Education Commons^™

Leveraging Students’ Passion And Creativity: Ethos At The University Of Dayton, Margaret Pinnell, Malcolm Daniels, Kevin P. Hallinan, Gretchen Berkemeier

Kevin Hallinan

The Engineers in Technical Humanitarian Opportunities of Service-learning (ETHOS) program was developed in the spring of 2001 by an interdisciplinary group (electrical, chemical, civil and mechanical) of undergraduate engineering students at the University of Dayton (UD). ETHOS was founded on the belief that engineers are more apt and capable to appropriately serve our world if they have an understanding of technology’s global linkage with values, culture, society, politics, and the economy. Since 2001, the ETHOS program at UD has grown and changed. From conceptualization, to implementation, to maturation and national recognition, the program has addressed challenges of academic acceptance, programmatic …

Reflections On Math Students’ Circles: Two Personal Stories From Colorado, Diana White, Lori Ziegelmeier

Lori Beth Ziegelmeier

Math Students’ Circles provide an opportunity for mathematicians to work in their communities to engage young students in mathematics as a human, aesthetic, and social endeavor. Sometimes referred to simply as Math Circles, these venues give mathematicians experience in introducing children to topics not typically seen in school curricula in an exciting, hands-on format. This article explores two Math Students’ Circles (MSCs) in the state of Colorado from the point of view of two pre-tenure faculty members. One participated in MSCs for four years while working on her Ph.D. in mathematics, the other started an MSC as an offshoot of …

Math Class "Unsettled": Teaching And Learning Mathematics Within And Across Multiple Spaces, Jeremiah I. Holden

Remi Holden

No abstract provided.

The Interconnectedness Of Relational And Content Dimensions Of Quality Instruction: Supportive Teacher-Student Relationships In Urban Elementary Mathematics Classrooms, Dan Battey, Rebecca A. Neal, Luis Leyva, Karlyn Adams-Wiggins

Rebecca Neal

Mathematics Uncovered Through Action Science, William H. Robertson

William H. Robertson

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Kevin Watson

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Boris Handal

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Katrina Eddles-Hirsch

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Astronauts In Outer Space Teaching Students Science: Comparing Chinese And American Implementations Of Space-To-Earth Virtual Classroomspdf, Song An, Daniel Tillman, William H. Robertson, Meilan Zhang

William H. Robertson

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Marguerite Maher

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Jean MacNish

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Conceptualising Changes To Pre-Service Teachers’ Knowledge Of How To Best Facilitate Learning In Mathematics: A Tpack Inspired Initiative, Frank G. Bate, Lorraine Day, Jean Macnish

Jean MacNish

In 2010, the Australian Commonwealth government initiated an $8m project called Teaching Teachers for the Future. The aim of the project was to engage teacher educators in a professional learning network which focused on optimising exemplary use of information and communications technologies in teacher education. By taking part in this network, participants were afforded opportunities to transform their practice through a range of localised initiatives that applied information and communications technologies to the art and science of teaching and learning. One of these initiatives involved re-engineering a university mathematics unit targeted at pre-service teachers. Information and communications technologies were purposefully …

Effectiveness Of Professional Learning: Enhancing The Teaching Of Fractions In Primary Schools, Derek Hurrell

Derek Hurrell

No abstract provided.

Conceptualising Changes To Pre-Service Teachers’ Knowledge Of How To Best Facilitate Learning In Mathematics: A Tpack Inspired Initiative, Frank G. Bate, Lorraine Day, Jean Macnish

Lorraine Day

In 2010, the Australian Commonwealth government initiated an $8m project called Teaching Teachers for the Future. The aim of the project was to engage teacher educators in a professional learning network which focused on optimising exemplary use of information and communications technologies in teacher education. By taking part in this network, participants were afforded opportunities to transform their practice through a range of localised initiatives that applied information and communications technologies to the art and science of teaching and learning. One of these initiatives involved re-engineering a university mathematics unit targeted at pre-service teachers. Information and communications technologies were purposefully …

