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).

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.

The effect of the use of computer assisted instruction (CAI) on attitudes and computational scores of developmental mathematics students at two inner city schools with predominantly Black enrollment

This study examined the effects of computer assisted instruction (CAI) 1 hour per week for 18 weeks on changes in computational scores and attitudes of developmental mathematics students at schools with predominantly Black enrollment. Comparisons were made between students using CAI with differing software--PLATO, CSR or both together--and students using traditional instruction (TI) only.^ This study was conducted in the Dade County Public School System from February through June 1991, at two senior high schools. The dependent variables, the State Student Assessment Test (SSAT), and the School Subjects Attitude Scales (SSAS), measured students' computational scores and attitudes toward mathematics in 3 categories: interest, usefulness, and difficulty, respectively.^ Univariate analyses of variance were performed on the least squares mean differences from pretest to posttest for testing main effects and interactions. A t-test measured significant main effects and interactions. Results were interpreted at the.01 level of significance.^ Null hypotheses 1, 2, and 3 compared versions of CAI with the control group, for changes in mathematical computation scores measured with the SSAT. It could not be concluded that changes in standardized mathematics test scores of students using CAI with differing software 1 hour per week for 18 class hours combined with TI were significantly higher than changes in test scores for students receiving TI only.^ Null hypotheses 4, 5, and 6 tested the effects of CAI for attitudes toward mathematics for experimental groups against control groups measured with the SSAS. Changes in attitudes toward mathematics of students using CAI with differing software 1 hour per week for 18 class hours combined with TI were not significantly higher than attitude changes for students receiving TI only.^ Teacher effect on students' computational scores was a more influential variable than CAI. No interaction was found between gender and learning method on standardized mathematics test scores (null hypothesis 7). ^

The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method.^ Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system.^ Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means, not significantly, for the experimental group in problem solving achievement. The study did not indicate a significant difference in attitude mean scores.^ It was concluded that using an intelligent tutoring system in problem solving instruction may impact student's overall mathematics achievement and problem solving achievement. Other factors must be considered, such as the teacher's classroom experience, the teacher's experience with the intelligent tutoring system, trained technical support, and trained student support; as well as student learning styles, motivation, and overall mathematics ability. ^

A fourth-grade teacher's classroom perspective

Countless books have been written about what is good and what is bad about our educational system. No matter what the book or what the theory, all agree the classroom teacher is critical to the education process. Many influences affect classroom teaching, some of which are beyond her control, but a caring classroom teacher has a central role in the instruction of children The purpose of this case study was to inquire into the beliefs and behaviors of one elementary school teacher in a low socio-economic school and study her classroom perspective. This teacher of five years was a reading specialist and was teaching a full fourth grade curriculum for the first time. Because she suffered from math phobia, she was apprehensive about teaching mathematics. ^ This qualitative study required intense, time-consuming interviews, long and frequent observations, critical journaling, field notes and artifacts provided by the teacher. The resulting descriptive data was coded into categories and reassembled into themes that captured the essence of the teacher's beliefs. ^ The overarching themes found were: first, the teacher's caring attitude towards her students, cultivated by her affectionate family, her mother who is an elementary school teacher, and rich and rewarding elementary school experiences, second, her implementation of the curriculum, influenced by her passion for reading, her math phobia, and standardized tests and third, her attitudes toward her workplace, school administrators and collegiality among teachers. During the school year this teacher “owned” her classroom and was a full participant in its life! Her dedication to teaching was fostered by the satisfaction of knowing she has a profound impact and makes a significant difference in her students' lives. ^ This study suggested areas for further research on the following topics: consideration of teachers with math phobia, the effect of standardized tests on areas of the curriculum and the value of computers in the elementary school classroom. ^

Teacher talk: A community of colleagues that values practical teacher knowledge through sharing experiences

The purpose of this study was to describe the experiences of five educators participating in a teacher-initiated learning community that valued practical teacher knowledge. Connelly and Clandinin (2000) argued that practical teacher knowledge grew out of experience through interaction in the professional knowledge landscape. Collaboration that promoted teacher learning was the foundation to effective school change (Wood, 1997). This teacher-initiated learning community consisted of members who had equal status and collaborated by participating in discourse on curriculum and instruction. The collegiality of the community fostered teacher professionalism that improved practice and benefited the school. This study focused on the following research questions: (1) What was the experience of these five educators in this learning community? (2) What did these five individuals understand about the nature of practical teacher knowledge? (3) According to the participants, what was the relationship between teacher empowerment and effective school change? ^ The participants were chosen because each voluntarily attended this teacher-initiated learning community. Each participant answered questions regarding the experience during three semi-structured tape-recorded interviews. The interviews were transcribed, and significant statements of meaning were extracted. Using a triangulation of ideas that were common to at least three of the participants ensured the trustworthiness of the analysis. These statements were combined to describe what was experienced and how the participants described their experience. The emerging themes were the characteristics of and the relationships, methods, conditions, and environment for the teachers. The teachers described how a knowledge base of practical teacher knowledge was gained as a spirit of camaraderie developed. The freedom that the teachers experienced to collaborate and learn fostered new classroom practice that affected school change as student interaction and productivity increased. ^ The qualitative analysis of this study provided a description of a learning community that valued practical teacher knowledge and fostered professional development. This description was important to educational stakeholders because it demonstrated how practical teacher knowledge was gained during the teachers' daily work. By sharing every day experiences, the teacher talk generated collaboration and accountability that the participants felt improved practice and fostered a safe, productive learning environment for students. ^

The effectiveness of training educators on their ability to identify function of problem behavior

