Use of the Maple System in Math Tuition at Universities

The following article explores the application of educational technologies at a University level and their contribution in enhancing the educational effectiveness. It discusses the capabilities of computer algebra systems, such as Maple. It is integrated in the math tuition of the Technical University (TU) in Varna and is used by its students during laboratory exercises.

Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^

The Effect of Incorporating Math Skills into Physical Education Classes on Math Achievement of Second Grade Elementary Students

The effect of embedding math skills into physical education lessons on math achievement of second grade students in two classes was investigated. There were no statistical differences between the experimental (PE/Math) group and the control group. However, practical observations indicated more research is needed in this area.

Illustrating Cognitive Connections between Math and Language in Pre-Service Teachers’ Perceptions of Common or Everyday Terms

This paper introduces a new construct that we term Math Mediated Language (MML) focusing on the notion that common or everyday terms with mathematical meanings are important building blocks for students’ mathematical reasoning. A survey given to 96 pre-service early childhood educators indicated clear patterns of perceptions of these terms.

Changing Parental Perceptions of Math and Science Curriculum Through Hands-on Workshops

Many parents hold negative perceptions of math and science because they have never been taught these domains from a hands-on, constructivist approach. Only 20 - 30% of adults have actually experienced activity-based science inquiry. Instead, these individuals were exposed to didactic science programs that emphasize drill, skill and memorization (Shymanksy, 2000). This has had a negative impact upon their content knowledge in these areas and their perceptions of math and science. Consequently, parents are hesitant to incorporate math and science into their home life. There is a dire need to determine if parental perceptions of math, science, and their content knowledge will be positively effected as a result of participation in hands-on science workshops.

Strategies for Reducing Math Anxiety in Post-Secondary Students

This literature review explores how educators might address adult math anxiety. Curricular, instructional, and non-instructional strategies are reviewed. The suggested approaches emphasize treating the cognitive and physical manifestations of math anxiety.

Adults Learning Math Online: A Surprising Harmony

Adults returning to school face challenges including overcoming math anxiety. Many choose online courses as they balance life and work schedules. Online math courses therefore can be restructured to prevent math anxiety by catering to individual learning styles, providing tools that aid concept attainment, and using problem-based learning strategies.

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

The Effectiveness of an Intervention Package on Math Computation

Abstract: Four second-grade students participated in a B-A-B withdrawal single-subject design experiment. The intervention package implemented consisted of three components: self-monitoring, performance feedback, and reinforcers. Participants completed math probes across phases. Accuracy and productivity was recorded and calculated. Results demonstrated the intervention package improved accuracy and productivity for all participants.

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

Utilizing Traditional Cognitive Measures of Academic Preparation to Predict First-Year Science, Technology, Engineering, and Mathematics (STEM) Majors' Success in Math and Science Courses

For the past several years, U.S. colleges and universities have faced increased pressure to improve retention and graduation rates. At the same time, educational institutions have placed a greater emphasis on the importance of enrolling more students in STEM (science, technology, engineering and mathematics) programs and producing more STEM graduates. The resulting problem faced by educators involves finding new ways to support the success of STEM majors, regardless of their pre-college academic preparation. The purpose of my research study involved utilizing first-year STEM majors’ math SAT scores, unweighted high school GPA, math placement test scores, and the highest level of math taken in high school to develop models for predicting those who were likely to pass their first math and science courses. In doing so, the study aimed to provide a strategy to address the challenge of improving the passing rates of those first-year students attempting STEM-related courses. The study sample included 1018 first-year STEM majors who had entered the same large, public, urban, Hispanic-serving, research university in the Southeastern U.S. between 2010 and 2012. The research design involved the use of hierarchical logistic regression to determine the significance of utilizing the four independent variables to develop models for predicting success in math and science. The resulting data indicated that the overall model of predictors (which included all four predictor variables) was statistically significant for predicting those students who passed their first math course and for predicting those students who passed their first science course. Individually, all four predictor variables were found to be statistically significant for predicting those who had passed math, with the unweighted high school GPA and the highest math taken in high school accounting for the largest amount of unique variance. Those two variables also improved the regression model’s percentage of correctly predicting that dependent variable. The only variable that was found to be statistically significant for predicting those who had passed science was the students’ unweighted high school GPA. Overall, the results of my study have been offered as my contribution to the literature on predicting first-year student success, especially within the STEM disciplines.

