Digital Commons Network^™

Accessing Mathematical Content Through The Proficiency Strands, L Day

Education Conference Papers

The Australian Curriculum: Mathematics differs from previous state versions of curricula by the inclusion of four Proficiency Strands alongside the three Content Strands. The Proficiency Strands are the power behind the curriculum as they shape the way in which the content should be accessed. Mathematically rich tasks that use a problem solving or inquiry approach allow students to develop deep understanding of mathematical concepts through reasoning and communication that will lead to greater fluency.

Are There Any Winners In High-Stakes Mathematics Testing? A Qualitative Case Study Exploring Student, Parent And Teacher Attitudes Towards Naplan Numeracy Tests In Years 3 And 5, L Cranley, G Hine

Education Conference Papers

Through the annual implementaion of National Assessment Program - Literacy and Numeracy (NAPLAN), testing of mathematical standards across Australia invokes questions about the impact that high-stakes testing has for the teaching and learning of mathematics. According to recent studies on high-stakes testing, the role of the teacher is instrumental in children's achievement results. The purpose of this case study is to explore perspectives about NAPLAN from key participants at one Western Australian Primary School, namely: students, teachers, and parents. The paper will report on the extent to which instructional pedagogy at one school has been affected by the implementation of …

Mathematics Classrooms - Why Are Some Fireworks And Others Just Sparklers?, D Hurrell

Education Conference Papers

The name of this paper and the presentation which accompanies it is "Mathematics classrooms - why are some fireworks and others just sparklers?" Why is it that some classrooms are vibrant places of lively debate, reasoning and mathematical inquiry and others are places of anxiety and disengagment? The following article will address research that underpins some of the affective elements that need to be considered in order to tackle the content of mathematics in a way that makes students feel engaged in the mathematics learning process.

Preservice Teachers’ Perceptions Of Mathematics Through Drawings, Adam Akerson

Faculty Publications

Research indicates that mathematics anxiety is particularly high in pre-service teachers (Bekdemir, 2010; Gresham, 2007; Hembree, 1990). These future teachers will soon be entering classrooms of their own, responsible for teaching mathematics to young children, who need strong teachers. A 2013 report from The National Assessment of Educational Progress (NAEP), found that 42% fourth-graders performed at or above the proficient level in math (NCES, 2013. The purpose of this study was to examine elementary pre-service teacher candidates (PSTCs) perceptions of mathematics, through drawings. Drawings were analyzed before and after a semester-long field experience in a constructivist mathematics environment. The participants …

Evaluating High School Mathematics Performance Measures And Student Attributes For Predicting Remedial Mathematics Success And Student Retention In College, Sherri L. Stepp

Theses, Dissertations and Capstones

The purpose of this study was to evaluate multiple high school student attributes and performance measures that could be considered for use in predicting success in developmental mathematics courses and college-level math courses at Marshall University in Huntington, West Virginia. This study also evaluated the predictive ability of the same high school student attributes and performance measures in determining first-year fall-to-fall retention rates for successful math students.

The study population consisted of first-time freshmen who entered the case study institution in the fall semesters of 2010 through 2014 and graduated from West Virginia public high schools. The population was stratified …

Follower And Extender Sets In Symbolic Dynamics, Thomas Kelly French

Electronic Theses and Dissertations

Given a word w in the language of a one-dimensional shift space X, the follower set of w, denoted F_X(w), is the set of all right-infinite sequences which follow w in some point of X. Extender sets are a generalization of follower sets and are defined similarly. To a given shift space X, then, we may associate a follower set sequence {|F_X(n)|} which records the number of distinct follower sets in X corresponding to words of length n. Similarly, we may define an extender set sequence {|E …

An Examination Of The Nature Of Post-Observation Feedback Provided To Middle School Mathematics Teachers, Christine Trinter, Heather Carlson-Jaquez

