Microteaching Lesson Study: Mentor interaction structure and its relation to elementary preservice mathematics teacher knowledge development

This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a southern urban university were part of the study. This included 72 participants who completed MLS across three different mentor interaction structures as part of their course requirements and 31 elementary preservice teachers who did not complete MLS as part of their methods course and served as a comparison group for a portion of the study. A sequential mixed-methods research design was used to analyze the relationship between MLS mentor interaction structure and growth in preservice teachers' mathematics teacher knowledge. Data sources included pre and post assessments, group developed lesson plans and final reports, a feedback survey with Likert-type and open-ended questions, and transcripts of audio-recorded debriefing sessions. The pre and post assessments were analyzed using Analysis of Variance (ANOVA) and descriptive statistics were used to analyze the Likert-type feedback survey questions. Group MLS lesson plans, final reports, and transcripts of debriefing sessions along with the open-ended questions from the feedback survey were coded in a three-step process as described by Miles and Huberman (1994). In alignment with findings from M. Fernandez (2005, 2010), elementary preservice teachers participating in MLS grew in content knowledge related to MLS topics taught by one another. Results from the analysis of pre and post content knowledge assessments revealed that participants grew in their understanding of the mathematics topics taught during MLS irrespective of their mentor interaction structure and when compared to the participants who did not complete MLS in their methods course. Findings from the analysis of lesson plans for growth in pedagogical content knowledge revealed the most growth in this area occurred for participants assigned to the interaction structure in which the MLS mentor participated in the first two debriefing sessions. Analysis of the transcripts of the discourse during the debriefing sessions and the feedback surveys support the finding that the elementary preservice teachers assigned to the interaction structure in which the MLS mentor participated in the first and second debriefing sessions benefited more from the MLS experience when compared to elementary preservice teachers assigned to the other two interaction structures (MLS mentor participated in only the first debriefing session and MLS mentor participated in only the last debriefing session).

Motivational Strategies to Increase Completion of Assignments in Mathematics Classes

The purpose of this paper is to share the results of an 8-week study that focused on the effects of incorporating real-life applications and rewards to measure their impact on student motivation. The goal was to reduce the number of students unmotivated to complete their mathematics assignments satisfactorily.

Analyzing Elementary Preservice Teachers’ Development of Content and Pedagogical Content Knowledge in Mathematics through Microteaching Lesson Study

This study examines the effect of Microteaching Lesson Study participation on the mathematics content and pedagogical content knowledge of 52 elementary preservice teachers. Preliminary findings, which are positive, are discussed.

Improving Student Mathematics Achievement through Self Regulation and Goal Setting

As middle school students’ mathematic scores decline in comparison to other countries, researchers have found self-regulation to be a tool to improve students’ mathematics achievement. The following is an action research project conducted in a middle school where result showed an increase in students’ mathematics achievement.

Mathematics: Going Beyond the Academic Discipline

Mathematics is rigidly classified as an academic discipline. This determines curriculum content and teaching and evaluation methods. These methods can give rise to negative views of mathematics, resulting in increased math anxiety. Educators, therefore, need to look beyond the discipline to provide a classroom environment that meets students’ needs.

Self-Identified Capabilities and Experiences with Mathematics of Adults Who Have Taken a Developmental Algebra Course

Some were born to do math, some persevered past fearful environments, while others withdrew. In this qualitative study, adults describe life with algebra and the meaning they sought. For all, pedagogy was critical, either positively or negatively; and all found salvation in intervention.

An Investigation of Participants’ Perspectives About a Learning Assistant Program and Their Thinking about Becoming a Mathematics Teacher

A Learning Assistant program that recruits strong STEM undergraduates to become mathematics teachers was explored through a qualitative study. Three program participants were purposely selected and interviewed. The program reaffirmed one participant’s choice to become a teacher and clarified for one that it might be a career for him.

Effects of Cooperative and Individual Integrated Learning System on Attitudes and Achievement in Mathematics

The purpose of this study was to determine the effects of a computer-based Integrated Learning Systems (ILS) model used with adult high school students engaging mathematics activities. This study examined achievement, attitudinal and behavior differences between students completing ILS activities in a traditional, individualized format compared to cooperative learning groups.

