Pelajar sekolah sering menghadapi masalah miskonsepsi dalam algebra di mana para guru gagal untuk mengenalpasti atau memahami (Smith, diSessa, & Roschelle, 1994).  Miskonsepsi telah didefinisikan sebagai kejadian apabila pelajar menyalahgunakan strategi yang telah dipelajari untuk menyelesaikan masalah baru (Russell, O’Dwyer, & Miranda, 2009). Jawapan yang salah ini bukanlah sesuatu yang boleh di pandang ringan kerana ini adalah masalah yang melibatkan peraturan dan ianya merupakan pengalaman yang akan dibawa oleh pelajar (Russell et al., 2009). Pendedahan miskonsepsi sangat penting kerana pelajar ini akan mengalami kesukaran sepanjang proses pembelajaran di sekolah mahupun di peringkat yang lebih tinggi.

Perspectives

Algebra selalunya dianggap sebagai konsep abstrak dengan pelbagai kebolehan definisi. Sesetengah pengkaji algebara telah membahagikannya kepada tiga bahagian iaitu 1) Model, 2) Fungsi dan 3) Algebra Umum (Kaput, 2008).  Model termasuk penyelesaian masalah ing knowledge includes solving open number sentences, understanding equivalence, and using variables.  Functions in the elementary grades include possessing the ability to recognize, describe, extend, and create linear and nonlinear patterns. Generalized arithmetic includes simplifying (i.e., simplify calculations using number relations and compensation strategies) and generalizing (i.e., utilizing mathematical properties like the commutative property, property of zero, etc.) (Wagner & Kieran, 1989).   

Data Sources and Methods

In this qualitative multiple case study, I analyzed the experiences of three in-service teachers and their students.  The teachers teach first, second, and fifth grade, respectively, at two high-poverty, low-achieving schools in a large urban school district in the Pacific Northwest. The student participants included 17 first grade students, 15 second grade students, and 20 fifth grade students, for a total of 52 students.   

To confirm findings and ensure data quality, data collection was triangulated through three different methods: multiple teacher interviews with each teacher participant, student interviews with each student participant, and classroom observations with each classroom (Miles & Huberman, 1994).  Teachers were asked about and students were asked to solve items in all three areas of algebra: modeling (i.e., equivalence problems such as 8+4=__+5), generalized arithmetic (i.e., simplification problems such as 15+7-6=__), and functions (i.e., linear patterns such as 3, 5, 7, 9, 11, __).  Data collection efforts began in January of 2011; data was collected over a period of four months. 

Results and Conclusions

The findings revealed that the students held a number of algebraic misconceptions that occurred throughout the three strands of algebra: modeling, generalized arithmetic, and functions.  In the area of modeling, for example, students across the three grade levels were able to solve open-number sentences such as 8+__=15 fairly easily, with rates of success for first, second, and fifth grade students of 65%, 87%, and 100%, respectively.  When this task was made conceptually more difficult, however, by introducing an equivalence task such as 6+7=__+4, these rates of success for first, second, and fifth grade students decreased to 6%, 13%, and 60%, respectively.  Misconceptions occurring here included adding the first two numbers, adding all three numbers, or ignoring the first number.  When asked to make this concept still more complex by introducing variables into the problem such as 6+B=9, the rates of success for first, second, and fifth grade student remained low at 29%, 47%, and 80%, respectively.  The primary misconception occurring with this problem

involved visualizing B numerically (i.e., A=1 so B=2).  This type of analysis continued for the other two areas of algebra (i.e., functions and generalized arithmetic). 

Importance

The importance of this work lies in the concept that students who hold misconceptions surrounding algebraic reasoning in elementary school may continue to struggle with algebra in the later grades (National Mathematics Advisory Panel, 2008).  Carpenter and colleagues described this problem as: “If not addressed, misconceptions about equality and variables persist and provide serious impediments for learning high school algebra and other advanced mathematics” (p. 96).  This research supports Carpenter and colleagues’ (2005) work indicating that elementary students may be experiencing misconceptions in algebra that may need attention.  Further, this research supports the idea that teachers may need professional development in the area to improve student algebraic thinking skills.  Several researchers (Jacobs, Franke, Carpenter, Levi, & Battery, 2007; Carpenter, et al., 2005) have seen improvement of student algebraic reasoning skills through conducting professional development with teachers.  Despite several limitations, these analyses strive to gather an initial description of student misconceptions in algebra. 

This session will review the literature, discuss the misconceptions, and engage the audience in a discussion regarding potential solutions to remedy algebra misconceptions.  This session will address diagnostic assessment tools (i.e., to discover misconceptions) and professional learning (i.e., to inform teachers how to remedy such misconceptions).

Lead Speaker:Nicole C. Ralston

Description of Presentation:

Students often have misconceptions in algebra that their teachers fail to recognize or understand. Discovering misconceptions is crucial: any not remedied may persist throughout school. The speaker will describe a qualitative, multiple-case-study design used to reveal the algebra misconceptions of first-, second-, and fifth-grade students.

Session Type: Poster Session