The purpose of this study was to investigate the effectiveness of training educators in the pre-behavioral intervention process of functional behavioral assessment. An original evaluation instrument was developed entitled, The Survey for Students Exhibiting Challenging Behavior. The instrument included measures of participating educators, knowledge of function of problem behavior and their ability to generate recommendations for a behavior intervention plan. The instrument was distributed to schools in a large urban district and completed by special educators. Educators trained and untrained in the functional behavioral assessment process were compared in the study. ^ The study incorporated a post-test only design. All instruments were analyzed using a factorial ANOVA. Those educators who were trained in the district functional behavioral assessment program answered general questions related to function of problem behavior significantly better than those who did not receive training. There is no significant difference between educators on their ability to generate recommendations for behavior intervention plans. It is important that educators receive training in functional behavioral assessment to gain an understanding of the basic notions being function of problem behavior. Current training does not translate into educators' ability to make strong recommendations for behavior intervention plans. ^

The relationship of student and teacher variables on academic achievement in Florida schools

Since 1995, Florida has been one of the leading states in the country initiating a high-stakes school accountability system. Public schools in Florida receive letter grades based on their performance on the Florida Comprehensive Assessment Test (FCAT). These school grades have significant effects on schools' reputations and funding. Consequently, the plan has been criticized for grading all schools in the same manner, without taking into account such variables as student poverty and mobility rates which are beyond the control of the school. ^ The purpose of this study was to examine the relationship of student variables (poverty and mobility rates) and teacher variables (average years of teacher experience and attained degree level) on FCAT math and reading performance. This research utilized an education production function model to examine which set of inputs (student or teacher) has a stronger influence on student academic output as measured by the FCAT. ^ The data collected for this study was from over 1500 public elementary schools in Florida that listed all pertinent information for 2 school years (1998/1999 & 1999/2000) on the Florida Department of Education's website. ^ It was concluded that student poverty, teacher average years of experience and student mobility taken together, provide a strong predictive measure of FCAT reading and math performance. However, the set of student inputs was significantly stronger than the teacher inputs. High student poverty was highly correlated with low FCAT scores. Teacher experience and student mobility rates were not nearly as strongly related to FCAT scores as was student poverty. The results of this study provide evidence for educators and other school stakeholders of the relative degree to which student and teacher variables are related to student academic achievement. The underlying reasons for these relationships will require further examination in future studies. These results raise questions for Florida's school policymakers about the educational equity of the state's accountability system and its implementation. ^

The effects of the use of technology in mathematics instruction on student achievement

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics FCAT results were examined to determine if the GSP produced any effects. Students’ scores were compared based on assignment to the control or experimental group as well as gender and SES. SES measurements were based on whether students qualified for free lunch. The findings of the study revealed a significant difference in the FCAT mathematics scores of students who were taught geometry using GSP compared to those who used the traditional method. No significant differences existed between the FCAT mathematics scores of the students based on SES. Similarly, no significant differences existed between the FCAT scores based on gender. In conclusion, the use of technology (particularly GSP) is likely to boost students’ FCAT mathematics test scores. The findings also show that the use of GSP may be able to close known gender and SES related achievement gaps. The results of this study promote policy changes in the way geometry is taught to 10th grade students in Florida’s public schools.

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.

Two Educators’ Experiences of Double Dose Reading Classes

The purpose of this qualitative study was to gain knowledge of the phenomenon of double dose reading classes. A reading coach and a reading teacher were interviewed. Data revealed teachers navigate a complicated set of negotiations in order to deliver quality instruction while simultaneously satisfying mandated requirements from supervisors.

Teacher perception of self -determination skills in the inclusive and special education classroom

It has been proposed that special education teachers, who promote self-determination and link it to educational standards, help students with a disability succeed in school. The current school reform movement has focused on accountability through mandates such as the No Child Left Behind Act, 2001, and has emphasized participation in the general curriculum through amendments to the Individuals with Disabilities Education Act (IDEA) of 1997 and 2004. This study informs educators if educational setting, students' type of disability, and subject area taught, influence teachers' opinions about the importance of teaching components leading to self-determination and self-management. ^ The research questions that drive this study are: (1) do secondary school teachers who instruct students with a disability think that self-determination components taught in the classroom will make an important difference in students' school and later postsecondary achievements? and (2) does the type of classroom setting, students' type of disability, or specific subject matter influence teachers' opinions regarding the importance of teaching components related to self-determination and self-management? The collection and interpretation of data were done using descriptive and quantitative methods employing a teacher survey. The survey was administered to secondary teachers who instruct students with disabilities. Data were analyzed using descriptive and inferential statistics. The sample consisted of 97 special education teachers currently teaching at the secondary level. ^ The results of the study indicated that teachers believe that self-determination is important for both school life and post school life. However teachers thought these skills to be more important for post school success. Teachers believe that self-determination is more important than self-management skills. Type of disability, educational environment, and subject area were not significant factors. ^

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.

Effects of Family, Child, and Teacher Demographics on Prekindergarten Children's Access to and Use of Numeracy and Spatial Materials in the Early Education Setting

Florida’s Voluntary Pre-Kindergarten program (VPK) aims to ensure that all 4-year-olds are prepared to excel in K-12 mathematics. Early numeracy/spatial skills are predictive of success in K–12 mathematics. No research has examined whether VPK classrooms are equipped with the materials necessary to teach numeracy/spatial skill. The Pre-Kindergarten Numeracy and Spatial Environment Survey was created to examine the frequency of access to and use of numeracy/spatial materials in VPK classrooms. The 69-item survey was completed by the lead educator from a sample of 62 pre-kindergarten classrooms in Miami-Dade County. Regression analysis results suggest the location of the pre-kindergarten center, the sex distribution of the children in the classrooms or the number of years of experience that the educator has as a lead teacher along with the extra training courses undertaken by the teachers does not affect the access to or the use of, numeracy and spatial materials in the classrooms.