Abstract
Through a series of drawings, narratives, and focus groups interviews, this study examined prospective teachers' perceptions of teaching and learning mathematics at the elementary level. They were asked to illustrate mathematics teaching situations of their past, present, and idealized future classrooms. A theoretical framework guided data collection and analysis, which characterized three unique experiences: past reflection of mathematical experiences as a student (Remembering), current experience as a prospective teacher (Apprenticing), and the future image of the student in the role of the practicing teacher (Actualizing). Analysis of the drawings applied a method developed by Haney, Russell, Cengiz, and Fierros (Schools Middle: Theory Pract 6(5):38–43, 1998), which included creating a coding scheme, then, applying Kappa estimates to measure for inter-rater reliability. These drawings and additional focus group interviews revealed that the prospective teachers’ perceptions of old, new, and idealized mathematical teaching experiences demonstrated an evolving awareness of pedagogy and curricula that constitute effective mathematics instruction.
An earlier version of this chapter titled Prospective Teachers’ Perception of Teaching and Learning Mathematics Through Images and Drawings was presented at the 2005 annual meeting of the American Chapter of the International Group for the Psychology of Mathematics Education, Roanoke, Virginia and was published in the conference proceedings.
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Appendix A: Code Definitions for Teacher Drawing Project
Appendix A: Code Definitions for Teacher Drawing Project
Teacher: | |
Not depicted: | No teacher depicted |
1+ depiction of same teacher: | Same teacher shown more than once |
1+ teachers: | More than one teacher shown |
At blackboard/in front of room: | Teacher is either at the front of the room or at the blackboard |
In center of class: | Teacher shown at the center of the class |
Instructing class/talking/asking: | Teacher is clearly instructing the whole class, talking to the class, or asking questions of the class |
Instructing group/talking/asking: | Teacher is clearly instructing a smaller group of students, can include talking or asking questions |
Sitting in chair/instructing: | Teacher is instructing students, while sitting in a chair |
Walking toward students/moving: | Teacher is moving toward students or moving around students in class |
Teacher affect: | Check only if teacher is depicted in drawing or write-up |
None discernable: | Cannot make out the teacher’s expression |
Neutral/bored | |
Positive feelings | |
Negative feelings: | Sad, scared |
Students: | |
Not depicted: | No students depicted |
At blackboard: | Student(s) is/are standing at blackboard |
At centers: | Students are shown working at centers |
At rug: | Students are working or receiving instruction at a rug |
Instructing class/group: | Students are clearly teaching something to the class or a small group |
Raising hands: | Students are shown with their hands raised |
Sitting in chairs: | Students are shown sitting in chairs without desks/tables |
Sitting at desks/tables: | Students are sitting at desks or tables |
Talking to students: | Students are talking to each other |
Talking to teacher/responding: | Students are talking to the teacher or answering a question posed by the teacher |
Students moving: | Students are moving about the classroom |
Student affect: | Check only if students are depicted in drawing or write-up |
None discernable: | Cannot make out the students’ expressions |
Neutral/bored | |
Positive feelings | |
Negative feelings: | Sad, scared |
Desks: | As seen in drawing or indicated in write-up |
None drawn | |
In groups: | Desks are in clusters – not in rows or lines. Difference between groups of desks and tables is that lines are drawn signifying individual desks |
In pairs: | Desks in pairs |
In rows: | Desks form a line of sorts – could be a “u” shape – so that students may be seated next to each other but are not facing each other |
Tables: | Students are using tables for desks – not to be confused with additional worktables or tables in centers |
Furnishings: | As seen in the drawing or indicated in the write-up |
None depicted | |
Minimal: | Usually desks or tables and perhaps a blackboard or wall fixtures |
Animals | |
Book corner/library: | A place with books for students to go to and read |
Centers: | Subject-specific learning areas separate from the desks and tables. If there is a computer center, check this also |
Clock/timer: | Some apparatus visible that is keeping track of time |
Computer | |
Easel | |
Manipulative cart/shelves: | Place specifically designated for storage of math manipulatives |
Maps | |
Meeting rug or area: | Place for students to sit together for instruction or discussion |
Musical instrument | |
Overhead projector | |
Plants | |
Record player/CD/tape player, television | |
Work table(s) | Tables not designated as centers or desks but as places where small groups can receive instruction |
Math content: | Select as many as overtly indicated in drawing or write-up. Do not select content areas related to those obviously indicated |
None observed | |
Addition, subtraction | |
Classification/sorting | |
Counting, decimals, division | |
Fractions, geometry, graphing | |
Money, multiplication, patterning | |
Place value/number sense | |
Unclear math concept | |
Tasks/activities: | Select any that are shown in the drawing or indicated in the write-up |
None observed | |
Activity: active | Students engaging in active pursuits beyond writing, listening, reading, answering teacher’s questions |
Art/music | |
Competitive: | Activity in which there are winners and losers – often in the form of a contest or game – may include vying for teacher’s attention |
Cooperative: | Activity in which two or more people work together to achieve a common goal; students working collaboratively together. Note: a single drawing may be coded as both containing competitive and cooperative task elements as in team competitions |
Interdisciplinary: | Any lesson/activity that teaches a mathematical principal through another discipline (e.g., science) |
Manipulatives: | Used in the activity for the purpose of teaching math |
Paper/pencil: | A paper-and-pencil activity |
2+ activities: | More than one activity is going on at once |
Individual/seat work: | Individuals working alone on their own work |
Group/partner work: | Students are working in groups or in pairs |
Whole class activity: | The whole class is working on the same activity/lesson. Teacher is leading the class. |
Level of representation: | Check all indicated in drawing or write-up |
None discernable | |
Abstract: | Mathematical concept presented symbolically, orally, can include mental math |
Concrete: | Mathematical concept presented with objects |
Pictorial: | Mathematical concept presented with pictures, diagrams, and graphs |
2+ levels: | More than one level of representation is depicted in the lesson |
Manipulatives: | Check any that are depicted in the drawing or write-up |
None discernable | |
Base-ten-blocks | |
Blocks (generic), shape blocks (attribute, tangrams, pattern blocks) | |
Calculators | |
Clay | |
Counters/household objects | |
Cubes (unifix, multilink, other connecting cubes) | |
Flashcards | |
Food/candy | |
Games/bingo | |
Money/coins | |
Paper manipulatives: | Looks like manipulatives but made of paper (e.g. pattern blocks made of paper) |
Science objects | |
Workbooks/worksheets | |
Other | |
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Albert, L.R. (2012). Images and Drawings: A Study of Prospective Teachers’ Perceptions of Teaching and Learning Mathematics. In: Rhetorical Ways of Thinking. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4065-5_3
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