The purpose of this study was to determine the degree to which the interpretation and use of test scores from a school district's mathematics test may be meaningful and valid for making instructional decisions, for measuring growth, and for making accountability decisions. The data used for the study came from six levels of a standardized mathematics test that grouped items into six specific categories to match the district's curriculum. The district's mathematics curriculum referred to the six item categories as "strands." The six strands were Number Sense, Data Analysis, Algebra, Geometry, Measurement, and Structure/Logic. The test items were grouped in each test booklet by item categories (strands) and thus formed six strand subtests. Factor analysis was used to examine the structure of each of the six test levels. Findings from the factor analysis indicated that there was more than one dimension (underlying construct) at each test level. Factor loadings were found to group by strand and not by item difficulty. Analysis of variance and correlation procedures were used to gather evidence that was confirmatory in nature to help verify the findings from the factor analysis. An analysis of variance found a significant difference between some of the strands in pairwise comparisons, which supported the findings from the factor analysis indicating that more than one construct (dimension) was being measured. Strand intercorrelation coefficients that were corrected for attenuation showed strong relationships among strands, which supported test unidimensionality. It was concluded that there was evidence to support an overall dimension called mathematics, but that there was also evidence to support other dimensions which reflected the six mathematics strands.

<p>Science, Technology, Engineering, and Mathematics (STEM) education curriculum is designed to strengthen students&rsquo; science and math achievement through project based learning activities. As part of a STEM initiative, SeaPerch was developed at Massachusetts Institute of Technology. SeaPerch is an innovative underwater robotics program that instructs students in how to build an underwater Remotely Operated Vehicle (ROV) following a STEM curriculum, including spatial thinking and rotation ability. This research study investigated if the students&rsquo; SeaPerch program and its spatial experience and training gave the opportunity to develop strategies not only in manipulating three dimensional objects but in strengthening mathematical ability (e.g. spatial thinking) in elementary, middle, and high school students with specific focus on gender and age. </p><p> This research study sample consisted of two groups of students: one that participated in the after-school SeaPerch program and the other that did not participate in the after-school SeaPerch program for the 2011&ndash;2012 school year. Both groups comprised students in similar grade levels and the MRT preassessment scores. </p><p> To measure students&rsquo; spatial rotation, the researcher used the Vandenberg and Kuse Mental Rotation Test (MRT). An independent samples t test was conducted to determine the effect of the SeaPerch program on MRT scores. The SeaPerch students (<i>M</i> = 1.35, <i>SD</i> = 2.21) scored significantly higher gains than the Non-SeaPerch students (<i> M</i> = &minus;.03, <i>SD</i> = 1.72), t (737) = 8.27, p = &lt;.001. The effect size as measured by Cohen&rsquo;s <i>d</i> = .697, indicated a medium practical significance. At each school level, MRT post assessment scores for students in the SeaPerch program increased significantly more than scores for students in the non-SeaPerch program. </p>

Matrices are important mathematical tools that facilitate the process of organizing and manipulating data. In this work, the matrix operations of addition, subtraction, scalar multiplication, and matrix multiplication are built logically from the intuition of the students and their knowledge of real numbers. From this knowledge, the concepts of inverses, determinants, and consistency and inconsistency of linear systems of equations are formed. Interesting applications of matrices in the areas of Markov chains, curve fitting, and eigenpairs are included and are not beyond the comprehension of pre-calculus students when they are presented carefully. Pre-calculus students can also appreciate many of the numerical challenges that can be encountered when real-world problems are solved; therefore, we include a discussion of some of these topics.

<p> This dissertation responds to critical gaps in current research on formative assessment practice which could limit successful implementation of this practice within the K-12 classroom context. The study applies a socio cultural perspective of learning to interpret a cross-case analysis of formative assessment practice occurring during one mathematics instructional unit in a 5^th and one in a 6^th grade classroom. It illustrates how a fully defined theoretical foundation deepens understanding of the roles of formative assessment in learning, posits a working definition by which the describe what formative assessment practice looks like and sounds like as it is occurring in actual classrooms, and explains how the classroom social context influences formative assessment practice. The study has implications for future researchers investigating formative assessment practice; practitioners interested in implementing formative assessment practice; and policy makers evaluating the effectiveness of teachers' instructional practice.</p>

