- College of Staten Island, Education, Faculty Memberadd
- Educations, Education, Higher Education, E-learning, Science Education, Teacher Education, and 18 moreTechnology, Mathematics, Educational Technology, Mathematics Education, Science, Mathematical reasoning and proof, Technological Pedagogical Content Knowledge (TPACK), Special Education, Science Teaching Methods, Dynamic Geometry Sofware, Preservice Teacher Education, Teacher Efficacy, Teachers' Attitudes to ICT, Alternative Teacher Certification, Danielson's Framework, Symbolic Geometry Software, Data Collection Technology, and STEM Educationedit
- Dr, Irina Lyublinskaya received her Ph.D. in Theoretical and Mathematical Physics from Leningrad State University in ... moreDr, Irina Lyublinskaya received her Ph.D. in Theoretical and Mathematical Physics from Leningrad State University in 1991. She is a professor of mathematics and education at the Teachers College, Columbia University in New York City. She has taught at the university as well as the high school level for over 30 years. She is a recipient of various awards for teaching excellence, including Radioshack/Tandy Prize for Teaching Excellence in Mathematics, Science, and Computer Science, NSTA Distinguished Science Teaching Award and citation, Education’s Unsung Heroes Award for innovation in the classroom, and NSTA Vernier Technology Award. In 2011, she has been inducted to NYS Mathematics Educators Hall of Fame. In 2019 she has been elected as a full member of the Russian Academy of Natural Sciences. She is a recipient of several outstanding paper awards from AACE and SITE, an author of 16 books about teaching of mathematics and science, co-author of 6 chapters in books, and has published substantially in internationally recognized academic journals.edit
For a long time, Soviet students learned ‘pure’ mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid... more
For a long time, Soviet students learned ‘pure’ mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid national curriculum. Even when in the 1990s the world was moving towards including applications in school mathematics, Russian students continued to engage in pure mathematics learning in their mathematics classrooms. It was physics teachers’ responsibility to teach applications of mathematics; therefore, physics courses were highly mathematics-intensive, making extensive use of mathematics from algebra to calculus in the formulation of scientific laws and the investigation of their consequences. The collapse of the Soviet Union and some liberalization in educational policy led to changes in graduation requirements in mathematics and physics as well as diversity in mathematics and physics curricula in schools. Based on a review of textbooks, standards, curriculum documents, and other resources, in this paper we analyze changes that affected the teaching and learning of mathematics in physics classrooms in Russia from the Soviet period to the present.
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Statistical properties of fluorescent light from a single two-level atom driven by a beam of antibunched light are discussed in the weak field limit. Fields generated by realistic open systems with pumping and dissipation are chosen to be... more
Statistical properties of fluorescent light from a single two-level atom driven by a beam of antibunched light are discussed in the weak field limit. Fields generated by realistic open systems with pumping and dissipation are chosen to be the models for antibunched light. As examples, we consider fields produced in intracavity second harmonic generation and in the homodyned degenerate parametric oscillator. These fields can be described in terms of real Gaussian random processes with coherent components. Analytical expressions for fluorescent light intensity and second order intensity correlation function in the steady state are derived. Effects of driving field correlations, detuning, and parameters characterizing the driving field on the statistics of scattered light are investigated. It is found that over a certain range of parameters characterizing the driving field the second order intensity correlation function may vanish at non-zero time. These and other interesting features will be discussed.
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For a long time, Soviet students learned ‘pure’ mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid... more
For a long time, Soviet students learned ‘pure’ mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid national curriculum. Even when in the 1990s the world was moving towards including applications in school mathematics, Russian students continued to engage in pure mathematics learning in their mathematics classrooms. It was physics teachers’ responsibility to teach applications of mathematics; therefore, physics courses were highly mathematics-intensive, making extensive use of mathematics from algebra to calculus in the formulation of scientific laws and the investigation of their consequences. The collapse of the Soviet Union and some liberalization in educational policy led to changes in graduation requirements in mathematics and physics as well as diversity in mathematics and physics curricula in schools. Based on a review of textbooks, standards, curriculum documents, and other resources, in this paper we analyze changes that affected the teaching and learning of mathematics in physics classrooms in Russia from the Soviet period to the present.
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Students with disabilities have limited opportunities to become problem solvers due to the deficit‐thinking mindset of their teachers. Thus, technology could facilitate the development of problem‐solving skills for these students, which... more
Students with disabilities have limited opportunities to become problem solvers due to the deficit‐thinking mindset of their teachers. Thus, technology could facilitate the development of problem‐solving skills for these students, which requires an understanding of student computer attitudes in science, technology, engineering, and mathematics (STEM) problem‐solving. However, there is limited research about computer attitudes in problem‐solving for students with disabilities. To address this challenge, this study first developed a questionnaire on computer attitudes in problem‐solving in STEM (Colorado assessment of problem‐solving [CAPS]‐STEM) and validated this instrument for the population of elementary school students with disabilities (N = 199). The questionnaire was then used in a sequential explanatory mixed methods study to examine factors affecting CAPS‐STEM for students with disabilities in two inclusive classrooms. Results of the study indicate significant positive correl...
