Education Commons^™

Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.

Physics Inventory Of Quantitative Literacy: A Tool For Assessing Mathematical Reasoning In Introductory Physics, Suzanne W. Brahmia, Alexis Olsho, Trevor I. Smith, Andrew Boudreaux, Philip Eaton, Charlotte Zimmerman

Physics & Astronomy

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either understanding of physics concepts or problem-solving abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL) as a tool for measuring Quantitative Literacy, a foundation of mathematical reasoning, in the context of introductory physics. We present the development of the PIQL and evidence of its validity for use in calculus-based introductory physics courses. Unlike …

The Activity Of Abstraction In Physical Chemistry Problem Solving And Instruction, Jessica M. Karch

Graduate Doctoral Dissertations

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well understood. Undergraduate physical chemistry relies particularly heavily on abstraction because it uses many overlapping and imperfect mathematical models to represent and interpret phenomena occurring on multiple scales. To reconcile these models, extract meaning from them, and recognize when to apply them in problem solving requires processes of abstraction. This dissertation aims to …

An Exploration Of Manipulatives In Math Education, Jade Monte

Honors Program Theses and Projects

Pre-existing literature has shown that the education system needs to re-evaluate mathematical teaching practices in a manner that can boost students’ confidence in mathematics. Thus, the research is to investigate the use of manipulatives in reducing students’ anxiety by increasing their learning experience and engagement in mathematics. Furthermore, the purpose of this thesis is to explain the interconnectedness of math manipulatives, student engagement, and problem-solving. An in-depth literature review is conducted, which contains definitions, important benefits and methodologies of manipulatives, as well as the teacher’s role regarding these three terms. When manipulatives, student engagement, and problem-solving are in harmony, students …

Mentoring Prospective Engineering Students Through The After School Program "Girls In Engineering" Focused On Building An Underwater Remotely Operated Vehicle, Vukica M. Jovanović, Deborah Marshall, Jeff Warren Larson Jr., Abdul Rahman Badawi, Neil R. Stclair, Otilia Popescu, Murat Kuzlu, Petros J. Katsioloudis, Linda Vahala, Michael Anthony Crespo

Engineering Technology Faculty Publications

A number of studies by engineering education researchers have pointed out that all-female teams, rather than mixed teams, result in better forms of participation and interaction in engineering related after-school programs and clubs. In particular, for after-school programs or clubs that form in response to a STEM competition, all-female teams have better chances of developing. One such competition, which will be discussed in this paper, is a regional Marine Advanced Technology Education (MATE) competition in which students from Blind_Review High School have been participating for many years.For each year’s competition, an all-female team of students enrolled in the Career and …

Keefektifan Pendekatan Contextual Teaching Learning Dan Problem Solving Ditinjau Dari Prestasi Dan Kepercayaan Diri Siswa, Usi Susanti, Dhoriva Urwatul Wutsqa

Jurnal Riset Pendidikan Matematika

Tujuan dari penelitian ini adalah untuk mendeskripsikan keefektifan pendekatan Contextual Teaching and Learning (CTL) dan problem-solving ditinjau dari prestasi belajar dan kepercayaan diri. Penelitian ini merupakan penelitian eksperimen semu dengan populasi semua siswa kelas VII SMP Negeri 1 Yogyakarta Tahun Ajaran 2015/2016 yang terdiri dari delapan kelas. Sampel penelitian dipilih secara acak, dari delapan kelas yang ada terpilih dua kelas yaitu VII A dan VII B. Kelas VII A sebagai kelas eksperimen I diajar dengan pendekatan CTL dan kelas VII B sebagai kelas eksperimen II diajar dengan pendekatan problem solving. Instrumen yang digunakan dalam penelitian ini adalah tes prestasi belajar …

Review Of Mathematical Imagining: A Routine For Secondary Classrooms By Christof Weber, Geoff Krall

Colorado Mathematics Teacher

This book review of Christof Weber's Mathematical Imagining yields insight into the routine of mathematical imagining and offers practitioners advice on how to incorporate the routine in the classroom. A brief summary of the book is provided, followed by commentary on potential benefits of mathematical imagining, connection to other research, and suggestions for accommodating for emergent bilingual students. Readers are encouraged to follow up with a reading of the original book.