<p> This study explores adult returning students' mathematical experience and ways of thinking prior to enrolling in a community college arithmetic review course. It further examines one student's experience of the course. The first part of the study documents everyday activities adult students perceive as mathematical using Bishop's pan-cultural mathematical activities (Bishop, 1994), and queries students' prior experience with mathematics in school. The second part examines students' ways of thinking about proportion prior to instruction, using a framework developed from previous research (e.g., Lamon, 1993). The third part of the study examines the interaction between informal ways of thinking about mathematics that adult students bring to school and the mathematics they encounter in the classroom. Findings include: (1) Adult students view a variety of activities from their everyday lives as mathematical, (2) adult students' reasoning about proportional situations varies along a developmental trajectory described in previous research on proportional reasoning conducted with younger students, and (3) one student's experience in the arithmetic review course illustrates that she typically suppressed contextual ways of reasoning about problems she brought to the course and, when she did share prior experience, it was not leveraged to support the development of her and other students' mathematical understanding. These findings suggest that adult students' experience of everyday mathematics and ways of thinking about proportion should be the foundation that support students as they build upon informal ways of thinking toward the more formal ways of reasoning expected in school. </p>

<p> This study compared the effects of the Detect, Practice, and Repair (DPR) intervention package versus traditional Cover, Copy, and Compare (CCC) procedures in increasing multiplication math fact accuracy and fluency using an alternating treatments design with a modified control condition. Interventions were administered one-on-one across 4 fourth grade students. Three mutually exclusive multiplication sets were used with one set being assigned to each condition. Effectiveness was assessed through traditional curriculum-based measurement (CBM) procedures and through flashcard card procedures to measure accuracy. In addition, the efficiency of each intervention (i.e., amount of learning per instructional minute) was calculated. Maintenance data were collected to determine if newly learned math facts would be better maintained when taught with the DPR intervention or with the traditional CCC intervention procedures. Social validity data were collected with teachers and students to determine whether one intervention was preferred over another. Although DPR has been examined in five published research studies, it has never been examined through a one-on-one implementation or in a study directly comparing its effectiveness, efficiency, maintenance, and social validity against another intervention. In addition, this study serves as a component analysis since CCC is one component of the DPR package. </p>

<p> The purpose of this study was to examine the differences in the achievement rates of developmental mathematics students when a student success course was taken in combination with mathematics. The study investigated changes that occurred in the developmental mathematics completion rates of the learners by examining age and the course sequence of mathematics in conjunction with a student success course at a large community college in central Florida. Age was of interest as it related to the time lapsed from high school graduation and potential for mathematics atrophy. Course sequence was valued to determine if taking a student success course during or within one year of developmental mathematics could enhance mathematics course completion. These attributes were further divided and assessed according to the two specific developmental mathematics courses. Level 1 consisted of learners in deep remediation needing the most basic developmental mathematics course. Level 2 was composed of people who placed into the developmental mathematics course just below that of 100-level coursework. </p><p> The results of the study from multiple analyses of association revealed that developmental mathematics course completion was significantly correlated to student success courses. Students who took a student success course as a corequisite to their developmental mathematics course completed their mathematics course more often than those who took mathematics alone. Additionally, students in the higher level developmental mathematics course also performed significantly better when a student success course was taken before but within one year of their developmental mathematics course. </p><p> In the age groups of participants in the study, students who had been out of high school longer did not experience any observable mathematics atrophy when taking mathematics without a student life skills course. As compared to younger students (20 years of age or younger), older students had a significantly higher course completion rate. Moreover, all age groups in the study were shown to have benefitted significantly from the inclusion of a student success course. Younger learners in the lowest level developmental mathematics course, however, benefitted most. This study provides implications for practices and policies that enhance developmental mathematics course completion and facilitate academic momentum to degree completion in community colleges. It also provides insights to enhance developmental mathematics curriculum success from an approach peripheral to the discipline.</p>

<p> The parallel research traditions of explicit-objective and tacit-emergent vary greatly in how they define, assess, and enable development of teacher mathematical knowledge. Despite these diversities, widespread agreement exists in mathematics education research that a teacher's mathematical knowledge is a key competency of an effective teacher. This research report investigates the nature and development of teacher mathematical knowledge of fraction multiplication defined from a tacit-emergent perspective. Questions about the nature and development of teacher mathematical knowledge for fraction multiplication were investigated in this report at the individual and collective levels. In addition, this research report also investigated the developmental links between these levels. The concept study design and the framework for teacher knowledge used in this report derived from the work of Davis and colleagues (Davis &amp; Simmt, 2006; Davis &amp; Renert, 2014). </p><p> The results from this report were multifaceted for both the individual and collective levels of mathematical knowledge. Teachers' individual mathematics-for-teaching (M4T) knowledge of fraction multiplication developed throughout their participation in the mathematical environments of the concept study. Furthermore, two types of collective action emerged as proposed links between the collective and individual development of teachers' M4T knowledge of fraction multiplication. These proposed links, titled <i>synergistic realizations</i> and <i> recursive elaborations</i> emerged in this report as patterns of mathematical action existent in moments of coaction. Recursive elaboration defines the decision-making mechanism where the collective expands the realm of what is possible for a single mathematical realization. Synergistic realization defines the collective decision action in which all previous realizations are abandoned for one innovation in the mathematical realization of a mathematical concept. A discussion of the implications for defining teachers' mathematical knowledge of fraction multiplication as nested systems of individual and collective knowledge is included in the conclusion of this report.</p>