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Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a... more
Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course in a sequence. This method was tested on a dataset of Calculus 1 and Calculus 2 grades of 164 undergraduate students majoring in mathematics at a private university in Kazakhstan. The results showed that while the currently used practice of setting prerequisite grade requirements is accurately identifying successful completions of Calculus 2, the ROC method is more accurate in identifying possible failures in Calculus 2. The findings also indicate that prior completion of Calculus 1 is positively associated with success in a Calculus 2 course. Thus, this study contributes to the field of mathematics education by providing a new data-driven methodology for determining the op...
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This case study analyzed the TPACK development and a learning trajectory of a single pre-service special education elementary school teacher during TPACK-based graduate pedagogy course and TPACK transfer from this course to the teaching... more
This case study analyzed the TPACK development and a learning trajectory of a single pre-service special education elementary school teacher during TPACK-based graduate pedagogy course and TPACK transfer from this course to the teaching during induction year. The case study was guided by the following research questions: 1) What instructional strategies and experiences in the graduate pedagogy course supported TPACK development of this pre-service teacher? and 2) What are the internal and external factors affecting TPACK transfer for this teacher? The study showed that TPACK level of the participant increased to exploring level of TPACK throughout the graduate course, but regressed to Adapting level during first year of teaching showing partial transfer of TPACK. The study described course experiences and instructional strategies that supported preservice teacher's TPACK development in the graduate course and identified some external and internal factors that could have affect t...
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Since the development of the technological pedagogical content knowledge (TPACK) framework, researchers have been developing a variety of instruments to measure the TPACK of pre-service and in-service teachers. The task of developing an... more
Since the development of the technological pedagogical content knowledge (TPACK) framework, researchers have been developing a variety of instruments to measure the TPACK of pre-service and in-service teachers. The task of developing an efficient, reliable, and valid instrument is difficult. Even validated instruments require guidance for consistent use that preserves the instrument fidelity. The purpose of this study is to provide guidance for using the TPACK Levels Rubric, a validated instrument that was developed on the basis of the model for the progressive levels of TPACK. The authors systematically examined the criteria of the rubric in order to understand the differences in the levels of TPACK for each rubric component, and developed lesson exemplars to create guidelines for educators using this tool in assessing the TPACK levels of teachers. The iterative instrument analysis also led to the revision of the original rubric to establish the horizontal and vertical alignments a...
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This chapter describes a process for the implementation of data collection technology that the authors introduced into the science and mathematics methods courses for preservice elementary-school teachers in a public, urban college. The... more
This chapter describes a process for the implementation of data collection technology that the authors introduced into the science and mathematics methods courses for preservice elementary-school teachers in a public, urban college. The curriculum of the methods courses was developed to include inquiry-based lab activities that utilize probeware and various data collection interfaces. The lesson plans and the reflections that the authors collected from the 124 preservice teachers over three semesters show that the courses not only exposed them to a variety of data collection instruments, but also changed their attitudes and confidence levels about using such technology in the classroom. The results of this project suggest that preservice teachers perceive data collection technology as a tool for the clear demonstration of otherwise hard to teach science and mathematics concepts to their students. After using data collection technology in their method courses, preservice teachers wer...
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A one year course with main emphasis on the development of students' research skills has been offered at the Arkansas School for Mathematics and Science. The content core of the course is optics and the use of optical instrumentation... more
A one year course with main emphasis on the development of students' research skills has been offered at the Arkansas School for Mathematics and Science. The content core of the course is optics and the use of optical instrumentation for research in science, mathematics, and art. The course presents a combination of rigorous content, interdisciplinary curriculum, and hands-on experiences. The course offers unique opportunities for students to engage in meaningful, non-traditional learning in real-life research settings.
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ABSTRACT
We examine elementary school teachers’ prior understandings of concept of fractions within different contexts. We argue that teacher' understanding on fractions significantly improves when they are offered opportunities to investigate... more
We examine elementary school teachers’ prior understandings of concept of fractions within different contexts. We argue that teacher' understanding on fractions significantly improves when they are offered opportunities to investigate fractions in new context, specifically, in the situations when they can not rely on procedural approaches. This leads to cognitive conflict when approaching problems involving continuous quantities, and wholes consisting of several objects. These situations arise when problems related to Egyptian fraction are introduced. Pre-service teachers' investigations of these problems have lead to deeper conceptual understanding of fair share concept (in the new context), comparing fractions, relations between different wholes, fractions part-part-whole representations (one bigger fraction represented as sum of two smaller fractions), connection of different fraction representations with numerical measure (number of cuts), and on the different level it l...