Critical Connections Between Numeracy And Mathematics: Supplementary Materials, Dave Tout

Student learning processes

This publication contains three professional development activities targeted at teachers of mathematics. The activities for both groups and individuals focus on the challenge of word problems in maths and connecting maths to the real world. Also included are references, materials and resources related to the issue of the connections between numeracy and mathematics.

Letting Go, Kevin Junod

Colorado Mathematics Teacher

Change perspectives and methods to make mathematics instruction more problem based.

Tasks That Promote Problem Solving, Wendy Ward Hoffer

Colorado Mathematics Teacher

What makes a rich, juicy task that can deeply engage learners in thinking and understanding important mathematical ideas? I have found that a great task offers varied entry points, is open-ended, and invites multiple representations.

Success With Tasks That Promote Problem Solving, Joanie Funderburk

Colorado Mathematics Teacher

I provide resources and suggestions for teachers to find or adapt tasks to promote students' reasoning and problem solving.

From The Editor's Desk, Sandie Gilliam

Colorado Mathematics Teacher

In Principles to Actions (PtA), NCTM suggests that there is too much focus on learning procedures without any connection to meaning, understanding, or the applications that require these procedures. I share my vision to address this challenge.

Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou

Journal of Humanistic Mathematics

In this work, a faculty member takes a journey along with students as they enhance their understanding of how people solve mathematical problems through a mainly qualitative statistical project. Student authors of this paper registered for a problem solving seminar led by the faculty author, and then created and analyzed self-built assessment tools to explore problem solving techniques. Here we share our findings and recommendations, which we hope will inspire others to explore novel pedagogical techniques in the teaching of mathematical problem solving. We incorporate into our presentation ur voices, reflecting on how we and others solve problems.

Pengembangan Perangkat Pembelajaran Menggunakan Problem Solving Dalam Problem Posing Berbasis Pendekatan Saintifik, Ahmad Lutfi

Jurnal Riset Pendidikan Matematika

Penelitian ini bertujuan untuk menghasilkan produk berupa perangkat pembel-ajaran aljabar menggunakan problem solving dalam problem posing berbasis pendekatan saintifik yang valid, praktis dan efektif ditinjau dari keyakinan terhadap pelajaran matematika (KTM) dan kemampuan berpikir kreatif (KBK) siswa SMA. Penelitian pengembangan ini menggunakan model Plomp. Hasil penelitian ini adalah perangkat pembelajaran aljabar menggunakan problem solving dalam problem posing berbasis pendekatan saintifik yang berorientasi pada keyakinan terhadap pelajaran matematika dan kemampuan berpikir kreatif siswa SMA berupa RPP dan LKS. Kualitas perangkat pembelajaran yang dikembangkan ditinjau dari aspek kevalidan, aspek kepraktisan dan aspek keefektifan. Hasil penelitian menunjukkan bahwa RPP dan LKS valid dan …

Validitas Dan Efektivitas Prototipe Buku Ajar Fisika Dasar Reflektif-Integratif Berbasis Problem Solving Untuk Meningkatkan Pengetahuan Metakognisi, Muhammad Asy'ari, Samsun Hidayat, Muhali Muhali