The Predictive Power of Homework Assignments on Student Achievement in Mathematics

This study examined the relationship between homework performance (percent of homework completed and percent of homework correct), student characteristics (Stanford Achievement Test score, gender, ethnicity, and socio-economic status), perceptions, and challenges and academic achievement determined by the students’ average score on weekly tests and their score on the Florida Comprehensive Assessment Test (FCAT) Norm Reference Test (NRT) mathematics assessment.

Development of a Game-Based Mathematics Curriculum for Preschool

America’s deficiency in mathematics can be benefitted by an emphasis in mathematics from an early age. An effective math curriculum for preschool should consist of the most important aspects of early childhood mathematics, including number writing and identification, one-to-one correspondence, cardinality, number comparison, ordinality, number sequence, and number bonds.

The role of *language in early childhood mathematics

Math literacy is imperative to succeed in society. Experience is key for acquiring math literacy. A preschooler's world is full of mathematical experiences. Children are continually counting, sorting and comparing as they play. As children are engaged in these activities they are using language as a tool to express their mathematical thinking. If teachers are aware of these teachable moments and help children bridge their daily experiences to mathematical concepts, math literacy may be enhanced. This study described the interactions between teachers and preschoolers, determining the extent to which teachers scaffold children's everyday language into expressions of mathematical concepts. Of primary concern were the teachers' responsive interactions to children's expressions of an implicit mathematical utterance made while engaged in block play. The parallel mixed methods research design consisted of two strands. Strand 1 of the study focused on preschoolers' use of everyday language and the teachers' responses after a child made a mathematical utterance. Twelve teachers and 60 students were observed and videotaped while engaged in block play. Each teacher worked with five children for 20 minutes, yielding 240 minutes of observation. Interaction analysis was used to deductively analyze the recorded observations and field notes. Using a priori codes for the five mathematical concepts, it was found children produced 2,831 mathematical utterances. Teachers ignored 60% of these utterances and responded to, but did not mediate 30% of them. Only 10% of the mathematical utterances were mediated to a mathematical concept. Strand 2 focused on the teacher's view of the role of language in early childhood mathematics. The 12 teachers who had been observed as part of the first strand of the study were interviewed. Based on a thematic analysis of these interviews three themes emerged: (a) the importance of a child's environment, (b) the importance of an education in society, and (c) the role of math in early childhood. Finally, based on a meta-inference of both strands, three themes emerged: (a) teacher conception of math, (b) teacher practice, and (c) teacher sensitivity. Implications based on the findings involve policy, curriculum, and professional development.

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

A relationship between the Florida Comprehensive Assessment Test 2.0 mathematics scores and racial and ethnic concentration when considering socio-economic status, ESOL student population, and school climate

From the moment children are born, they begin a lifetime journey of learning about themselves and their surroundings. With the establishment of the No Child Left Behind Act of 2001, it mandates that all children receive a high-quality education in a positive school climate. Regardless of the school the child attends or the neighborhood in which the child lives, proper and quality education and resources must be provided and made available in order for the child to be academically successful. The purpose of this ex post facto study was to investigate the relationship between the FCAT 2.0 mathematics scores of public middle school students in Miami-Dade County, Florida and the concentrations of a school's racial and ethnic make-up (Whites, Blacks, and Hispanics), English for Speakers of other Languages (ESOL) population, socio-economic status (SES), and school climate. The research question of this study was: Is there a significant relationship between the FCAT 2.0 Mathematics scores and racial and ethnic concentration of public middle school students in Miami-Dade County when controlling SES, ESOL student population, and school climate for the 2010-2011 school year? The instruments used to collect the data were the FCAT 2.0 and Miami-Dade County Public Schools (M-DCPS) School Climate Survey. The study found that Economically Disadvantaged (SES) students socio-economic status had the strongest correlation with the FCAT 2.0 mathematics scores (r = -.830). The next strongest correlation was with the number of students who agreed that their school climate was positive and helped them learn (r = .741) and the third strongest correlation was a school percentage of White students (r = .668). The study concluded that the FCAT 2.0 mathematics scores of M-DCPS middle school students have a significant relationship with socio-economic status, school climate, and racial concentration.

The efficacy of an interactive computer system for teaching developmental mathematics to college students

Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^