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We wrote this book with the hope to help teachers to engage their students in learning geometry and encourage them in their development of logical thinking. This book offers 43 interesting geometry problems that resulted from a... more
We wrote this book with the hope to help teachers to engage their students in learning geometry and encourage them in their development of logical thinking. This book offers 43 interesting geometry problems that resulted from a collaboration of Russian and American educators. They reflect the content of the standard high school curriculum. Altogether these problems demonstrate the most important methods of geometry. The unique features of these problems include use of symbolic geometry software, Geometry Expressions. Each problem includes student black line master and detailed teacher notes with solutions, proofs, and steps for working with Geometry Expressions. We hope that this book will be useful to educators who are interested in teaching students geometry using modern technology in the classroom. We believe that use of symbolic geometry software in teaching and learning is a key element in the future of mathematics education. It will raise students’ interest in geometry while h...
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Using science experiments in different courses of mathematics helps ground students’ understanding of abstract mathematics concepts in real-world applications. Hands-on activities connect mathematics with science in a way that is... more
Using science experiments in different courses of mathematics helps ground students’ understanding of abstract mathematics concepts in real-world applications. Hands-on activities connect mathematics with science in a way that is accessible to teachers and students alike. Students apply a variety of techniques to verify their experimental results and develop conjectures. Provided example of such activity explores a scientific phenomenon, connecting it to precalculus concept of the graph of a cosine function. This activity uses fan cart along with the TI graphing calculator, data interface, and dual force sensor. The experiment can be used as hands-on activity or demonstration.
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This book can help your students in learning major facts of calculus. The 29 explorations that cover major topics of standard course of calculus are completed with the help of the constrain-based dynamic software package, Geometry... more
This book can help your students in learning major facts of calculus. The 29 explorations that cover major topics of standard course of calculus are completed with the help of the constrain-based dynamic software package, Geometry Expressions. The special features of this software help to 1) provide dynamic visualization of for both, theoretical ideas of calculus and specific problems, 2) provide a symbolic output, which allows to receive general results, 3) connect algebraic and geometric methods of mathematics in one holistic approach to learning calculus. Using Geometry Expressions in learning calculus, students have opportunities to develop general investigation skills, to make connections between geometric and algebraic representations of major calculus ideas, thus developing the skill of interpreting analytic problems visually and geometric problems algebraically, and to develop idea using computer in proving general mathematics statements.
The purpose of this book is to provide you with practical and concise guide in your preparation to become an elementary school teacher. The main focus of this book is on teaching mathematics and science with technology in the elementary... more
The purpose of this book is to provide you with practical and concise guide in your preparation to become an elementary school teacher. The main focus of this book is on teaching mathematics and science with technology in the elementary classroom. It is common that mathematics and science are most intimidating subjects for the elementary school teachers. Very often teacher’s intimidation impacts their students’ attitudes and interests in mathematics and science. Thus, it is really important for you to develop confidence and excitement about teaching mathematics and science, so that your students become engaged and motivated to learn these subjects in early age. Mathematics and science are naturally connected, which allows teachers to integrate these subjects with ease. In this book you will find various examples on how to make these connections in order to help your students to learn both subject areas at a conceptual level. Technology has become a very important part of life and wo...
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Activities give users the opportunity to directly experience, through dynamic visualization and manipulation, the topics covered in precalculus, including: polynomial, exponential, and trigonometric functions; parametric functions; polar... more
Activities give users the opportunity to directly experience, through dynamic visualization and manipulation, the topics covered in precalculus, including: polynomial, exponential, and trigonometric functions; parametric functions; polar coordinates; and complex numbers. Also includes activities that are appropriate for use in the first few weeks of a calculus course. Chapters include: Function Transformations, Circular Functions, Trigonometric Properties, Other Functions, Data and Probability, Vectors and Matrices, Polar Coordinates and Complex Numbers, Sequences and Series, and Introduction to Calculus.
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Suggested activities are designed for pre-service students preparing to become elementary school teachers and who are taking courses on science and mathematics teaching methodologies. The activities are also for their future elementary... more
Suggested activities are designed for pre-service students preparing to become elementary school teachers and who are taking courses on science and mathematics teaching methodologies. The activities are also for their future elementary school students in grades 1 – 5. Use of hands-on activities within science and mathematics content provides additional opportunities for teacher candidates and their future students to make connections and to master standards-based concepts and skills. Another important part of this approach is the use of various technologies and measuring equipment, all necessary to prepare our students for the challenges of the 21st century.