Jurnal Inovasi Pendidikan IPA

Penelitian ini bertujuan menghasilkan prototipe buku ajar fisika dasar reflektif-integratif berbasis problem solving yang valid dan efektif untuk meningkatkan pengetahuan metakognisi peserta didik. Desain penelitian ini adalah eksperimen semu menggunakan one group pretest-posttest design, dengan sampel 25 peserta didik program studi pendidikan fisika FPMIPA IKIP Mataram. Instrumen penelitian ini menggunakan lembar validasi untuk mengukur validitas produk, dan tes berbentuk essay yang mengukur efektivitas produk untuk meningkatkan pengetahuan metakognisi peserta didik. Data dan analisis yang digunakan yaitu: (1) validitas produk dilakukan oleh 2 (dua) ahli yang berkompeten dan dianalisis secara deskriptif, dan (2) efektivitas produk diukur setelah pembelajaran dan dianalisis …

Developing Numeracy And Problem-Solving Skills By Overcoming Learning Bottlenecks, Anita Lee-Post

Marketing & Supply Chain Faculty Publications

Purpose The purpose of this paper is to present an educational approach to elevating problem-solving and numeracy competencies of business undergraduates to meet workplace demand. The approach is grounded in the theory of constraints following the Decoding the Discipline model. The authors investigated a cognitive bottleneck involving problem modeling and an affective bottleneck concerning low self-efficacy of numeracy and designed specific interventions to address both bottlenecks simultaneously. The authors implemented the proposed approach in an introductory level analytics course in business operations.

Design/methodology/approachThe authors use an empirical study to evaluate the effectiveness of the proposed approach in addressing deficiency in …

An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison

Numeracy

Ethan D. Bolker and Maura B. Mast. 2016. Common Sense Mathematics.(Washington DC.: Mathematics Association of America) ISBN-13: 978-1-93951-210-9.

Common Sense Mathematics is an integrative quantitative reasoning (QR) textbook that is built around scores of exercises derived from authentic circumstances from public media and other public sources. The exercises elicit responses from students requiring extensive communication and analyses and distinguish the book from ones typically encountered in a mathematics or science course. Responses to exercises often require one-half page or more of writing and can occupy considerable class time in discussion. The book has material for a one- or two-semester …

Pengaruh Pendekatan Problem Solving Terhadap Kemampuan Representasi Dan Literasi Matematis Siswa, Muh. Fajaruddin Atsnan, Rahmita Yuliana Gazali, Maisea Ledua Nareki

Jurnal Riset Pendidikan Matematika

Pada konteks penilaian berskala internasional seperti PISA, kompetensi pemecahan masalah dalam bidang matematika dan sains terkait permasalahan nyata merupakan fokus pengembangan kompetensi representasi dan literasi matematis siswa. Mengingat pentingnya pemecahan masalah, kemampuan representasi dan literasi matematis, maka penelitian ini bertujuan untuk mengetahui pengaruh pendekatan problem solving terhadap kemampuan representasi dan literasi matematis siswa SMP. Metode yang digunakan pada penelitian ini adalah metode eksperimen kuasi (quasi experimental), dengan desain penelitian yang digunakan adalah Randomized Posttest-Only Control Group Design, yakni dua kelas yang telah dipilih secara acak, selanjutnya diberikan perlakukan yang diakhiri dengan tes kemampuan representasi dan literasi matematis pada kedua …

Exploring The Neural Mechanisms Of Physics Learning, Jessica E. Bartley

FIU Electronic Theses and Dissertations

This dissertation presents a series of neuroimaging investigations and achievements that strive to deepen and broaden our understanding of human problem solving and physics learning. Neuroscience conceives of dynamic relationships between behavior, experience, and brain structure and function, but how neural changes enable human learning across classroom instruction remains an open question. At the same time, physics is a challenging area of study in which introductory students regularly struggle to achieve success across university instruction. Research and initiatives in neuroeducation promise a new understanding into the interactions between biology and education, including the neural mechanisms of learning and development. These …

Decision Making In The Sciences: Understanding Heuristic Use By Students In Problem Solving, Elizabeth Csikar

