Level I: Draft Interdisciplinary Mathematics/Science Investigation, "An Earful Investigation,"

Methods Instructor Activity Discussion/Instruction

Developers: Anna Graeber and Randy McGinnis, UMCP

"An Earful Investigation" Discussion Notes

I. Introduction

This lesson is an interdisciplinary (mathematics and science) investigation of ratio and infections of the body (middle ear) caused by bacteria and virus. It is a sample lesson for prospective mathematics and science specialist MCTP teachers. The lesson is designed for grades 6 - 8. It is developed using a constructivist model. Prospective upper elementary/ middle level teachers participate in the lesson by attempting portions of the lesson's tasks while discussing pedagogical aspects led by the instructor at punctuated points in the lesson and in a post-lesson debriefing. Through this deconstruction of the lesson, the various pedagogical moves can be highlighted and analyzed.

II. Overview

This activity consists of two tiers. Tier I engages learners in problem setting scenarios that need to be solved. To do so, they work in cooperative learning teams while applying mathematical and scientific skills. The two core activities, "An Earful of Microbes" and "An island of Microbes" are included in this tier. Tier II engages students in a progression of the story line developed in tier I core activities. It continues examining ratio but introduces the biological concept of bacterial resistance to antibiotics. In both tiers, the prior content knowledge of the students is elicited in small groups, discussed in large group discussions, and confronted in hands-on activities. In this way, the instructor role models an exemplary middle school teaching strategy before discussing with the method students the pedagogical moves used in the lesson.

III. Instructor Actions and Pedagogical Discussion Points

Conceptual Change Phases: Elicitation/elaboration/confrontation

Equipment: Problem setting scenario slips for each team; clinic log's for each team

Instructor Actions:

Place method students in small group learning teams. This can be done in various ways (count off, letters, etc). Give students problem setting scenario part 1. Record student comments to scenario questions on transparency or poster paper. Save these notes for later review.

Pedagogical Discussion Point:

Catalyst questions:

(a) What pedagogical move(s) did you see in the preceding instruction sequence?

(b) Why was it selected to be done by the teacher?

Discuss:

* the use of cooperative learning groups

* the value of using a problem setting scenario

* the importance of eliciting from students their prior knowledge

* the differing options to gain insight into students' knowledge bases,

* how awareness of students' prior knowledge can inform the teacher's decision-making

* the role of naive conceptions in teaching and learning

Conceptual Change Phase: Conceptual Structuring or Restructuring

Equipment: Materials required for the potential activities.

Instructor Action:

Share the collection of anticipated potential activities and materials located in the class learning center which address the content areas of the structure of the ear and ratio. Solicit from the method students other ways they can get information on the structure of the ear, ear infections, and ratio. If agreed upon as a general need, the entire class can watch a video on the structure of the ear before proceeding to the core activities.

Pedagogical Discussion Point:

Catalyst questions:

(a) What pedagogical move(s) did you see in the preceding instruction sequence?

(b) Why was it selected to be done by the teacher?

Discuss:

* the concept of student empowerment to select information sources to meet their individual needs.

* the role of the teacher as a collector of potential student hands-on activities.

* the role of the teacher as decision-maker

Conceptual Change Phases: Elicitation/Elaboration/Application

Equipment: Copies of the core activities, "An Earful of Microbes" and "An Island of Microbes"

Instructor Actions:

A. Give methods students "An Earful of Microbes" activity. Lead a large group discussion on what teams decided they will ask the laboratory to collect for them. Encourage inter-group discussion of the merit of each team's plan and explanation. Underscore scientific problem-solving behavior such as collecting samples of microbes in infected ears to use for identification of invading agent. Allow method students the opportunity to look over the activity questions and attempt answers to a few. Lead large group discussion on activity and remediate as needed.

B. Give method students "An Island of Microbes" activity. Allow method students the opportunity to look over the activity questions and attempt answers to a few. Lead large group discussion on activity and remediate as needed.

Pedagogical Discussion Point:

Catalyst questions:

What pedagogical move(s) did you see in the preceding instruction sequence?

Why was it selected to be done by the teacher?

Discuss:

A.

* the use of this problem setting scenario

* the importance of eliciting from students their hypotheses

* and how they can be tested

* the value of students confronting each other's knowledge claims and agreeing upon a scientifically compatible method of either resolving these disagreements or confirming consensus shared beliefs.

* the use of a hands on activity

* the decision to model the identification of microbes by sending it to laboratory technicians

B.

* the purpose of having students classify the microbes by type and name.

the purpose for the mathematics information gained by determining ratio and by making circle graphs.

* the use of aggregating small group's data to make a large class data set

Conceptual Change Phase: Assessment

Instructor Actions:

Share alternative assessment ideas with method students. Allow students to attempt a task or two. Lead a large class discussion on developing and using a rubric for the assessments.

Pedagogical Discussion Point:

Catalyst questions:

What pedagogical move(s) did you see in the preceding instruction sequence?

Why was it selected to be done by the teacher?

Discuss:

*the coordination of instruction and assessment

* the reasons for the use of alternative assessments

Conceptual Change Phase: Reflection

Instructor actions:

This lesson moved the method students through the steps of a constructivist model that integrates mathematics and science in an engaging manner for upper elementary/middle level students. Reflections were elicited in the pedagogical discussion points throughout the lesson. Now is the time to look back over the entire lesson and lead a large class discussion that focuses on personal conceptual changes and a deconstruction of the lesson. Share the notes collected throughout the lesson of the method students' statements. Discuss with them sources of erroneous beliefs. Was there an apparent logic to the erroneous beliefs: an over generalization from other situations, a belief caused by everyday language?

Pedagogical Discussion Point:

Catalyst questions:

What pedagogical move(s) did you see in the preceding instruction sequence?

Why was it selected to be done by the teacher?

Discuss:

: * the purpose of student reflections throughout the lesson and at the end

* the conceptual change model used in this lesson:

Eliciting/elaboration

Confronting

Structuring/restructuring conceptual growth

Application

Reflection

Assessment

* The integration of mathematics and science (including identifying the mathematics and science elements of the investigation)

* Multicultural considerations

* Alternative assessment