C & I 332: An Investigative Approach to Elementary Mathematics Instruction

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Instructors:
Brad Thompson	Tedi Cox	Kefei Bi

Technical Assistant:

Michael McKelvey

E-mail class:	Cohort 1
Cohort 2	Cohort 3
Cohort 4	Cohort 5

Course Description

C & I 332: An Investigative Approach to Elementary Mathematics Instruction
This course will model and examine an investigative approach to elementary mathematics instruction, which is purposeful, inquiry-based, and meaningful mathematics instruction, and which is integrated across math topics and with other content areas. Moreover, this course will offer students experience in developing mathematics lessons appropriate for elementary instruction. Students will explore appropriate technologies that enhance mathematics instruction.

1. In C & I 331, you began laying the foundation for how children learn mathematics. You learned many important concepts in mathematics and aspects of how children learn those concepts. This course will build upon these ideas and offer you an environment to develop more expertise with creating and planning mathematics instruction.

What is mathematical power? The National Council of Teachers of Mathematics (NCTM) has called for fostering the mathematical power of ALL students (1989). In its most recent articulation of Principles and Standards for School Mathematics (2000), NCTM has reinforced this call with a clear vision for school mathematics. Mathematical power involves

a positive disposition toward mathematics (e.g., the interest and confidence to learn and to use mathematics),
the skills to conduct mathematical inquiry (e.g., problem solving and reasoning skills), and
understanding (well-connected knowledge).

This course considers how K-8 instruction can foster each of these components of mathematical power. More specifically, it examines the rationale for an investigative approach (purposeful, inquiry-based, and meaningful instruction) and how to implement such an approach. The course will focus on choosing worthwhile mathematical tasks... interesting and rich tasks that engage children's curiosity, involve them in processes of mathematical inquiry, and prompt them to construct a more connected (deeper) understanding of mathematical content. Because instruction is based on rich tasks, it frequently entails integrated learning ... learning that cuts across mathematical topics and content areas (e.g., science, language arts, consumer education...).

Diverse learners in a diverse world: Our world is changing rapidly. The classrooms in which you will teach are NOT the classrooms in which you learned. NCTM (2000) reminds us that ALL students must have the "opportunity to study and support to learn" substantial and important mathematics that is necessary to function and soar in the world in which they live. Throughout all of your methods coursework, you will be addressing how instruction can meet the needs of students who have a multitude of personal characteristics, cultural backgrounds, and physical challenges. This is a never-ending process as a teacher, and it is hoped that in this course, you will begin this process of understanding.

What is the role of technology? Emergent technologies are an important means by which many students in today's world can learn more mathematics and learn it more deeply. Manipulatives, computer software, calculators, video, data collection devices, and the wealth of internet resources on the World Wide Web are some of the technological tools that can help our students learn. It is incumbent upon us as mathematics teachers at the door of the next century to embrace these tools, for our goal is that ALL students have the opportunity to learn. Learning to use technology takes time and requires a level of comfortability--sometimes just to not be afraid of the technology!! This course will explore some of those technologies and assist you in developing your personal presence with instructional technologies in mathematics.

In summary, this course expects to accomplish many things:

To examine, illustrate, and model various approaches to teaching elementary mathematics.
To provide participants with "hands-on" experiences with cooperative learning groups and investigative math lesson planning.
To explore how assessment can be integrated with instruction.
To deepen participants' understanding of mathematics and children's mathematical learning.
To address how mathematics instruction can meet the needs of diverse learners in a diverse world.
To empower the participants, fostering confidence in their ability to teach inquiry-based mathematics.
To assist the participants with understanding of instructional technologies that are appropriate for learning mathematics in elementary and middle grades.

At the beginning of the semester, a diagram of a methods class might look somewhat like the one above. The skew lines going off in all different directions are representations of the teacher candidates (that's you!) and the circle in the middle could represent the methods class (that's C&I 332!). Do you see the star on the circle (It's difficult to see!) That is often a good representation of a topic in the methods class. The instructor is trying to focus on a particular aspect of mathematics education, but because of the different contexts of your practice teaching environments, it is quite difficult to intersect (i.e., make connections) with all of the teacher candidates. It is our goal to begin with the flat dimensional diagram above and, over the course of the semester, develop into the 3 dimensional model below. Here, the connections are numerous and are of all different types. There is a support structure that is inherent to this diagram and, we hope, to C&I 332. It is a richer picture of what practice teaching and an accompanying methods course can be. Let us see if we can develop our own sphere of learning.

Our hopes and purposes of C&I 332 are at least three-fold:

To provide you a base of support as you make the transition from student to practicing member of the profession.
To examine methods of delivering mathematics instruction to meet the needs of diverse elementary learners in a diverse world
To immerse you in the emerging field of mathematics education research and thought, thus enabling you to continue the lifelong learning and professional development that is crucial in a changing world.