STEMPS Theses & Dissertations

The purpose of this study was to examine the use of heuristics by students and gain insight into the thought process behind their problem-solving skills. The study used an adaptive narrative as the information delivery medium. An adaptive narrative was chosen because it could be designed to simulate decision making processes encountered in real world situations. Students enrolled in an introductory biology major class were chosen for the study because their fields of interest all require complex problem solving and decision-making skills. It was of interest to investigate what decisions were made when heuristics were given and how that may …

Zooming Into A Tinkering Project: The Progression Of Learning Through Transitional Objects, Priyanka Parekh, Elisabeth R. Gee

Interdisciplinary Journal of Problem-Based Learning

The Maker Movement has been received by the field of K–12 education with great enthusiasm as a way of teaching STEM content to children. We call attention to and identify learning opportunities in children’s projects created in a playful, informal environment with easily available materials. In keeping with research in the field of maker education and learning sciences, we describe tinkering as a constructionist learning activity in which meaning making is captured through transitional objects (Bamberger, 1995). First, we examine one specific tinkering project and identify transitional objects within the project. Next, we discuss the process of meaning making as …

Reading Strategies In Content Area Math, Jennifer Bachman O’Brien

Certificate of Advanced Studies (CAS) in Literacy

Since the introduction of the CCSS, expectations in math have placed greater responsibility for problem-solving on students. No longer is computation the primary focus of elementary math instruction; instead the goal has shifted to student understanding of the mathematical contexts. The aim of this action research study, guided by Vygotsky’s theory of social constructivism, was to determine the effectiveness of integrating reading and content area math, while deepening students’ skills in vocabulary, journaling, and visualizing. Nine fifth-grade students receiving Tier 2 math intervention were selected to participate in the study. Data collection consisted of pre and post measures including criterion-referenced …

Effective Teaching For Place Value Understanding: A Case Study Of A Literacy-Integrated Math Curriculum Module, Young Rae Kim, Mi Sun Park

Curriculum and Instruction Faculty Publications

A lesson sequence for place value was developed as an early intervention for kindergarteners. The sequence begins with a children’s picture book involving language familiar to children and continues with hands-on activities for children to make connections between and within multiple representations of place value. Through engaging in the literacy-integrated math curriculum module, kindergartners deepened their understanding of place value and the base-ten number system, as they were consistently engaged in problem solving and mathematical discourse triggered by their own mathematical thinking, as well as purposeful questions prompted by the teacher.

Supporting Mathematics Coaches' Learning Of Probability Through Professional Development Tasks, Mary C. Enderson, Melva R. Grant, Yating Liu

Teaching & Learning Faculty Publications

This study was conducted to propose a framework of professional development tasks (PDTs) that may be used to enhance mathematics coaches’ content knowledge and understanding of student work, as well as to help them conceptualize their role in facilitating a professional learning community in school. In this qualitative design experiment, researchers developed and implemented a set of PDTs to use with elementary and middle school mathematics coaches. The PDTs, with a focus on K-8 probability topics, required coaches to conduct mathematics problem solving, student work analysis, and create a community to reflect individually and collaboratively on such experiences. Qualitative data …

The Effects Of Teaching Exponential Functions Using Authentic Problem Solving On Students’ Achievement And Attitude, Yamamah Sawalha

Wayne State University Dissertations

Most of the current mathematics education focuses on procedures and pays very little attention to conceptual understanding in many classrooms. NCTM (2000) called for improving students’ understanding to help improve their achievement. To help prepare students for the future, they need to be taught to value mathematics and realize that it is relevant to their lives. Students need to use their mathematical knowledge to solve real life problems. This can’t be achieved by focusing only on the procedures and expecting students to understand how to apply it to real life. The purpose of this study was to examine the effect …

The Utility Of Storytelling Strategies In The Biology Classroom, Elizabeth Csikar, Jill E. Stefaniak