MERC Publications

Many studies have examined teacher evaluation but few address the discipline expertise of evaluators and the type of post-observation feedback provided to teachers. With the current focus in mathematics education on processes and justification, the type of post-observation feedback teachers receive is critical to improving instruction. This qualitative study examined the type of feedback and use of observation protocols by evaluators with different mathematical backgrounds. Findings reveal the difference in the nature of discipline specific feedback between observers as well as the difference in the way the teacher evaluation system was employed among observers. The evaluative nature of observer's roles …

African American Urban Public High School Graduates’ Experiences Concerning Mathematics, Lorenzo A. Rashid

ETD Archive

This interpretive qualitative study explored African American urban public high school graduates’ experiences concerning mathematics, how these experiences may play a role in the choice to further their mathematics education, and how the Model of Academic Choice (MAC) may facilitate in the understanding of the experiences.

It examined the lived experiences of seven African American urban public high school graduates concerning their mathematics education. Through criterion-based sampling, the seven participants selected had graduated from a public high school located in Northeast Ohio school districts having similar characteristics.

Data were collected through semi-structured interviews that explored participants’ kindergarten through post-secondary mathematics …

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover

A Simple Introduction to Rates

Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …

Support Model For Transfer Students Utilizing The Stem Scholarship Program, Lynn Olson, Amy J. Moll, Doug Bullock, Amit Jain, Janet Callahan

Materials Science and Engineering Faculty Publications and Presentations

This paper describes how the College of Engineering at Boise State University utilized a National Science Foundation S-STEM award from 2011 to 2016 to support transfer students in their path toward graduation. The need for this support was a result of both Boise State University College of Engineering’s transition from a 2-year pre-engineering program to the establishment of Bachelors of Science in Engineering Degree programs in 1997 as well as the establishment of the College of Western Idaho as a regional community college in 2007. Both of these factors led to an increase in the numbers of incoming engineering students …

Rate Of Change 2, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Limits5, Ruth Dover

Limits

Limits and continuity.

Limits2, Ruth Dover

Limits

More on limits, both algebraic and graphical, including one-sided limits.

3. Derivatives Of Exponential Functions, Ruth Dover

More on Derivatives

Exploring the derivative of exponential functions.

Series 03, Ruth Dover

Series

Considers the creation of a general Maclaurin series.

Belief, Construction, And Language: Philosophical Lenses On Issues Of Understanding And Cognition In Mathematics, Bradley Thomas Baker

Theses & ETDs

This thesis takes two issues which crop up in mathematics in general, but which are specifically invoked through examples drawing on mathematical pedagogy. Chapter one focuses on the problem of what it means to understand mathematics, and what it means to have different levels or kinds of understanding. Chapter two then takes up a similar question regarding mathematical cognition, focusing on what sense can be made of different kinds of mathematical cognition from a philosophical standpoint. More specifically, this thesis takes up three thinkers who represent two opposing ontological camps in the philosophy of mathematics. For each thinker, the goal …

Hidden Symmetries And Commensurability Of 2-Bridge Link Complements, Christian Millichap, William Worden

Faculty Publications

In this paper, we show that any nonarithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of 3-manifolds with nontrivial JSJ-decomposition and rank-two fundamental groups. We also show that the only commensurable hyperbolic 2-bridge link complements are the figure-eight knot complement and the 6²₂ link complement. Our work requires a careful analysis of the tilings of R² that come from lifting the canonical triangulations of …

Predicting Mathematics Teachers' Acceptance Of Reflective Blogging To Improve Instruction, Diana Sue Fesmire

Walden Dissertations and Doctoral Studies

An internal district audit identified that a rural, socioeconomically disadvantaged Southwestern school district has a lack of congruent and consistent implementation of the Common Core State Standards in mathematics. Innovative and cost-saving avenues for professional development (PD), such as reflective blogging, foster teacher learning to reconcile the enacted curriculum with the intended curriculum. This correlational study investigated the predictive power of technology acceptance and motivation constructs on reflective mathematics teachers' social media use intention and participation in informal, virtual Communities of Practice (vCoP). The framework that guided this study is the unified acceptance and use of technology and self-determination theory. …

On Tensor Autoequivalences Of Graded Fusion Categories, Ian Swenson Marshall

Doctoral Dissertations

Fusion categories generalize the representation theory of finite groups. The simplest examples of fusion categories come from finite groups, their representations, and their cohomology. In general, it is useful to examine group theoretical features of fusion categories such as groups of (isomorphism classes of) tensor invertible objects, and gradings by finite groups. Indeed, every fusion category has a maximal pointed subcategory (generated by tensor invertible objects) and a universal grading by a finite group. We use such features to study tensor autoequivalences.

