Technology Reading #5 – McCoy Research Summary

McCoy, L., P., (1996). Computer-based mathematics learning. Journal of Research on Computing in Education, 28(4), 438-460. CARET summary.

Abstract:  The research on computer-based mathematics learning was examined in the context of constructivist learning and the National Council of Teachers of Mathematics Standards.  The reviewed studies examined the effectiveness of computer software in three key categories of programming, computer-assisted instruction, and tools.  Recommendations emphasized the need for further study of instructional design that best utilizes computers and use of the Internet in mathematics.

RQs

1. How can technology influence student academic performance?
2. How can technology develop higher order thinking and problem solving?
3. How can technology be infused into curriculum and instruction effectively?

Notes:

This article is basically a culmination in research on computer-based mathematics learning beginning around 1988 and through the mid 1990’s.  It focused on three areas: programming, computer-assisted instruction, and tools all with a basis rooted in constructivst learning, as advocated by the NCTM.  The author refers to the progamming environment as a mathematical laboratory where students can manipulate mathematical ideas as they create their own concepts.  In this environment, logic is established and students may practice and develop their reasoning skills.  In the computer-assisted instruction environment (CAI) computers are used in assistive modes such as drill and practice, tutorials, or simulations.  Simulations model the real world in some manner and include microworlds, which create a model environment for students to actively experience mathematics (in line with constructivist theory).  Tools refers to software that assists the user in performing some mathematical function.  The culmination of all this research indicates that computer-based materials are effective in facilitating mathematics achievement.  This is particularly true in Logo programming (note: Scratch’s grandfather), CAI microworlds, and algebra and geometry tool software.  However, the author notes that instructional materials and methods must be evaluated in terms of their usefluness and overall goals.  The author also stresses that useful research needs to occur in the area of instructional design, as a key recurring conclusion of the studies indicate the importance of teacher, designer, and researcher input in structuring computer-based activities such that the students can understand procedural and conceptual knowledge properly.  (Technology counselor?????)  Specific research findings in the 3 areas of computer-based mathematics learning are discussed in a bit more detail below.

In the “programming” mode, students work with reasoning to “teach” the computer.  In doing so, they are creating mathematics and the computer is providing immediate feedback to assist them in exploring and refining their knowledge.  Much of this research has had to do with LOGO, but there is some use of BASIC as well.  The research focuses on the effect of programming on students’ cognitive abilities, though it is generally difficult to measure problem-solving skills.  As for assessment, most of the studies used interviews on concepts and/or a post-test.  Overall, the studies showed that:

• LOGO had better results than BASIC and is most effective in learning geometry, but can also be effective in learning variables.  It is believed that the very visual nature has much to do with this.
• Research shows that specifically, learning infused with LOGO had some positive success in the topics of distance, figural creativity, angles/shapes/motion, angles/polygons, fractions, problem solving, and variables. 
• Shorter treatments had significantly higher achievement than longer treatments.
• Programming experiences provide a “mildly effective approach for teaching students cognitive skills in a classroom setting.”
• LOGO programming, especially turtle geometry at the elementary level, is an effective medium for providing mathematics experiences.
• Teacher needs to be involved in planning and overseeing the LOGO experience to ensure that students discover and understand the target concepts.  Otherwise, unintended results can occur rather easily.  As one study by Olive found, “…Students had to do well on LOGO tasks in order to do well on the geometry measure, but that some students were successful on the LOGO, but not on the geometry.”  Clements and Batista also found that while the LOGO group improved more in student achievement than control group, both groups still had misconceptions about angles and figures, though the LOGO group had more experience and were able to construct and communicate the concepts. 

CAI use of computers is a more structured use, but potentially powerful none-the-less.  In general, research showed that CAI is effective because it allows students to experiement through active manipulation within a structure of a mathematical model (microworlds, tutorials) and serves as supplements (drill) with immediate feedback and direction.  The research focuses on students’ learning of mathematical concepts, as emphasized by the NCTM standards and most assessment was done by interviews and posttests.  The author really focused on microworlds, citing their ability to to be used for exploration in a constructivist mode, yet containing a definition of certain mathematical tools, or in other words, built in varying levels of scaffolding.  Many micorworlds were often created in LOGO.  (This may not be as true now…)  However, they were all different in how they are created and used, which made it difficult to make generalizations and emphazised the need to evaluate materials in their usefulness and overall goals.  For instance, Blocks was created by Thompson and used to help students understand the relationship between blocks and numerals (symbolic/iconic).  His research indicated that it did not help students learn the relationship and that they could not unlearn their incorrect algorithms from whole numbers.  On the other hand, Dots and Rules (Zehavi) was deemed to be effective in helping students in understaning graphing.    Four studies found specific microworlds to be effective in helping students learn mathematical concepts.  Those studies included the use of Motions, which focused on geometry and was evaluated using interviews and a delayed posttest.  Other microworlds include one by Thompson and Wang for working with coordinate Cartesian graphing, one by Edwards, working with tranformational geometry, and Dots and Rules.  Five major features of a microworld were identified: changes in problem situations, immediate feedback, motivation, flexibility and dynamic connections between symbols and graphics, and integration of spatial and graphic representations.  This appears to be a common theme in much research regarding technology based learning.  One negative from the microworlds is that a visual solution can be acheived without conceptual understanding.  Thus, explicit connections must be established in order to link procedural knowledge and conceptual understanding (prinicple #2).   Teachers must facilitate guided discovery, a theme that consistently appears in the 3 categories of research here as well as outside these studies.

Research of other types of CAI (drills, tutorials) shows that, potentially,  problem solving skills can be improved through the use of software, but again different software had differing results.  It warrants the mention that further examination has to be done on the differential effects of mathematics software on different students.  One study found that CAI increased the gap between low and high achieving students.  So does software need to be better geared towards specific learners? It also warrants mention that groups and pairs had higher achievement in CAI than individual students.  This aligns with the constructivist learning theme.

Mathematics tools are advocated highly by NCTM for accomplishing routine calculations so that students can focus on conceptual understanding.    They are also useful in the constructivist mode for providing models of different parallel representations to help students build on conceptual connections.  The mathematical functions performed most effectively by computer tools are algebra (graphing, symbol manipulation) and geometry (construction, visualization of figures).  Most math educators would agree that a graphing utility is an absolute necessity in algebra or calculus.  Graphing software is also important because it facilitates work with real-world problems (ex: statistics).  Some common software applications that are used are: Maple, Derive, Mathematica, Theorist, MathCad (in algebra they promote experimentation and concept building by allowing a linked representation of algebraic, tabular, and graphic models so that any change is reflected in all representations), Geometric Supposer, Geometer’s Sketchpad, Cabri:The Interactive Geometry Notebook (in geometry they provide a variety of geometric constructions and measures).   Overall research showed that results varied among the use of the previously named software applications, with a general increase in conceptual skills, but no difference in most overall math skills.  This has also been a common theme in research – increase in problem-solving and concepts, but no difference in the computational and manipulation skills to get the right answer!