STEMPS Faculty Publications

Conveying scientific information with high intrinsic cognitive load to students is a challenge. Often, students do not have the existing schema to incorporate the information in a comprehensive manner. One method that has shown promise is storytelling. Storytelling has been successfully used to convey public health information to non-experts. Therefore, it was of interest to determine whether storytelling could be used in the classroom to present information with high intrinsic load to students in a meaningful manner. This study used a post-test only quasi-experimental study design to explore the utility of storytelling as an instructional strategy in anatomy and physiology …

Pengaruh Model Pembelajaran Problem Solving Terhadap Kemampuan Komunikasi Matematis Ditinjau Dari Gender, Hodiyanto Hodiyanto

Jurnal Riset Pendidikan Matematika

Tujuan penelitian ini adalah untuk mengetahui: (1) manakah kemampuan komunikasi matematis siswa yang lebih baik antara model pembelajaran problem solving (PS) dan model pembelajaran langsung. (2) manakah kemampuan komunikasi matematis siswa yang lebih baik antara kelompok laki-laki dan perempuan. (3) pengaruh model pembelajaran PS terhadap kemampuan komuniksi matematis. Metode penelitian yang digunakan adalah penelitian eksperimental semu. Populasi dalam penelitian ini adalah siswa kelas VII SMP Negeri 02 Mojolaban Sukoharjo. Pengambilan sampel dilakukan dengan teknik cluster random sampling. Instrumen untuk mengumpulkan data adalah tes kemampuan komunikasi matematis. Pengujian hipotesis pada penelitian ini menggunakan analisis anova dua jalan dengan sel tak …

A Program Evaluation Of Double-Period Algebra, Jason Major

Dissertations

Students in ninth grade traditionally take algebra courses, but many students come in lacking foundational skills in mathematics. High schools have tried to solve this problem by introducing double-period algebra courses with sporadic results. During this program evaluation, I interviewed an administrator and a teacher from two different high schools about the methods they used to begin and evaluate the program; I found that student-teacher relationships were the most important factor in the effectiveness of the program. Using quantitative data was a good starting point to determine the students who would benefit from the program and who would be successful, …

Pemahaman Konsep Ipa Siswa Smp Melalui Pembelajaran Problem Solving Pada Topik Perubahan Benda-Benda Di Sekitar Kita, Ikhwan Khairu Sadiqin, Uripto Trisno Santoso, Arif Sholahuddin

Jurnal Inovasi Pendidikan IPA

Telah dilakukan penelitian untuk mendeskripsikan pemahaman konsep IPA siswa SMP melalui pembelajaran problem solving. Teknik pemilihan sampel dilakukan secara purposive sampling. Subyek penelitian ini adalah siswa kelas VII berjumlah 66 orang. Data penelitian diperoleh menggunakan instrumen tes. Teknik analisis data dengan cara melihat perkembangan n-gain. Hasil penelitian diperoleh rata-rata pemahaman konsep siswa sebelum pembelajaran adalah 52,28 tergolong kategori kurang baik. Skor setelah pembelajaran adalah 77,40 tergolong kategori baik. Model problem solving sesuai untuk pembelajarain sains sekolah menengah pertama dan dapat mendorong siswa untuk membangun pemahaman konsep. Terjadi konstruksi pemahaman konsep siswa melalui proses menghubungkan pengetahuan dalam menyelesaikan masalah …

How Does A Next Generation Science Standard Aligned, Inquiry Based, Science Unit Impact Student Achievement Of Science Practices And Student Science Efficacy In An Elementary Classroom?, Kayla Lee Whittington

Dissertations and Theses

This study examined the impact of an inquiry based Next Generation Science Standard aligned science unit on elementary students' understanding and application of the eight Science and Engineering Practices and their relation in building student problem solving skills. The study involved 44 second grade students and three participating classroom teachers. The treatment consisted of a school district developed Second Grade Earth Science unit: What is happening to our playground? that was taught at the beginning of the school year. Quantitative results from a Likert type scale pre and post survey and from student content knowledge assessments showed growth in student …