teacher had a conference with Jenny, she enthusiastically reported the results of her mixtures, but she was unable to make generalizations. William, however, did find a pattern in his work and made a conjecture: Lighter liquids will sit on top of heavier ones. He then tested the theory with one of the pan balances available in each workshop.
The workshop's main question—What happens when different solids and liquids are mixed?—is broad enough to provide many possible entry points into the activity. This emphasis on big ideas, together with the flexibility of the workshop format, allows children of different developmental levels to construct knowledge appropriate to their abilities.
After the activity period, students reflected on their work. Each responded in drawings or words to the open-ended prompts "I learned . . ." and "I wonder . . . ." After the teacher read the children's responses, she selected several responses to present anonymously to the class the next day. One statement—"I wonder why two liquids always make two layers"—prompted many children to give examples of what happened when they combined two liquids that did not form layers. At the children's direction, the teacher demonstrated some of these combinations. This follow-up to the student's reflection encouraged them to use their notes and memories to communicate and support their beliefs. It also helped dispel misconceptions.

Why Workshops?

The philosophy and format of math and science workshops are based on a progressive, constructivist technique that many teachers already use to teach writing—the writing workshop. Research indicates that when teachers try to use methods that are totally different from their own, they make only superficial changes to their teaching behavior (Olson, 1981; Welch, Klopfer, Aikenhead, & Robinson, 1981). By modeling the math and science workshop on a program that teachers already know, they are more likely to make meaningful changes.
  1. Children learn best when they are actively involved in math and science and physically interact with their environment (Cole, 1995; Foster, 1999; Jeffries, 1999; National Council of Teachers of Mathematics, 2000; National Research Council, 1996). This interaction also promotes developmental growth (Cohen, 1984).
  2. Children develop a deeper understanding of math and science when they are encouraged to construct their own knowledge. This knowledge is personal and is based on each child's developmental readiness and experiences. Blindly memorizing and repeating the ideas of others does not lead to understanding (Battista, 1999; Foster, 1999).
  3. Children benefit from choice, both as a motivator (McCombs, 1997) and as a mechanism to ensure that students are working at an optimal level of understanding and development (National Council of Teachers of Mathematics, 2000; Phillips & Phillips, 1994).
  4. Children need time and encouragement to reflect on and communicate their understanding. By writing, speaking, and drawing what they did and learned, students' conceptual understanding increases (Battista, 1999; Jurdak & Abu Zein, 1998; National Council of Teachers of Mathematics, 2000; National Research Council, 1996).
  5. Children need considerable and varying amounts of time and experiences to construct scientific and mathematical knowledge (National Council of Teachers of Mathematics, 2000; National Research Council, 1996).

Workshop Format

The format of the math and science workshop is similar to that of the writing workshop, consisting of a minilesson, an activity period, and reflection. The workshop comes in two varieties: teacher-directed and student-directed.
In teacher-directed workshops, the teacher guides student learning through addressing one common question. The teacher then solicits student ideas, helps draw connections to past experiences, and sets expectations for what students will focus on during the rest of the workshop. In the activity period, students answer the initial question by working with teacher-selected materials. They then share and reflect on these experiences.
Student-directed workshops also begin with a minilesson, but the focus is not on a question presented by the teacher. In student-directed workshops, children wrestle with personal questions and explore their own selection of materials in ways that they choose. Student-directed minilessons help students review workshop rules or introduce new manipulatives—these lessons get the activity period off to a calm start.
The student-directed activity period begins with students choosing from a wide variety of math and science manipulatives and tools. Plastic dinosaurs, base 10 blocks, feathers, rocks, and geoboards share shelf space with dozens of other collections in the workshop classroom. Thermometers and measuring cups are readily available measuring tools. Students find their own place to sit and work.
If a visitor were observing a student-directed activity period, he or she would see a great variety of behaviors, depending on each child's development and interests. Benjamin is stacking blocks as he investigates the question, How high can I build this? Later he will measure the stack using a technique that seems sensible to him—counting plastic links—to see if he can top his previous record, set during the last workshop.
Anne and Evelyn are counting lima beans. Anne groups her beans into tens so that she doesn't lose count. Evelyn has developed another method: She counts only the beans that can fit into a bottle cap, then she calculates the number of beans on the basis of how many bottle caps she filled. Evelyn shares her idea with Anne, but Anne rejects it and continues to count. Anne's method doesn't yet make sense to Evelyn.
Jose` is using a geoboard and rubber bands to make designs. He shares his idea with the teacher, who asks if he can cut the board with a pretend knife so that each half looks the same. Jose` finds two ways to cut it, and the teacher tells him that those are called lines of symmetry. Students are more likely to remember vocabulary that is introduced in response to something that they choose to do.
Bart is working with the same solids and liquids that he investigated in the earlier workshop. The teacher makes this set available all year; just because students have learned a lesson doesn't mean that every child has developed an accurate understanding or that he or she can't learn more from the same materials.
During the activity period, children can follow their abilities and interests. Each period is a self-differentiated inquiry session in which students choose objects that appeal to them and work at their own unique levels of development. They informally devise questions, design investigations, and seek solutions using methods that seem reasonable. Math and science become sense-making mechanisms to solve problems of personal interest.
Like the teacher-directed variety, student-directed workshops end with a reflection period. Before they clean up their objects, students share their creations with others. Students then write about what they did and learned. Prompts help them direct their thoughts. In addition to "I learned . . ." and "I wonder . . .", other common prompts are "What was the hardest part of your work?" and "What will you tell your mom you did in math workshop today? Give lots of details."

