Mathematics assessment report, Spring 1977 /

WI docs. no.: Ed.3/2:9320

Guidelines to mathematics, K-8 /

WI docs. no.: Ed.3/2:2126

Mathesis : recueil mathm̌atique, a l'usage des čoles spčiales et des ťablissements d'instruction moyenne /

Suspended 1916-1920.

Instruction to support mental computation development in young children of diverse ability

Fostering young children's mental computation capacity is essential to support their numeracy development. Debate continues as to whether young children should be explicitly taught strategies for mental computation, or be afforded the freedom to develop their own. This paper reports on teaching experiments with two groups of students in their first year of schooling: those considered 'at-risk', and those deemed mathematically advanced. Both groups made considerable learning gains as a result of instruction. Importantly, the gains of the at-risk group are likely to renew both their own, and their teacher's confidence in their ability to learn. In this paper, the instructional programs are documented, highlighting the influence of instruction upon the children's development.

Online Education: What Works in Mathematics

Florida State University and University of Helsinki Information technology has the potential to deliver education to everybody by high quality online courses and associated services, and to enhance traditional face-to-face instruction by, e.g., web services offering virtually unlimited practice and step-bystep solutions to practice problems. Regardless of this, tools of information technology have not yet penetrated mathematics education in any meaningful way. This is mostly due to the inertia of academia: instructors are slow to change their working habits. This paper reports on an experiment where all the instructors (seven instructors and six teaching assistants) of a large calculus course were required to base their instruction on online content. The paper will analyze the effectiveness of various solutions used, and finishes with recommendations regarding best practices.

Matematikaoktatás a bolognai típusú gazdasági képzésekben (Maths instruction in Bologna-type economics tuition)

A gazdálkodási és közgazdasági alap- és mesterszakok tanterveiben számos matematikai tárgy szerepel. A kétciklusú bolognai képzésre történő áttérés Európa-szerte igényelte a matematikaoktatás szerkezetének, mennyiségének és mélységének újragondolását a gazdálkodási és közgazdasági képzési területeken. Mivel az átállás országonként és intézményenként párhuzamosan és jelentős mértékben egymástól függetlenül ment végbe, egyetemenként számos eltérő megoldással találkozhatunk. Az egyetemek operatív tanterveit és tantárgyi adatlapjait felhasználva, utólagosan már összehasonlítható az egyes egyetemek matematikaoktatása. A tanulmány a matematika közgazdaságtanban betöltött szerepének áttekintése után a vezető európai egyetemek és négy magyar egyetem gazdálkodási és közgazdasági képzésén folyó matematikaoktatásának összehasonlító elemzése alapján arra az alapvető következtetésre jut, hogy Magyarországon a vizsgált képzési területen a matematikaoktatás mennyiségileg és minőségileg kritikus szintre süllyedt. / === / The basic and master's curricula for business and economics include plenty of mathematics subjects. Business and economics courses had to be rethought when the change was made across Europe to the two-cycle Bologna system. This change took place simultaneously but independently in each country and institution, so that notably different solutions can be found in each university. A retrospective comparison of maths instruction in various universities can be made by examining their operative syllabuses and subject data-sheets. The study reviews the part mathematics plays in economics, then uses comparative analysis of the maths teaching in business and economics courses at leading European and four Hungarian universities to reach a general conclusion: maths teaching in Hungary, in the field examined, has sunk to a critical level, in terms of quality and quantity.

Intuition as it relates to curriculum, instruction, and resulting academic success in elementary school

Regardless of the fact that children learn in significantly different ways, most curriculum and instruction are guided by the idea that sequential organization of the material to be learned is the best and most efficient way of presenting information to children. Children who learn and think intuitively are denied their preference, forced to conform to the sequential nature of the curriculum and instruction. Based on the theory of psychological type, this study sought to identify any relationship between a student's cognitive style of learning, either Sensing or Intuitive, and his/her academic success in elementary school. The Murphy-Meisgeier Type Indicator for Children was used to identify the cognitive style of students in grades two through eight in a small, private, parochial school. Scores on a standardized achievement test and grades were then analyzed to see if there was a relationship of cognitive style to grades and achievement test scores. Also, the researcher investigated whether or not the teacher's cognitive style had any relationship to students' cognitive style and academic achievement. Although none of the results was statistically significant, the achievement test scores indicated that Sensing students score higher in reading, mathematics concepts, and mathematics computation. However, Intuitive students had higher mean grades in reading and language arts, and virtually equal means mathematics concepts and computation. It was also found that all students, both Sensing and Intuitive, had higher mean grades in the classes of Intuitive teachers. ^

