The act of constructing–not memorizing–knowledge takes a great deal of energy and activity. It demands collaboration, real-world tools, critical thinking, creativity, and a genuine desire to learn. Knowledge construction also is exciting. It engages the learner and opens up a limitless world of self-directed inquiry.
In 248 Washington state classrooms, you can mark the moment when a struggling math learner constructs–not reproduces–new knowledge about mathematics. A simple document camera, coupled with a learner-centered teaching style, is the key. Empower the learner. Use a simple, real-world technology.
Over the past six years, the NO LIMIT! (New Outcomes: Learning Improvement in Mathematics Integrating Technology) project has transformed the learning environment in these classrooms, primarily in grades five through nine. We provide funds for NO LIMIT! projects from the competitive portion of the state’s Title II, Part D (Enhancing Education Through Technology) grants.
Working closely with the school districts at the outset, we created a standards-based platform that triangulates technology (document cameras), instructional materials, and a sustainable framework for collegial professional development.
The NO LIMIT! model is structured enough to deliver academic rigor, but sufficiently open-ended to encourage creativity and new ideas. The results speak for themselves.
Figure it out. Share it with the class.
Real-world technology integrates easily into a learner-centered environment where teachers are free to coach, guide, and lead their students to new understandings of mathematics. NO LIMIT! students work alone or in pairs to document their thinking about a new concept. During the summary of the math lesson, they share their ideas with the class by projecting the work through a document camera. Guided by the teacher, these students explain their thought process and solutions to each other.
Integrating the simple technology of a document camera blurs the line between teachers and learners. As students learn from each other, as well as from the teacher, the result has been remarkable–students develop real confidence in their ability to understand, apply, and demonstrate their unique mastery of mathematics.
The NO LIMIT! classroom promotes a constructivist learning environment. Students collaborate and discuss their work, learning and developing what it is they are trying to communicate about the lesson. The children bring their paper work to the document camera, rethinking their ideas out loud as they explain them to the class. The document camera is fast and easy to set up. Teachers report that dispensing with the need to make an overhead transparency keeps the focus on the students’ work. As one teacher wrote to us, “The document camera and projector lets students share on the spot. Things move quicker, since we don’t have to rewrite or make transparencies.”
Another comment from one of our teachers captures how the NO LIMIT! approach can transform the learner and the teacher: “The more I watch kids and examine their work, the more I understand how kids think and learn. I tried some interview assessments this year, and it really changed how I taught the content. I knew better where to start teaching!”
She is not alone with this perception. As we evaluate the longer-term outcomes of this project, we see clearly that the more opportunities a teacher has to observe how students share work and explain their thinking, the more this learner-centered approach illuminates how children learn. The teacher becomes a learner, too, as he or she listens carefully to understand student thinking.
NO LIMIT! students are free to share their unique way of approaching a new idea as they explore, internalize, and apply an unfamiliar math concept. Documenting the way they figured out the solution to a problem, they step naturally through the stages of knowledge construction–connecting and reshaping old ideas, and identifying how the new schema matches similar concepts within their experience.
Here’s a sampling of the anecdotal feedback from NO LIMIT! teachers:
•”[Students] all feel they are teachers as well as learners–powerful stuff!”
• “Students are motivated by other students when they get the ah-has. They are excited because they understand.”
• “My students like to learn from each other. When one of their peers explains how [he or she] figured out a math problem, you can watch the light come on.”
• “I noticed that sometimes students are more able to grasp a concept if another student is showing how [he or she] solved the problem.”
Build equity among learners.
Clearly, students are more willing to share their work when they have a document camera to use, partly because the document camera makes showing their work so much easier.
However, there is a deeper, more significant change at work in a NO LIMIT! classroom. The NO LIMIT! learning environment is less threatening to the shy child or the student who lacks confidence in his or her language skills.
Teachers report that NO LIMIT! students are really eager to explain their thinking to their classmates without the normal self-consciousness that plagues children from different cultural backgrounds, and those with limited language proficiency.
In one particularly successful implementation, Hispanic students who are learning to speak English in kindergarten and first grade in Paterson (a small town in southeastern Washington) found the document camera to be an electronic friend that has given them confidence to try their limited vocabulary in front of the class.
And here is where the document camera provides an enormous assist to the teacher: This simple technology draws class attention to the work, not the student presenter. Under the light of the document camera, smart ideas and skillful solutions speak through the child.
Teachers tell us that children who are reluctant to speak out become keen to share their ideas. During the debriefing session that followed a lesson presentation at Paterson School District, one teacher told me, “It was impressive to see how comfortable some of the kids were sharing–shy students coming out of their shell.”
The director of the English Language Learners program at Paterson encouraged teachers to combine math and language lessons. He suggested they plan sentences in English that each student could repeat before starting a presentation. For example, “I think that the answer is [X] because [Y]”. When many students repeat a phrase exactly, they reinforce the correct syntax of a sentence in English as they explain their math lesson.
The gain for many of our NO LIMIT! educators is a clear increase in the number of English-language learners willing to use the document camera to share their work and learn from others.
Build a learning community for educators.
We modeled a unique professional development program for NO LIMIT! projects, anchored by three fundamentals: (1) Build a learning community among all NO LIMIT! educators. (2) Deepen the math content knowledge of teachers. (3) Share effective strategies for mathematics instruction.
NO LIMIT! funding pays for the document cameras and high-value instructional support materials.
In the classroom, the principles of our unique professional development model have a direct and positive impact on the confidence of these math teachers and the rising level of student engagement with the math curriculum.
We count these important principles as lessons learned from the NO LIMIT! experience:
•Engage school administrators. The active involvement of school administrators is critical. We need their understanding and support for the instructional approach and the new ideas evolving from the NO LIMIT! learning community.
•Know more about state standards. Educators respond to, and find great value in, expanding their understanding of state standards–Washington’s Grade Level Expectations–and learning how to use these tools to improve instruction.
•Create high-proficiency users. Technology integration is only possible when educators know how to use learning technologies–a document camera, projector, laptop computer, and so on. High-proficiency users can explore the potential of these tools to support project-based learning and create a constructivist environment for powerful teaching.
•Build equity in the classroom. Technology integration can help an educator address diverse learning styles. When we reach and teach students where they live–in a digital world–we open new channels for communication, achievement, and self-expression.
The NO LIMIT! project demonstrates that technology can be a key that unlocks a child’s ability to communicate in a way that honors cultural background and life experience. By creating learner-centered classrooms where students construct their own knowledge, the project also dispels the idea that math is too hard.
Dennis Small is the educational technology director for the Washington Superintendent of Public Instruction’s office. Mary Anderson is the NO LIMIT! math integration specialist at Educational Service District 123 in Pasco, Wash.