Pointed fusion categories: categories for which all simple objects are tensor invertible, provide our prototype for graded fusion …

Limits4, Ruth Dover

Limits

An introduction to limits as something goes to infinity.

Approximations 4, Ruth Dover

Integrals

Trapezoidal Rule.

Pisa For Development Technical Strand A: Enhancement Of Pisa Cognitive Instruments, Ray J. Adams, John Cresswell

OECD Programme for International Student Assessment (PISA)

The OECD is planning to enhance existing PISA assessment instruments in reading, mathematics and science so that they will be more suitable to the context of developing countries. The main purpose of this paper is to identify the main technical issues associated with this aim. The paper reports detailed analysis of the existing PISA item pool and its suitability for countries which have students of average limited capacity. The paper cautions that the fit of developing country data to the PISA model is not good and that modifications to address some of the deviations should be explored. The use of …

My Math Gps: Elementary Algebra Guided Problem Solving (2016 Edition), Jonathan Cornick, G Michael Guy, Karan Puri

Open Educational Resources

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.

A Computational And Theoretical Exploration Of The St. Petersburg Paradox, Alexander Olivero

Undergraduate Honors Thesis Collection

This thesis displays a sample distribution, generated from both a simulation (for large n) by computer program and explicitly calculated (for smaller n), that is not governed by the Central Limit Theorem and, in fact seems to display chaotic behavior. To our knowledge, the explicit calculation of the sample distribution function is new. This project outlines the results that have found a relation to number theory in a probabilistic game that has perplexed mathematicians for hundreds of years.

Executive Functioning Predicts Reading, Mathematics, And Theory Of Mind During The Elementary Years., Rachelle H. Cantin, Emily K. Gnaedinger, Kristin C. Gallaway, Matthew S. Hesson-Mcinnis, Alycia M. Hund

Faculty Publications – Psychology

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. Ninety-three 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about …

Series 07, Ruth Dover

Series

Where did the Lagrange error bound come from?

Series 08, Ruth Dover

Series

More on error.

Analyzing Math-To-Mastery Through Brief Experimental Analysis, Gregory E. Everett, Honora S. Swift, Elizabeth L.W. Mckenney, Jeremy D. Jewell

SIUE Faculty Research, Scholarship, and Creative Activity

The current study evaluated the effectiveness of individualized math-to-mastery (MTM) interventions, selected though brief experimental analysis (BEA), at increasing math fluency skills for 3 elementary-aged females. As MTM has only been investigated as a multicomponent intervention, the present study utilized BEA to identify those specific components which led to math skills gains in the most efficient manner possible. BEA results indicated that for 2 of 3 participants only a partial MTM intervention was necessary to prompt fluency gains, while the entire intervention was the most effective for the third. During extended analysis all 3 participants displayed math skills gains above …

Number Knowledge And Error Types Of Elementary Portuguese Students: Implications For Instruction, Silvana Watson, Sharon Judge, João Lopes, Célia Oliveira, Ana Catarina Jesus

Communication Disorders & Special Education Faculty Publications

In the present study, we examined number knowledge skills of 697 Portuguese elementary students from first to fourth grade. Students completed three number knowledge tasks: 1) translating numbers into words, 2) symbolic magnitude (i.e., number comparison), and 3) decomposing numbers. We evaluated students’ answers by means of error analysis using a three-category coding system adopted from specific error types were computed by grade level. Results showed that there were significant differences among grades and that the prerequisite linguistic error type (i.e., pre linguistic rules or principles of the cardinal number system), particularly in the magnitude tasks, significantly contributed to students’ …