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In this paper, we argue that the TPACK framework (TPACK, Mishra & Koehler, 2006) can be used to develop excellence in teaching in a variety of classrooms, which includes differentiation of instruction. In order to examine how the quality... more
In this paper, we argue that the TPACK framework (TPACK, Mishra & Koehler, 2006) can be used to develop excellence in teaching in a variety of classrooms, which includes differentiation of instruction. In order to examine how the quality of differentiation changes as TPACK improves, 150 lesson plans of pre-service special educators were assessed using TPACK Levels Rubric (Lyublinskaya & Tournaki, 2012). Two lesson plans were randomly selected at each level of TPACK (with total of eight) and examined for evidence of differentiation of instruction. The study describes how strategies used for differentiation parallel the levels of TPACK that were achieved by each participant. Purpose The academic performance of students with disabilities is of concern to policy makers and educators since they exhibit poorer academic performance than their peers without disabilities (Wei, 2012). Therefore, teacher education programs need to be preparing effective special educators who will increase the ...
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The lab activities developed to introduce logistic model utilize prototype of the Texas Instrument Corporation's latest (not yet publicly released) handheld hardware/software package called TI-Nspire CAS. This revolutionary... more
The lab activities developed to introduce logistic model utilize prototype of the Texas Instrument Corporation's latest (not yet publicly released) handheld hardware/software package called TI-Nspire CAS. This revolutionary technology represents not only a new ...
Proficiency of integrating educational technology into teaching is now seen as an important qualification for elementary school teachers. We integrated Texas Instruments graphing calculators and Vernier data collection technology in our... more
Proficiency of integrating educational technology into teaching is now seen as an important qualification for elementary school teachers. We integrated Texas Instruments graphing calculators and Vernier data collection technology in our undergraduate science ...
Abstract: To prepare teachers to use technology in teaching, calculator technology was integrated into a double-sectioned science methods course. The purpose of this study was to find out how preservice teachers' confidence in the... more
Abstract: To prepare teachers to use technology in teaching, calculator technology was integrated into a double-sectioned science methods course. The purpose of this study was to find out how preservice teachers' confidence in the use of calculator technology was ...
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Abstract: Supported by the CUNY College Now technology initiative five science and mathematics high school teachers were provided with intensive 5-days summer training in TI technology and with course specific classroom equipment that... more
Abstract: Supported by the CUNY College Now technology initiative five science and mathematics high school teachers were provided with intensive 5-days summer training in TI technology and with course specific classroom equipment that included various calculator ...
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Abstract: The pressure to provide qualified teachers for all students has resulted in reform efforts, including the upgrading of credential and course requirements, as well as the proliferation of so-called alternative routes to teacher... more
Abstract: The pressure to provide qualified teachers for all students has resulted in reform efforts, including the upgrading of credential and course requirements, as well as the proliferation of so-called alternative routes to teacher certification, which seek to create ...
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This study examined the development of Technological Pedagogical Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. The course focused on the three domains of knowledge related... more
This study examined the development of Technological Pedagogical Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. The course focused on the three domains of knowledge related specifically to integrating instructional technology into mathematics and science teaching and learning namely, Technological Content Knowledge (TCK), Technological Pedagogical Knowledge (TPK) and TPACK. The Survey of Pre-service Teachers’ Knowledge of Teaching and Technology developed by Schmidt et al. (2009) was used to measure pre-service teachers’ perceptions of knowledge. A paired t-test revealed that upon completion of the course requirements, students perceived themselves to have had significant gains in each of the domains of teacher knowledge addressed in the course - effect sizes were large (between .69 and 1.10). Further, significant gains were also found in the area of Pedagogical Content Knowledge (PCK) but with moderate effect size.
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This study focuses on the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. TPACK development is measured through a survey... more
This study focuses on the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one
course. TPACK development is measured through a survey (teachers’ perceptions of knowledge) and lesson plans (teachers’ artifacts). Paired samples t-test revealed that upon completion of the course requirements, the participants’ TPACK scores increased significantly in regards to their perceptions as well as their lesson plans. Correlations between the two measures were not significant leading to a discussion about assessing constructs through measures of self–perception and teaching artifacts. Factor analysis of the survey raises questions about the domains of knowledge of the TPACK framework. Implications for teacher education programs are discussed.
course. TPACK development is measured through a survey (teachers’ perceptions of knowledge) and lesson plans (teachers’ artifacts). Paired samples t-test revealed that upon completion of the course requirements, the participants’ TPACK scores increased significantly in regards to their perceptions as well as their lesson plans. Correlations between the two measures were not significant leading to a discussion about assessing constructs through measures of self–perception and teaching artifacts. Factor analysis of the survey raises questions about the domains of knowledge of the TPACK framework. Implications for teacher education programs are discussed.