<p> In the USA, the No Child Left Behind Act of 2001 resulted in requirements placed on school districts to show student achievement in mathematics, based on measured adequate yearly progress. This caused school districts to search for standards-based programs that improve mathematics learning. A quantitative multi-year study was used to compare the state-assessed achievement levels of 1,695 fifth-grade Midwestern children in the state of Missouri, who learned mathematics from two different curriculum-delivery programs, <i>EveryDay </i> Mathematics and <i>EnVision</i> Mathematics. A 2 by 2 by 8 research design was used through the choice of two elementary schools using <i>EveryDay</i> Mathematics and two different elementary schools using <i>EnVision</i> Mathematics, across an eight-year timeline. The dependent variable was represented by the students' scores on the mathematics portion of the standardized required state test, the Missouri Assessment Program. Student scores from 2006-2013 were collected for the four public schools in the St. Louis Metropolitan area. The schools chosen were matched to control for socio-economic level, ethnicity mix, departmentalization of content areas, extent of teacher experience, and class sizes. The four schools represented two school districts. Each district uniformly used one of the mathematics programs examined in this study, over the eight years. Results of this study could not show that either mathematics program was significantly better, as measured by student test scores on mathematics topics. Unfortunately, results also showed no overall increase in mathematics learning at these four schools over the eight year period. The study concluded that curriculum materials choice, alone, is not sufficient to insure increased fifth-grade student learning of mathematics. Variables such as the extent of teacher professional development, teacher specialization, and curriculum launch practices at schools were discussed as possible influences on the results of the study. </p>

<p> The current dissertation examined the validity of a context-specific assessment tool, called Self-regulated learning (SRL) microanalysis, for measuring self-regulated learning (SRL) during mathematical problem solving. SRL microanalysis is a structured interview that entails assessing respondents' regulatory processes as they engage with a task of interest. </p><p> Participants for this dissertation consisted of 83 eighth grade students attending a large urban school district in Midwestern USA. Students were administered the SRL microanalytic interview while completing a set of mathematical word problems to provide a measure of their real-time thoughts and regulatory behaviors. The SRL microanalytic interview targeted the SRL processes of goal-setting, strategic planning, strategy use, metacognitive monitoring, attributions, and adaptive inferences. In addition, students completed two questionnaires measuring SRL strategy use, and one questionnaire measuring self-esteem. The participant's mathematics teacher completed a teacher rating scale of SRL for each participant. Mathematical skill was measured with three measures including a three item measure of mathematical problem solving skill completed during the SRL microanalytic interview, a fifteen item posttest of mathematical problem solving skill completed two weeks after the SRL microanalytic interview, and a standardized test of mathematics skill. </p><p> The primary objectives of this dissertation were to compare the newly developed SRL microanalytic interview to more traditional measures of SRL including two self-report questionnaires measuring adaptive and maladaptive SRL and a teacher rating scale of SRL. In addition, the current dissertation examined whether SRL microanalysis would diverge from a theoretically unrelated construct such as self-esteem. Finally, the primary interest of the current dissertation was to examine the relative predictive validity of SRL microanalysis and SRL questionnaires. The predictive validity was compared across three related but distinct mathematics outcomes including a short set of mathematical problem solving items, a more comprehensive posttest of MPS problem solving skill, and performance on a standardized mathematics test. </p><p> The results of this study revealed that SRL microanalysis did not relate to self-report questionnaires measuring adaptive or maladaptive SRL or teacher ratings of SRL. The SRL microanalytic interview diverged from the theoretically unrelated measure of self-esteem. Finally, after controlling for prior achievement and SRL questionnaires, the SRL microanalytic interview explained a significant amount of unique variation for all three mathematics outcomes. Furthermore, the SRL microanalytic protocol emerged as a superior predictor of all three mathematics outcomes compared to SRL questionnaires. </p>