Gender And Sex Differences In Student Participation, Achievement And Engagement In Mathematics, Sarah Buckley

Dr Sarah Buckley

Research in neuroscience, psychology and education explores gender differences in achievement and learning in many different ways with different implications for educators and policymakers. This paper presents some of the literature from these three research fields. Rather than being an exhaustive review, This paper provides a brief synthesis of relevant issues when considering gender in education. The paper has three main sections. The first section presents data on gender differences in mathematics participation, achievement and engagement in Australia. Note that for the purposes of this paper, the term ‘engagement’ will be used to describe students’ motivated involvement with mathematics, particularly …

Can You Tell Cr**P From Crayolas? Evaluating Information Sources For Researched Projects, Debbie Morrow

Debbie Morrow

Is Teaching Parallel Algorithmic Thinking To High School Students Possible? One Teacher’S Experience, Shane Torbert, Uzi Vishkin, Ron Tzur, David Ellison

Ron Tzur

All students at our high school are required to take at least one course in Computer Science prior to their junior year. They are also required to complete a year-long senior project associated with a specific in-house laboratory, one of which is the Computer Systems Lab. To prepare students for this experience the lab offers elective courses at the post-AP Computer Science level. Since the early 1990s one of these electives has focused on parallel computing. The course enrolls approximately 40 students each year for two semesters of instruction. The lead programming language is C and topics include a wide …

Nature And Utility Of Teacher Questioning: A Case Of Constructivist-Oriented Intervention, Jessica Hunt, Ron Tzur, Arla Westenskow

Ron Tzur

No abstract provided.

Interweaving Tasks And Conceptions To Promote Multiplicative Reasoning In Students With Learning Disabilities In Mathematics, Yan Xin, Ron Tzur, Luo Si, Dake Zhang, Casey Hord, Wei Luo, Suleyman Centintas

Ron Tzur

This case study examined the efficacy of tasks designed for promoting multiplicative reasoning in students with learning disabilities. Chad’s (grade 4) construction of a mixed-unit coordination scheme was nurtured in the context of a teaching experiment with 14 students in two USA Midwest elementary schools. The analysis focuses on how a sequence of tasks, tailored to Chad’s available conceptions, brought forth his transfer of a crucial mathematical idea to novel, realistic problem situations. We argue for the use of such conceptually tailored tasks as a means for promoting students’ progress from what they know to a transfer-enabling stage (anticipatory).

The Effect Of An Intelligent Tutor On Math Problem-Solving Of Students With Learning Disabilities, Xiaojun Ma, Yan Xin, Ron Tzur, Luo Si, Xuan Yang, Joo Park, Jia Liu, Rui Ding

Ron Tzur

Reform-based math instruction calls for students’ construction of conceptual understanding, solving challenging problems and explanation of reasoning. However, existing literature shows that students with learning disabilities (LD) easily get lost in reform-based instruction. As an outcome of collaborative work between math education and special education in instructing students with D, we’ve developed an intelligent tutor (PGBM-COMPS) to nurture multiplicative reasoning of students with LD. The intelligent tutor dynamically models individual student's evolving conceptions and recommends tasks to promote her/his advancement to a higher level in the learning trajectory and solve complex word problems using mathematical model equations. This study evaluated …

Jake’S Conceptual Operations In Multiplicative Tasks: Focus On Number Choice, Rachael Risley, Nicola Hodkowski, Ron Tzur

Ron Tzur

No abstract provided.

Students With Learning Disability In Math Are Left Behind In Multiplicative Reasoning? Number As Abstract Composite Unit Is A Likely ‘Culprit’, Ron Tzur, Yan Xin, Rachael Kenney, Adam Guebert

Ron Tzur

This study addressed the problem of why students with learning disabilities in mathematics too often fail to develop multiplicative and divisional concepts/operations. We conducted a constructivist teaching experiment with 12 students (nine 5th and three 4th graders). This report focuses on three students’ conceptual progress, particularly on Sandy’s (most pronounced). Our analysis indicates that, at the outset, those three could only reason additively because they lacked a robust concept of number as an abstract composite unit and were bound to rely on strategies of counting units of one. Once teaching engendered a concept of number in them, they made substantial …

Non-Traditional Use Of ‘Math-As-Human-Endeavour’: Two Chinese Middle School Teachers’ Attempts To Inspire Students’ Curiosity, Xianyan Jin, Ron Tzur

Ron Tzur

No abstract provided.