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The present study focuses on the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. This course provides an introduction to a variety... more
The present study focuses on the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. This course provides an introduction to a variety of strategies and techniques for using instructional technology in teaching concepts in science and mathematics to children with
learning and behavior disabilities. The TPACK Levels Rubric developed by Lyublinskaya and Tournaki (2011) was used to assess participants’ lesson plans created as part of the required course work at the beginning and at the end of the semester. The t-test revealed that upon completion of the course requirements, the participants’ TPACK scores increased significantly between lesson plan 1 and 2, but still the highest level of TPACK remained quite low, i.e. with the score of 2 out of 5. Implications for teacher education programs are discussed.
learning and behavior disabilities. The TPACK Levels Rubric developed by Lyublinskaya and Tournaki (2011) was used to assess participants’ lesson plans created as part of the required course work at the beginning and at the end of the semester. The t-test revealed that upon completion of the course requirements, the participants’ TPACK scores increased significantly between lesson plan 1 and 2, but still the highest level of TPACK remained quite low, i.e. with the score of 2 out of 5. Implications for teacher education programs are discussed.
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A year-long PD program was provided to four teachers teaching integrated algebra in a New York City Title I public school. The PD comprised teacher authoring of a curriculum that incorporated TI-NspireÔ technology. Teacher TPACK levels... more
A year-long PD program was provided to four teachers teaching integrated algebra in a New York City Title I public school. The PD comprised teacher authoring of a curriculum that incorporated
TI-NspireÔ technology. Teacher TPACK levels of development were measured through a TPACK Levels Rubric, created and validated by the authors. The rubric was used to assess the
teachers’ written artifacts and observed behaviors. Results indicated that the pattern of change in a given teacher’s TPACK level over the period of a school year was non-linear. The classroom teaching was either at the same level or lower than the TPACK level of the corresponding lesson plan. The students performed better in the courses taught by the teachers with higher TPACK
TI-NspireÔ technology. Teacher TPACK levels of development were measured through a TPACK Levels Rubric, created and validated by the authors. The rubric was used to assess the
teachers’ written artifacts and observed behaviors. Results indicated that the pattern of change in a given teacher’s TPACK level over the period of a school year was non-linear. The classroom teaching was either at the same level or lower than the TPACK level of the corresponding lesson plan. The students performed better in the courses taught by the teachers with higher TPACK
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TI-NspireÔ technology, a new generation of graphing calculators, was integrated into high school integrated algebra curriculum. Four teacher-participants were supported through a yearlong professional development emphasizing the use of... more
TI-NspireÔ technology, a new generation of graphing calculators, was integrated into high school integrated algebra curriculum. Four teacher-participants were supported through a yearlong
professional development emphasizing the use of technology through an inquiry based approach. The data included the teachers’ perceptions about TI-Nspire technology, teachers’ proficiency with TI-Nspire technology, quality of instruction determined through classroom observations, and the frequency of technology use in the classroom based on questionnaire completed by the students. Data analysis indicates that there is a significant positive correlation between quality of instructional practice, quality of use of technology, and teachers’ level of TPACK. In general, teachers with better perceptions used technology in the classroom more frequently, were more proficient
with the technology, had higher quality of instructions, and higher level of TPACK. Implications on years of experience and pre-service training are discussed.
professional development emphasizing the use of technology through an inquiry based approach. The data included the teachers’ perceptions about TI-Nspire technology, teachers’ proficiency with TI-Nspire technology, quality of instruction determined through classroom observations, and the frequency of technology use in the classroom based on questionnaire completed by the students. Data analysis indicates that there is a significant positive correlation between quality of instructional practice, quality of use of technology, and teachers’ level of TPACK. In general, teachers with better perceptions used technology in the classroom more frequently, were more proficient
with the technology, had higher quality of instructions, and higher level of TPACK. Implications on years of experience and pre-service training are discussed.
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In this paper two lab activities that can be used to introduce logistic model to the students taking various mathematics courses from Algebra to Calculus are discussed.
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Proficiency of integrating educational technology into teaching is now seen as an important qualification for elementary school teachers. We integrated Texas Instruments graphing calculators and Vernier data collection technology in... more
Proficiency of integrating educational technology into teaching
is now seen as an important qualification for elementary school
teachers. We integrated Texas Instruments graphing calculators
and Vernier data collection technology in our undergraduate
science methods classes for pre-service elementary school
teachers. The study purposes were set up to find out whether
pre-service teachers’ knowledge and comfort with the use of
graphing calculator technology was influenced by the
integration of this technology into the methods course and
whether pre-service teachers’ perspectives of using graphing
calculator technology for their own learning and as a teaching
tool evolved during the methods course? Data collected from
surveys and reflection journals show that pre-service teachers’
perspectives strongly depended on the intensity and length of
experience they had with the use of the technology. More
experience and practice provides pre-service teachers with a
better understanding of the benefits of technology for their
future students as well as for their own learning. However, their
confidence was somewhat independent to their perspectives.