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 comparison of content-based and context-based teaching on ninth-grade mathematics achievement

The purpose of this study was to determine if an experimental context-based delivery format for mathematics would be more effective than a traditional model for increasing the performance in mathematics of at-risk students in a public high school of choice, as evidenced by significant gains in achievement on the standards-based Mathematics subtest of the FCAT and final academic grades in Algebra I. The guiding rationale for this approach is captured in the Secretary's Commission on Achieving Necessary Skills (SCANS) report of 1992 that resulted in school-to-work initiatives (United States Department of Labor). Also, the charge for educational reform has been codified at the state level as Educational Accountability Act of 1971 (Florida Statutes, 1995) and at the national level as embodied in the No Child Left Behind Act of 2001. A particular focus of educational reform is low performing, at-risk students. ^ This dissertation explored the effects of a context-based curricular reform designed to enhance the content of Algebra I content utilizing a research design consisting of two delivery models: a traditional content-based course; and, a thematically structured, content-based course. In this case, the thematic element was business education as there are many advocates in career education who assert that this format engages students who are often otherwise disinterested in mathematics in a relevant, SCANS skills setting. The subjects in each supplementary course were ninth grade students who were both low performers in eighth grade mathematics and who had not passed the eighth grade administration of the standards-based FCAT Mathematics subtest. The sample size was limited to two groups of 25 students and two teachers. The site for this study was a public charter school. Student-generated performance data were analyzed using descriptive statistics. ^ Results indicated that contrary to the beliefs held by many, contextual presentation of content did not cause significant gains in either academic performance or test performance for those in the experimental treatment group. Further, results indicated that there was no meaningful difference in performance between the two groups. ^

Effects of cooperative and individual integrated learning system on attitudes and achievement in mathematics

This study compares the effects of cooperative delivery (CD) and individual delivery (ID) of integrated learning system (ILS) instruction in mathematics on achievement, attitudes and behaviors in adult (16-21 yrs.) high school students (grades 9-13). The study was conducted in an urban adult high school in Miami-Dade County Public Schools using a pre-test/post-test design. Achievement was measured using the Test of Adult Basic Education (TABE) by CTB MC-Graw-Hill and Compass Learning. An attitudinal survey measured attitudes towards mathematics, the computer-related lessons, and attitudes toward group activities. Behavior was assessed using computer lab observations. ^ Two-way analyses of variance (ANOVA) were conducted on achievement (TABE and Compass) by group and time (pre and post). A one-way ANOVA was conducted on the overall attitude by group on the five components (i.e., content mathematics, delivery/computers, cooperative, partners, and self efficacy) and a one-way ANOVA was conducted on the on-task behavior by group. ^ The results of the study revealed that CD and ID students working on mathematics activities delivered by the ILS performed similarly on achievement tests of the TABE. The CD-ILS students had significantly better overall mathematics attitudes than the ID-ILS students and the ID-ILS group was on-task significantly more than the CD-ILS group. This study concludes that regularity and period of time over which the ILS is used may prove to be important variables although there were insufficient data to fully investigate the impact of models of use. Additionally, a minimum amount of time-on-system is necessary before gains can become apparent in innumeracy and increasing exposure to the system may have beneficial effects on learning. ^

Effect of the Florida A+ Plan on curriculum and instruction in Title I public elementary schools

