#### Date of Award

2006

#### Level of Access

Campus-Only Thesis

#### Degree Name

Master of Science (MS)

#### Department

Teaching

#### Advisor

Eric A. Pandiscio

#### Second Committee Member

Robert Franzosa

#### Third Committee Member

Tod Shockey

#### Abstract

In August of 2005 changes to the Secondary Mathematics Teaching Certificate were implemented which eliminated the requirement for 35 credit hours of undergraduate mathematics in specific content areas such as geometry, calculus, statistics and probability. In its place is the requirement for 24 credit hours of mathematics content and successful completion of the PRAXIS II Mathematics Content Exam. These rule changes effected this investigation into the level of understanding geometry of pre-service elementary and secondary mathematics teachers, based on the van Hiele model, both before and after completion of the geometry course currently required by their education program of study. The van Hiele model, developed by two Dutch mathematics educators, has been used since the early 1980s to explain why students have difficulty with high school geometry in general, and specifically, higher order cognitive processes. The theory has three aspects, (1) there exists levels of understanding, (2) there are properties that are inherent to each level, and (3) movement to a level needs to be from the previous level. Specifically, there are five levels of understanding. There are five properties, or characteristics that are the same for all five levels. The fifth property, attainment, outlines the learning process that leads to complete understanding at the next higher level. This learning process has five phases. The National Council of Teachers of Mathematics (NCTM), in their publication Principles and Standards for School Mathematics (2000) outlines four areas in the Geometry Standard that lists what should be expected of the mathematics curricula for geometry context for grades PK – 12. The Principles and Standards for School Mathematics breaks down these general expectations for each grade level. This study shows that for students taking MAT107, the course required by the Elementary Education program at the University of Maine, there are a statistically significant findings that the mean van Hiele Level of Understanding Geometry of this sample, prior to and after completion of this course, is not at or above a Level 3, the level of understanding expected of students completing grade 8. This study shows that for students taking MAT475, Higher Geometry, the course required by the Secondary Mathematics Education program at the University of Maine, there are a statistically significant findings that the mean van Hiele Level of Understanding Geometry of this sample, prior to and after completion of this course, is not at or above a Level 4, the level of understanding expected of students completing grade 12. In addition, based on the sample data this study also determined that the van Hiele level of pre-service elementary and secondary mathematics teachers after completing their program required geometry course is statistically significantly lower than the level expected of students completing grade 8 and grade 12, respectively. Further investigation should be conducted to reinvestigate using an increased sample size. Other investigations that can be pursued include students enrolled in their program required geometry course at each of the University of Maine System campus’ that offer an elementary or secondary education program.

#### Recommended Citation

Knight, Kathleen Chesley, "An Investigation into the Change in the Van Hiele Levels of Understanding Geometry of Pre-service Elementary and Secondary Mathematics Teachers" (2006). *Electronic Theses and Dissertations*. 1361.

http://digitalcommons.library.umaine.edu/etd/1361