They could perceive this technology very useful, but they were
not confident to use it
is now seen as an important qualification for elementary school
teachers. We integrated Texas Instruments graphing calculators
and Vernier data collection technology in our undergraduate
science methods classes for pre-service elementary school
teachers. The study purposes were set up to find out whether
pre-service teachers’ knowledge and comfort with the use of
graphing calculator technology was influenced by the
integration of this technology into the methods course and
whether pre-service teachers’ perspectives of using graphing
calculator technology for their own learning and as a teaching
tool evolved during the methods course? Data collected from
surveys and reflection journals show that pre-service teachers’
perspectives strongly depended on the intensity and length of
experience they had with the use of the technology. More
experience and practice provides pre-service teachers with a
better understanding of the benefits of technology for their
future students as well as for their own learning. However, their
confidence was somewhat independent to their perspectives.
They could perceive this technology very useful, but they were
not confident to use it
Research Interests:
We examine elementary school teachers’ prior understandings of concept of fractions within different contexts. We argue that teacher' understanding on fractions significantly improves when they are offered opportunities to investigate... more
We examine elementary school teachers’ prior understandings of concept of fractions within different contexts. We argue that teacher' understanding on fractions significantly improves when they are offered opportunities to investigate fractions in new context, specifically, in the situations when they cannot rely on familiar procedural approaches. This leads to cognitive conflict when approaching problems involving both, continuous quantities and wholes consisting of several objects. These situations arise when problems related to Egyptian fraction are introduced to the pre-service teachers. Investigations of these problems have led to deeper conceptual understanding of fair share concept, fractions comparison, relations between different wholes, fractions part-part-whole representations (bigger fraction represented as sum of smaller fractions), connection of different fraction representations with numerical measure (number of cuts), and- to understanding of why Egyptians used unit fraction representation.
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Supported by the CUNY College Now technology initiative five science and mathematics high school teachers were provided with intensive 5-days summer training in TI technology and with course specific classroom equipment that included... more
Supported by the CUNY College Now technology initiative five science and mathematics high school teachers were provided with intensive 5-days summer training in TI technology and with
course specific classroom equipment that included various calculator based technology, such as classroom sets of graphing calculators, Vernier data collection probes and interfaces, and TI-Navigator wireless classroom learning systems to be used in their classrooms during the 2006/2007 school year. The use of these technologies by students and teachers were studied through pre and post surveys, observations, and reflective journals. The study found that while many high school students were initially proficient in basic use of TI technology, they were not familiar with various intermediate and advanced features of graphing calculators and data collection probes. The use of these technologies in the classroom was crucial for students to acquire more advanced skills in these technologies. The more often and appropriate these technologies were used in the classroom, the more confident students were in using them at more sophisticated level for problem solving and real-life applications in both,
mathematics and science courses. This study also demonstrates that gender difference in the use of technology could be significantly reduced through intensive use of technology in the classroom.
course specific classroom equipment that included various calculator based technology, such as classroom sets of graphing calculators, Vernier data collection probes and interfaces, and TI-Navigator wireless classroom learning systems to be used in their classrooms during the 2006/2007 school year. The use of these technologies by students and teachers were studied through pre and post surveys, observations, and reflective journals. The study found that while many high school students were initially proficient in basic use of TI technology, they were not familiar with various intermediate and advanced features of graphing calculators and data collection probes. The use of these technologies in the classroom was crucial for students to acquire more advanced skills in these technologies. The more often and appropriate these technologies were used in the classroom, the more confident students were in using them at more sophisticated level for problem solving and real-life applications in both,
mathematics and science courses. This study also demonstrates that gender difference in the use of technology could be significantly reduced through intensive use of technology in the classroom.
Research Interests:
To prepare teachers to use technology in teaching, calculator technology was integrated into a double-sectioned science methods course. The purpose of this study was to find out how pre-service teachers' confidence in the use of... more
To prepare teachers to use technology in teaching, calculator technology was integrated into a double-sectioned science methods course. The purpose of this study was to find out how pre-service teachers' confidence in the use of calculator technology was influenced by this methods course and how their perspectives of using calculator technology evolved through the course. Data collected from surveys and reflection journals show that pre-service teachers' perspectives strongly depended on the intensity and length of experience they had with the use of technology. More experience and practice provides pre-service teachers with a better understanding of the benefits of technology for their future students as well as for their own learning. However, pre-service teachers' confidence in the use of calculator technology was somewhat independent to their perspectives. In other words, pre-service teachers could perceive technology very useful, but they were not confident to use it.