The Power Of Natural Thinking: Applications Of Cognitive Psychology To Mathematics Education, Ron Tzur

Ron Tzur

Concurring with Uri Leron’s cross-disciplinary approach to distinct modes of mathematical thinking, intuitive and analytic, I discuss his elaboration and adaptation to our field of the cognitive psychology dual-processing theory (DPT). I reflect on (a) the problem significance, (b) aspects of the theory he adapts, and (c) elegance of presentation. Then, I further discuss DPT in light of a constructivist stance on the inseparability of thinking and learning. I link DPT to accounts of (i) brain-based conceptual learning and (ii) how mathematics teaching may promote such learning—and discuss advantages of those accounts.

Want Teaching To Matter? Theorize It With Learning..., Ron Tzur

Ron Tzur

No abstract provided.

Explicating A Mechanism For Conceptual Learning: Elaborating The Construct Of Reflective Abstraction, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel

Ron Tzur

We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstraction and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified.

Children's Development Of Multiplicative Reasoning: A Schemes And Tasks Framework, Ron Tzur, Heather Johnson, Evan Mcclintock, Rachael Kenney, Yan Xin, Luo Si, Jerry Woodward, Casey Hord, Xianyan Jin

Ron Tzur

In this paper we propose a developmental framework that makes distinctions and links among schemes—conceptual structures and operations children construct to reason in multiplicative situations. We provide a set of tasks (problem situations) to promote construction of such schemes. Elaborating on Steffe et al.’s (Steffe & Cobb, 1998) seminal work, this framework synthesizes findings of our teaching experimentsi with over 20 children who have disabilities or difficulties in mathematics. This empirically grounded framework contributes to articulating and promoting multiplicative reasoning—a key developmental understanding (Simon, 2006) that presents a formidable conceptual leap from additive reasoning for students and teachers (Harel & …

Culturally-Mathematically Relevant Pedagogy (Cmrp): Fostering Urban English Language Learners' Multiplicative Reasoning, Ron Tzur, Heather Johnson, Evan Mcclintock, Rachael Risley

Ron Tzur

In this paper we articulate an approach, termed culturally-mathematically relevant pedagogy (CMRP), for fostering urban English language learners’ mathematical progression. CMRP integrates three aspects, the use of (1) adaptive teaching to build on students’ funds of knowledge for mathematics, (2) tasks that make sense to students given their current mathematical conceptions, and (3) manipulatives and representations that, for the students, meaningfully signify quantities linked to numbers and operations used in a task. To situate CMRP, we use a continuum of conceptual transitions in multiplicative reasoning, which are critical for supporting students’ development of algebraic reasoning.

Conceptually Based Task Design: Megan’S Progress To The Anticipatory Stage Of Multiplicative Double Counting, Jerry Woodward, Rachael Kenney, Dake Zhang, Adam Guebert, Suleyman Centintas, Ron Tzur, Yan Xin

Ron Tzur

No abstract provided.

An Account Of A Teacher's Perspective On Learning And Teaching Mathematics: Implications For Teacher Development, Ron Tzur, Marty Simon, Karen Heinz, Margaret Kinzel

Ron Tzur

This report presents an account of one teacher's mathematics teaching and a perspective that underlies his teaching. Nevil was a fifth grade teacher participating incurrent mathematics education reforms in the United States. Through the account, we make distinctions about teachers' thinking and practice that can inform teacher education efforts. We constructed an account by analyzing four sets of classroom observations and interviews. We observed that Nevil decomposed hisunderstandings of the mathematics into smaller components and connections among those components. He created situations that he believed made those components and connections transparent and attempted to elicit those connections from the …