The purpose of this research was to study the effect of the Florida A+ Plan accountability program on curriculum and instruction in four Title I public elementary schools in the Miami-Dade County Public Schools system. It focused on the experiences of the school principals and the classroom teachers of the four schools as they related to curriculum and instruction. The study included an analysis of the school improvement plans in curriculum and instruction for each school during the school years 1998-2004. ^ The study was conducted in the format of interviews with the school principals and principal selected classroom teachers who taught third, fourth, or fifth grade during the first six years of the Florida A+ Plan. The analysis of the school improvement plans focused on the implementation of curriculum and instruction for each of the four schools. It focused on the goals and measurable objectives selected by each school to improve its instructional program in the academic subjects of reading, mathematics, writing, and science. ^ The findings indicated that under the pressure to improve their school grade on the Florida A+ Plan, each of the target schools, based on individual needs assessments, and restructured their instructional program each school year as documented in their school improvement plans. They altered their programs by analyzing student performance data to realign curriculum and instruction. The analysis of the interviews with the principals and the teachers showed that each school year they restructured their program to align it with the FCAT content. This realigning was a collaborative effort on the part of the administration and the instructional staff. ^

The effect of instruction on the study behaviors and academic achievement of community college students

The purpose of this study was twofold. It was designed to determine (a) the efficacy of an intervention designed to increase the frequencies of appropriate study behaviors on the part of community college students who were preparing for academic mathematics activities and (b) whether any increase in appropriate study behavior frequency was accompanied by increased academic achievement in college preparatory mathematics classes. A total of 126 Miami Dade College students participated in this study. Two developmental (remedial) mathematics classes were randomly assigned as the experimental group, and two others were assigned as the control group. All students also took a College Survival (SLS) class. The Study Behavior Inventory (SBI) and the Computerized Placement Test (CPT) were administered to the four classes. The SBI was used as a pre- and post-test. The SLS curriculum and classroom time were the same for both groups. However, students in the treatment groups received instruction designed to increase the frequency of effective study behaviors associated with the three factors identified in the SBI, while the students in the control group participated in activities that did not emphasize study behaviors. A series of analysis of covariance procedures were used to analyze four hypotheses. The first three hypotheses proposed that students who were instructed in the use of appropriate study behaviors would score higher on the three factors of the Study Behavior Inventory than those who were not. The fourth hypothesis proposed that a greater proportion of mathematics students who were instructed in the use of appropriate study behaviors would receive a passing grade in their course than students who were in the control group. The four hypotheses were tested at the .05 level of significance. This study revealed that students who received instruction in appropriate study behaviors scored higher in the use of appropriate study behaviors and in mathematics achievement than students who did not. Additional research is needed to investigate whether these effects would persist over time, or be found in subjects other than mathematics.

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).

The effect of dual -language instruction on academic achievement as measured by the SAT: An evaluation of the "International Studies Program" of Miami -Dade County Public Schools

This study investigated the influence that receiving instruction in two languages, English and Spanish, had on the performance of students enrolled in the International Studies Program (delayed partial immersion model) of Miami Dade County Public Schools on a standardized test in English, the Stanford Achievement Test, eighth edition, for three of its sections, Reading Comprehension, Mathematics Computations, and Mathematics Applications.^ The performance of the selected IS program/Spanish section cohort of students (N = 55) on the SAT Reading Comprehension, Mathematics Computation, and Mathematics Application along four consecutive years was contrasted with that of a control group of comparable students selected within the same feeder pattern where the IS program is implemented (N = 21). The performance of the group was also compared to the cross-sectional achievement patterns of the school's corresponding feeder pattern, region, and district.^ The research model for the study was a variation of the "causal-comparative" or "ex post facto design" sometimes referred to as "prospective". After data were collected from MDCPS, t-tests were performed to compare IS-Spanish students SAT performance for grades 3 to 6 for years 1994 to 1997 to control group, feeder pattern, region and district norms for each year for Reading Comprehension, Mathematics Computation, and Mathematics Applications. Repeated measures ANOVA and Tukey's tests were calculated to compare the mean percentiles of the groups under study and the possible interactions of the different variables. All tests were performed at the 5% significance level.^ From the analyses of the tests it was deduced that the IS group performed significantly better than the control group for all the three measures along the four years. The IS group mean percentiles on the three measures were also significantly higher than those of the feeder pattern, region, and district. The null hypotheses were rejected and it was concluded that receiving instruction in two languages did not negatively affect the performance of IS program students on tests taken in English. It was also concluded that the particular design the IS program enhances the general performance of participant students on Standardized tests.^ The quantitative analyses were coupled with interviews from teachers and administrators of the IS program to gain additional insight about different aspects of the implementation of the program at each particular school. ^

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.