Research Interests:
A year-long PD program was provided to four NYC integrated algebra teachers. The PD comprised of teacher authoring of curriculum that incorporated TI-Nspire technology. Teacher TPACK levels were measured through a TPACK Levels Rubric,... more
A year-long PD program was provided to four NYC integrated algebra teachers. The PD comprised of teacher authoring of curriculum that incorporated TI-Nspire technology. Teacher TPACK levels were measured through a TPACK Levels Rubric, created and validated by the authors. The rubric was used
to assess the teachers’ written artifacts (lesson plans and authored curriculum materials) and observed behaviors (PD presentations and classroom teaching through observations). Results indicated that, first teachers’ TPACK scores for written artifacts paralleled those of PD presentations. Second, the classroom teaching was either at the same level or lower than written artifacts. Third, teachers did not improve with every lesson they developed; instead, their scores vacillated within the two or three lower TPACK levels. Finally, the students taught by the teachers with higher TPACK level had higher average score
on the NYS Regents exam and higher passing rates.
to assess the teachers’ written artifacts (lesson plans and authored curriculum materials) and observed behaviors (PD presentations and classroom teaching through observations). Results indicated that, first teachers’ TPACK scores for written artifacts paralleled those of PD presentations. Second, the classroom teaching was either at the same level or lower than written artifacts. Third, teachers did not improve with every lesson they developed; instead, their scores vacillated within the two or three lower TPACK levels. Finally, the students taught by the teachers with higher TPACK level had higher average score
on the NYS Regents exam and higher passing rates.
Research Interests:
This chapter describes a process for the implementation of data collection technology that the authors introduced into the science and mathematics methods courses for preservice elementary-school teachers in a public, urban college. The... more
This chapter describes a process for the implementation of data collection technology that the authors introduced into the science and mathematics methods courses for preservice elementary-school teachers in a public, urban college. The curriculum of the methods courses was developed to include inquiry-based
lab activities that utilize probeware and various data collection interfaces. The lesson plans and the reflections that the authors collected from the 124 preservice teachers over three semesters show that the courses not only exposed them to a variety of data collection instruments, but also changed their attitudes and confidence levels about using such technology in the classroom. The results of this project suggest that preservice teachers perceive data collection technology as a tool for the clear demonstration of otherwise hard to teach science and mathematics concepts to their students. After using data collection technology in their method courses, preservice teachers were able to create their own inquiry-based activities, in which their students were involved in collecting real time data, generating hypotheses, analyzing data, and drawing conclusions. The data collected from the preservice teachers also showed that they needed more experience and practice to better understand the benefits of this type of technology for their future students as well as for their own learning.
lab activities that utilize probeware and various data collection interfaces. The lesson plans and the reflections that the authors collected from the 124 preservice teachers over three semesters show that the courses not only exposed them to a variety of data collection instruments, but also changed their attitudes and confidence levels about using such technology in the classroom. The results of this project suggest that preservice teachers perceive data collection technology as a tool for the clear demonstration of otherwise hard to teach science and mathematics concepts to their students. After using data collection technology in their method courses, preservice teachers were able to create their own inquiry-based activities, in which their students were involved in collecting real time data, generating hypotheses, analyzing data, and drawing conclusions. The data collected from the preservice teachers also showed that they needed more experience and practice to better understand the benefits of this type of technology for their future students as well as for their own learning.
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Teachers are searching through an overwhelming mountain of information labeled "Common Core" to find materials and activities that will be helpful in implementing the standards with their students. This group of apps consists of... more
Teachers are searching through an overwhelming mountain of information labeled "Common Core" to find materials and activities that will be helpful in implementing the standards with their students.
This group of apps consists of simple, short, and focused interactive demonstrations and explorations that are designed to help students master the important concepts of a single standard.""
This group of apps consists of simple, short, and focused interactive demonstrations and explorations that are designed to help students master the important concepts of a single standard.""
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Research Interests:
Research Interests:
The purpose of this book is to use Geometry Expressions software in order to facilitate and enhance the calculus syllabus by allowing students to ground calculus concepts in a geometric way. The 29 student explorations in this book cover... more
The purpose of this book is to use Geometry Expressions software in order to facilitate and enhance the calculus syllabus by allowing students to ground calculus concepts in a geometric way. The 29 student explorations in this book cover the major topics of a standard course of calculus, and are completed with the help of the constraint-based dynamic software package, Geometry Expressions. Using Geometry Expressions in learning calculus, students have the opportunity to develop general investigation skills, make connections between geometric and algebraic representations of major calculus ideas, interpret analytic problems visually and geometric problems algebraically, and develop facility with using a computer to prove general mathematics statements. Geometry Expressions enables more extensive calculus investigation than is possible in a traditional course of calculus.