The background impact in HEI math lectures: an experience in math in the 1st year of Accounting and Management Degree

It is a fact, and far from being a new one, that students have been entering Higher Education courses with many different backgrounds in terms of secondary school programs they attended. The impact of these basic skills is a general and worldwide challenge, fundamentally when facing some specific “constructive” subjects like foreign languages and Mathematics. Working with students with an extensive variety of Math qualifications is an outrageous challenge when they enter an advanced Math course, leading to an almost generalized expectations’ failure - from students enrolled in course and from their teachers, who feel powerless in trying to monitor knowledge construction from completely different “starting points”. If teachers’ "haste" is average, more than half of the students do not “go along” and give up, even before experiencing any kind of evaluation procedure. On the contrary, if the “speed” is too low, others are discouraged (feeling not progressing at all) and the teacher runs the risk of not meeting the minimum objectives (general and specific) of its course, which may have a negative impact on students’ future training development. Failure in Mathematics, despite being a recurrent and global issue, does not have any “magical solution”, however, in general, teachers in this area seem untiring, searching, investigating, trying and implementing new and old “recipes” to tackle and demystify this subject. In this article we describe a project developed in a Math course, with the first year students from an Accounting and Management bachelor degree, and its outcomes since it was brought to practice, revealing its impact in students’ success, from approval to dropout rates, in this course. We will shortly describe students’ differentiated Math backgrounds, their results in a pre-assessment analysis and how we try to deal with these differences and level them up, having in mind the same “finish line”. One should never forget that all these students where officially accepted in higher education institutions, so they are ones’ reality, the reality of institutions whose name one should value and strive to defend.

STUDENTS’ PERCEPTIONS OF TEACHER INSTRUMENTAL SUPPORT AS A PREDICTOR OF MOTIVATION IN READING AND MATH AND ACHIEVEMENT FROM SECOND THROUGH TWELFTH GRADE

In this study, relations among students’ perceptions of instrumental help/support from their teachers and their reading and math ability beliefs, subjective task values, and academic grades, were explored from elementary through high school. These relations were examined in an overall sample of 1,062 students from the Childhood and Beyond (CAB) study dataset, a cohort-sequential study that followed students from elementary to high school and beyond. Multi-group structural equation model (SEM) analyses were used to explore these relations in adjacent grade pairs (e.g., second grade to third grade) in elementary school and from middle school through high school separately for males and females. In addition, multi-group latent growth curve (LGC) analyses were used to explore the associations among change in the variables of interest from middle school through high school separately for males and females. The results showed that students’ perceptions of instrumental help from teachers significantly positively predicted: (a) students’ math ability beliefs and reading and math task values in elementary school within the same grade for both girls and boys, and (b) students’ reading and math ability beliefs, reading and math task values, and GPA in middle and high school within the same grade for both girls and boys. Overall, students’ perceptions of instrumental help from teachers more consistently predicted ability beliefs and task values in the academic domain of math than in the academic domain of reading. Although there were some statistically significant differences in the models for girls and boys, the direction and strength of the relations in the models were generally similar for both girls and boys. The implications for these findings and suggestions for future research are discussed.

Connecting the dots: Examining the role of parental beliefs and preschoolers’ affect and engagement in predicting parent-child number exploration during a meaningful math experience

The current study examined the frequency and quality of how 3- to 4-year-old children and their parents explore the relations between symbolic and non-symbolic quantities in the context of a playful math experience, as well as the role of both parent and child factors in this exploration. Preschool children’s numerical knowledge was assessed while parents completed a survey about the number-related experiences they share with their children at home, and their math-related beliefs. Parent-child dyads were then videotaped playing a modified version of the card game War. Results suggest that parents and children explored quantity explicitly on only half of the cards and card pairs played, and dyads of young children and those with lower number knowledge tended to be most explicit in their quantity exploration. Dyads with older children, on the other hand, often completed their turns without discussing the numbers at all, likely because they were knowledgeable enough about numbers that they could move through the game with ease. However, when dyads did explore the quantities explicitly, they focused on identifying numbers symbolically, used non-symbolic card information interchangeably with symbolic information to make the quantity comparison judgments, and in some instances, emphasized the connection between the symbolic and non-symbolic number representations on the cards. Parents reported that math experiences such as card game play and quantity comparison occurred relatively infrequently at home compared to activities geared towards more foundational practice of number, such as counting out loud and naming numbers. However, parental beliefs were important in predicting both the frequency of at-home math engagement as well as the quality of these experiences. In particular, parents’ specific beliefs about their children’s abilities and interests were associated with the frequency of home math activities, while parents’ math-related ability beliefs and values along with children’s engagement in the card game were associated with the quality of dyads’ number exploration during the card game. Taken together, these findings suggest that card games can be an engaging context for parent-preschooler exploration of numbers in multiple representations, and suggests that parents’ beliefs and children’s level of engagement are important predictors of this exploration.