Workshop into Action

Do the workshops increase student achievement? The Mathematics Workshop Project is a collaborative project that examines the uses and effects of science and math workshops. A teacher from Glenview, Illinois, directs the study with help from a DePaul University education professor. A group of teachers from Glenview use workshops in their classrooms or volunteer their students as control groups. Preservice teachers in the Glenview-DePaul Clinical Model Program (Heuser, 1999) collect student performance data, both voluntarily and as part of their DePaul course work.
Preliminary results from the three-year longitudinal study show that when teachers used the workshop, their 1st and 2nd grade students outperformed comparable nonworkshop classrooms in five out of seven measures of developmental structure growth. At the same time that children explored math and science concepts in a research-based, constructivist manner, they also developed the readiness to better understand those concepts.

Working with Workshops

Despite a wealth of evidence showing better ways to teach math and science so that more children can succeed, many teachers still cling to traditional teaching methods (O'Brien, 1999; Zemelman, Daniels, & Hyde, 1993). This may be because so few practical constructivist approaches are available (Fosnot, 1996; Noddings, 1990). Fortunately, many teachers have already succeeded with the workshop format for teaching writing. This success can foster an understanding in those who want to move from one-size-fits-all math and science instructional models to a model in which children in all different states of development can succeed and learn.
References

Battista, M. (1999). The mathematical miseducation of America's youth: Ignoring research and scientific study in education. Phi Delta Kappan, 80 (6), 424–433.

Cohen, H. (1984). The effects of two teaching strategies utilizing manipulatives on the developmental of logical thought. Journal of Research in Science Teaching, 21, 769–778.

Cole, R. (Ed.). (1995).Educating everybody's children. Alexandria, VA: ASCD.

Fosnot, C. (1996). Constructivism: A psychological theory of learning. In C. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (pp. 21–40). New York: Teachers College Press.

Foster, G. (1999). Elementary mathematics and science methods: Inquiry teaching and learning. Belmont, CA: Wadsworth.

Heuser, D., with Farwick Owens, R. (1999). Planting seeds, preparing teachers. Educational Leadership, 56 (8), 53–56.

Heuser, D. (2000). Mathematics workshop: Mathematics class becomes learner centered. Teaching Children Mathematics, 6 (5), 288–295.

Jeffries, C. (1999). Activity selection: It's more than the fun factor. Science and Children, 36 (2), 26–29.

Jurdak, M., & Abu Zein, R. (1998). The effect of journal writing on achievement in and attitudes toward mathematics. School Science and Mathematics, 98 (8), 412–419.

McCombs, B. (1997). Understanding the keys to motivation to learn [Online]. Available at www/mcrel.org/products/ noteworthy/noteworthy/barbaram.asp

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Research Council. (1996). National science education standards. Washington, DC: National Academy Press.

Noddings, N. (1990). Constructivism in mathematics education. Journal for Research in Mathematics Education, 72, 7–18.

O'Brien, T. (1999). Parrot math. Phi Delta Kappan, 80 (6), 434–438.

Olson, J. (1981). Teacher influence in the classroom: A context for understanding curriculum translation. Instructional Science, 10, 259275.

Phillips, D. R., & Phillips, D. G., with Melton, G., and Moore, P. (1994). Beans, blocks, and buttons: Developing thinking. Educational Leadership, 51 (5), 5053.

Welch, W. W., Klopfer, L. E., Aikenhead, G. S., & Robinson, J. T. (1981). The role of inquiry in science education: Analysis and recommendations. Science Education, 65, 3350.

Zemelman, S., Daniels, H., & Hyde, A. (1993). Best practice. Portsmouth, NH: Heinemann.

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