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We wrote this book with the hope to help teachers to engage their students in learning geometry and encourage them in their development of logical thinking. This book offers 43 interesting geometry problems that resulted from a... more
We wrote this book with the hope to help teachers to engage their students in learning geometry and encourage them in their development of logical thinking. This book offers 43 interesting geometry problems that resulted from a collaboration of Russian and American educators. They reflect the content of the standard high school curriculum. Altogether these problems demonstrate the most important methods of geometry. The unique features of these problems include use of symbolic geometry software, Geometry Expressions. Each problem includes student black line master and detailed teacher notes with solutions, proofs, and steps for working with Geometry Expressions.
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Research Interests:
From the back cover: Our goal was to use Geometry Expressions to develop a set of problems for second year algebra and/or precalculus courses addressing the topics of geometric transformations of functions and optimization. In this volume... more
From the back cover: Our goal was to use Geometry Expressions to develop a set of problems for second year algebra and/or precalculus courses addressing the topics of geometric transformations of functions and optimization. In this volume you will find eight interactive problems with different levels of difficulty. In each problem the main focus is on the development of the students ability to recognize and make connections using multiple representations of the same object, such as geometric shape and function. By connecting geometric and algebraic representations the student develops a more thorough understanding of the problem.
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This book offers science experiments for calculus classroom that can help the teacher to make connections between math and science and show students why math is important. The experiments cover important topics of the course, some require... more
This book offers science experiments for calculus classroom that can help the teacher to make connections between math and science and show students why math is important. The experiments cover important topics of the course, some require no special equipment or technology, while other need technology that could already be available in science classrooms. Teacher notes explain in details how to setup experiments and science background for each activity.
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This book offers science experiemnts for precalculus classroom that can help the teacher to make connections between math and science and show students why math is important. The experiments cover important topics of the course, some... more
This book offers science experiemnts for precalculus classroom that can help the teacher to make connections between math and science and show students why math is important. The experiments cover important topics of the course, some require no special equipment or technology, while other need technology that could already be available in science classrooms. Teacher notes explain in details how to setup experiments and science background for each activity.
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TI-Nspire CAS technology by Texas Instruments, USA, is the only dynamic educational system in the world that enables teaching and learning of all levels of secondary school mathematics. In addition, it includes data collection application... more
TI-Nspire CAS technology by Texas Instruments, USA, is the only dynamic educational system in the world that enables teaching and learning of all levels of secondary school mathematics. In addition, it includes data collection application for main science disciplines. The software component of the system supports geometry, algebra, precalculus and calculus, statistics and data collection with probes. In the third article, readers will use features of the Geometry application to solve locus problems.
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TI-Nspire CAS technology by Texas Instruments, USA, is the only dynamic educational system in the world that enables teaching and learning of all levels of secondary school mathematics. In addition, it includes data collection application... more
TI-Nspire CAS technology by Texas Instruments, USA, is the only dynamic educational system in the world that enables teaching and learning of all levels of secondary school mathematics. In addition, it includes data collection application for main science disciplines. The software component of the system supports geometry, algebra, precalculus and calculus, statistics and data collection with probes. In the first article, readers become acquainted with applications Graphs and Calculator using several examples of solving systems equations and inequalities, both graphically and algebraically.
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This article describes how to use Geometer’s Sketchpad version 5 as a dynamic authoring tool for creating demonstrations and investigations of geometry theorems. Fully constructed demonstrations and investigations for the considered... more
This article describes how to use Geometer’s Sketchpad version 5 as a dynamic authoring tool for creating demonstrations and investigations of geometry theorems. Fully constructed demonstrations and investigations for the considered theorems are provided on the journal’s CD, along with used custom tools.
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The paper demonstrates how new symbolic geometry software, Geometry Expressions™ can be used in problems dealing with proofs across secondary school mathematics curriculum. The paper suggests two different approaches of using software in... more
The paper demonstrates how new symbolic geometry software, Geometry Expressions™ can be used in problems dealing with proofs across secondary school mathematics curriculum. The paper suggests two different approaches of using software in proofs. In the first approach the software assists in formulating the conjecture and planning the path to the proof, while in the second approach the software confirms the generalized statements which could be considered as proof.
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Authors consider possibilities of computer support for the high school geometry course with Geometer’s Sketchpad using an example of one problem. Samples of student work are analyzed.
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Research Interests:
It is shown that the finite width of one particle 'energy levels in the system of interacting particles does not change the collective excitation spectrum of the system with an accuracy of the terms proportional to the squared inverse... more
It is shown that the finite width of one particle 'energy levels in the system of interacting particles does not change the collective excitation spectrum of the system with an accuracy of the terms proportional to the squared inverse life time. Macroscopic
characteristics of the system at low temperature contain corrections caused by additional terms in distribution functions.
characteristics of the system at low temperature contain corrections caused by additional terms in distribution functions.