• by Kathy Brown • IDRA Newsletter • August 2005
Imagine this: Adriana succeeds in advanced placement calculus. She finds delight and fascination in exploring mathematical concepts that once seemed foreign to her. Every day, Adriana sees the value of math in her own life. She used to think math was a duty. Passing the state standardized test, the Texas Assessment of Knowledge and Skills (TAKS), was her only indication of math achievement.
But Adriana’s math teacher integrates dynamic, real-time technologies into her math lessons on a regular basis to promote conceptual exploration and connections. She provides an array of tools for determining solution strategies and gives students the vehicles to communicate their reasoning. In the past, she targeted TAKS objectives, in isolation of one another, that students were weak in, and she gave students worksheets and TAKS review lessons.
Now this teacher provides opportunities for students to self-assess their learning and take ownership of what is possible. All of her students have access to math and knowledge. She believes in all of her students and encourages them to enroll in higher-level mathematics courses.
A Big Vision
IDRA has a vision that all students should have access to quality instruction in math that ensures success on all assessments, and enrollment and completion in higher-level mathematics courses. This vision is coming to fruition through various technical assistance opportunities that IDRA provides. One example is the secondary Math Smart! institutes that were first delivered through the STAR Center (the comprehensive center at IDRA that serves Texas).
This last spring, IDRA held four institutes called: Math Smart! Closing the Gap, Increasing Student Achievement and Meeting Annual Performance Standards in Secondary Mathematics. These popular institutes demonstrate integration of various dynamic, real-time technologies into math lessons to build concepts and address content area and technology standards. The models use innovative scientifically-based research strategies for success on the mathematics TAKS. Math Smart! provides support during and after the workshops to secondary teachers, math specialists, and administrators using various means for building communities of learners. For best results, campus teams that included algebra, geometry, pre-calculus, and calculus teachers attended. The following were the institute objectives and outcomes.
- Strengthen the belief that all students can learn math.
- Value students’ experiences as a basis for strengthening their math competency.
- Take advantage of a safe environment to explore mathematical concepts in new ways.
- Support peer collegiality among math teachers who are experiencing success.
- Move from a traditional math instruction approach to a broader paradigm that makes it possible to say that all students really can learn math.
- Compare the five dimensions of mathematical proficiency (Adding It Up! National Research Council) and the relationship to student math achievement.
- Illustrate lessons using technology for conceptual understanding, procedural fluency, strategic competency, adaptive reasoning, and productive disposition.
- Apply the ideas of the institute to affect TAKS and adequate yearly progress (AYP).
This institute incorporates the use of IDRA’s mobile lab, which consists of robust laptops; data collection devices such as CBL2s, CBRs, and Pasco Probeware; and dynamic software tools such as Geometer’s Sketchpad, Fathom, Tinkerplots, and Inspiration for mindmapping and planning. These tools provide participants, students, teachers, administrators, and regional service centers with experiences and insights into learning strategies for building mathematical knowledge and academic language for all students, including English language learners.
Participant Vision and Expectations for Students
During the spring Math Smart! institutes, participants shared their vision for their students. They then compiled graphs that represented their group’s ideas reflecting the probability of students in the first, second, third and fourth quartiles of their mathematics classes of enrolling and being successful in higher-level mathematics courses on a scale from 1-least likely to 5-most likely (see pictures).
The second picture demonstrates what we saw around the state. Teachers saw that their expectations differed among students. Teachers in all institute locations began to ask: “What does it mean to provide access to quality mathematics instruction that is empowering for all students?”
A paradigm shift began early in the institute when participants reflected on the compiled data and commented that the probability and the expectation should be the same across the board: all students should be expected to enter higher-level mathematics courses and experience mathematics achievement.
During one institute, a new set of innovative professional development strategies were incorporated. Eighteen math students who are enrolled in various mathematics course levels, Algebra I through pre-calculus, participated in two major aspects of the institute that incorporate student self-assessments and interviews for making instructional decisions as well as comparing traditional mathematics problems with meaningful mathematics situations.
The teachers interviewed the students, asking the following questions:
- What do you enjoy about learning mathematics?
- What do you find challenging about learning mathematics?
- What could your math teacher do to help you excel in your math class?
Student self-assessments on learning functional relationships using a CBR Motion Detector and TI-84 Plus Graphing Calculators provided teachers the mathematical insights needed to make future instructional decisions.
Students and teachers reflected on these activities, citing how their mathematics knowledge increased by this experience and the insight gained into student thinking. These activities were videotaped and presented at the next institute where participants viewed these authentic and valuable insights. Teachers at these institutes indicated that they will include, as ways of assessing student knowledge, student self-assessments and interviews.
Dynamic, Real-Time Technologies
Institute participants explored the concept of transformations of functions through the dynamic learning tool, Geometer’s Sketchpad. Teachers used this tool to explore parameter changes and to increase their own mathematical knowledge. Afterwards, the teachers were able to easily identify how this knowledge transferred to the 2004 TAKS release test where 20 percent of the test addressed this knowledge base. Teachers readily and directly made the connection between the power of integrating dynamic mathematics tools for deepening, building, and extending mathematical knowledge and language skills for English language learners.
As a culminating activity, teachers, math specialists, and administrators shared what was happening in their districts to address adequate yearly progress (AYP) needs on various levels: student, teacher, parent, campus administration, and district. Using the mind mapping tool called Inspiration, campus groups created strategic plans, posted these plans, and joined an online discussion board on the Math Smart! team web site.
Overall, 18 students and 117 teachers, administrators, math specialists, and education service center specialists attended the Math Smart! institutes. The majority of the strategic plans created by campus teams and school districts included the listening of student voices, raising our own expectations for all students to achieve in mathematics and successfully enroll and complete higher-level mathematics courses, and make mathematics accessible to all students.
For more information on Math Smart! contact IDRA or visit www.idra.org.
Kathy Brown, is the technology coordinator in the IDRA Division of Professional Development. Comments and questions may be directed to her via e-mail at email@example.com.
[©2005, IDRA. This article originally appeared in the August 2005 IDRA Newsletter by the Intercultural Development Research Association. Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]