The article titled, “Teaching Mathematics in Project- Based Learning Context: Initial Teacher Knowledge and Perceived Needs”, is collaboratively authored by Kim Beswick, Rosemary Callingham and Tracey Muir. This paper attempted to unearth teachers' initial knowledge (pedagogical content knowledge), skills and confidence to teach in a project-based learning context. The data were collected qualitatively, using the conceptual understanding test as an instrument. The conceptual understanding focused on teachers' mathematical content knowledge (quantitative reasoning) and pedagogical content knowledge. Results indicate that most teachers had a reasonable level of mathematical competence and pedagogical content knowledge, however, some of them were skeptical about their in-depth mathematical content knowledge to teach in a project-based learning context.

Project-based learning, a teaching methodology that utilizes student-centered projects to facilitate student learning is touted as superior to traditional teaching methods in improving problem solving and thinking skills, and engaging students in their learning (Berends,Boersma &Weggemann, 2003; Scarborough, Bresnen, Edelmann, Laurent, Newell & Swann, 2004; Tsang, 1997). This learning system enhances students' creativity, thinking ability, connectivity, communication skills, and ability to work collaboratively to solve problems, and then to discuss and reflect on what they learned.

The conventional teaching and learning of the mathematics begin with symbols and notations, are top choices in mathematics instruction for decades. These lead students failing to understand the key concepts of mathematics. Teachers focus more on the procedures rather than underlying concepts (Zachariades, 2007). It has become merely a list of procedures to follow and results only in usual routine in algebraic manipulations. As a result, students develop the skills of algebraic manipulation and memorizing the formulae instead of conceptual understanding. Students acquired an instrumental knowledge, an ability to apply rules without really understanding what they are doing. Thus, it’s paramount for a significant paradigm shift from the conventional teaching and learning approaches to contemporary teaching and approaches to meet the demand of 21st-century education.

Teaching in the context of project-based learning needs not only in-depth relevant content knowledge but also how students learn, understand and make the knowledge accessible to learners with the integration of technology. Moreover, in the transit from conventional teaching and learning to contemporary approach (project-based learning), teachers' philosophy of teaching should change. The article explicitly stated teacher should be a facilitator instead of instead of teaching. He /she should be confident to facilitate learning mathematics in a project-based learning context. Thus, the transition to project-based learning requires an increase in teachers’ mathematics content knowledge, pedagogical content knowledge and technological pedagogical content knowledge and self-efficacy and confidence while facilitating project-based learning.

The researchers used different instruments like questionnaires and conceptual understanding test to unearth teachers’ mathematics content knowledge, pedagogical content knowledge and their confidence in facilitating the project-based learning and its desired outcomes. Researchers asserted that to facilitate project-based learning, the teacher must possess strong content knowledge, pedagogical content knowledge and beliefs system compatible with a constructivist approach to teaching and learning. Most of the aforementioned requirements are easily not met.

In the project-based learning contexts, the teacher needs to understand the relevant content knowledge and relational understanding of the content to apply the knowledge. However, the research finding revealed that most of the teachers of that particular school lacked the conceptual/relational understanding of the content. None of the teachers had any qualification for teaching secondary mathematics. Moreover, some of them hold alternative or incomplete conceptions of subject matter. Their knowledge of the concepts and the process skills addressed by a project may not be sufficient to distill the concepts the project addresses, identify possible links between the central ideas in the project and other concepts in the subject area covered in the curriculum, or recognize ways other disciplines can be incorporated into projects. Thus, the implementation of project-based learning in our context also requires an increase in content knowledge, focusing more on enhancing the relational knowledge instead of instrumental knowledge.

Teachers may have sufficient understanding of the concepts, but may not have pedagogical content knowledge of probable alternatives; possible misconceptions of students; or activities, explanations, demonstrations, and analogies that can provide powerful illustrations of the concepts. Also, they may not be adept at modeling thinking and problem-solving strategies or scaffolding instruction in ways that progressively release responsibilities to students. Moreover, the finding indicated that most of the teachers lack the pedagogical content knowledge to teach quantitative reasoning in the project-based learning context. Most teachers expressed a need for professional development to enhance their pedagogical content knowledge in relation to quantitative reasoning to facilitate project-based learning. Thus, the transition to project-based learning requires an increase in teachers’ pedagogical content knowledge on different mathematical topics and another discipline.

Teachers' beliefs regarding their role, the goals of schooling, and how students learn are frequently antithetical to the assumptions underlying project-based instructional approaches. Teachers often view learning as a process of obtaining information rather than an active process of knowledge construction; they often view motivation simply as a problem of developing positive attitudes rather than enhancing cognitive engagement. Thus, they often select tasks with the goal of providing something interesting for students to do and give less attention to achieving cognitive goals. The researchers also articulated that teacher will take a longer time to develop the confidence to teach in the context of project-based learning as most of them are at the verge of transforming their beliefs from traditional content and text-booked oriented to project-based learning. The project-based learning can be instituted in our education system provided; teachers work zealously and re-conceptualize theirs as a facilitator of individual students' learning process.

In the article, researcher though intensively investigated the mathematical content, pedagogical content knowledge and their beliefs and confidence to facilitate project-based learning; however they fail to investigate the teachers’ technological pedagogical content knowledge. The 21st-century learners are digital natives, so it’s paramount for the facilitator to possessed required technological pedagogical content knowledge.TPACK emphasizes the connections among technologies, curriculum content, and specific pedagogical approaches, demonstrating how teachers’ understandings of technology, pedagogy, and content can interact with one another to produce effective discipline-based teaching. The technology can help develop an understanding of abstract mathematical concepts through visualization. Moreover, technology often reveals mathematical results simply and clearly. Bert Waits, co-founder of T3 (Teachers Teaching with Technology) mention that technology is a great pedagogical tool as it offers the multi-representational approaches in teaching and learning of mathematics. Tiwari (2007) also found that students who were taught with technology are more like likely to achieve a conceptual/relational understanding. Thus, PACK one of the important pre-requisite for teachers to facilitate project-based learning.

In nutshell, teaching mathematics in project-based context required strong content knowledge, pedagogical content knowledge, technological pedagogical content knowledge, and beliefs and confidence to facilitate project-based learning. Though, many studies supported that project-based learning is an effective means of reaching student mastery of curricular content and greater gains in content knowledge, skills than their traditionally taught peer, however failure to possess all the aforementioned skills and knowledge by the facilitator may result in failing the project-based learning. Thus, teachers need to work extra mile to acquire the aforementioned skills and knowledge, so that we can bring visible and quality change in our education system.

 

 

References

Parrot, M. A. S., & Eu, K. L. (2014). Teaching and Learning Calculus in Secondary Schools with the TI-Nspire. The Malaysian Online Journal of Educational Science (MOJES), 2(1), 27–33. Retrieved from http://files.eric.ed.gov/fulltext/EJ1086249.pdf

 

Zachariades, T., Pamfilos, P., Christou, C., Maleev, R., & Jones, K. (2007). Teaching Introductory Calculus: approaching key ideas with dynamic software. CETL–MSOR Conference 2007 on Excellence in the Teaching & Learning of Maths, Stats & OR, (September), 9. Retrieved from https://eprints.soton.ac.uk/50741/1/Jones-etc_teach_calculus_software_2007.pdf

The article titled, “Teaching Mathematics in Project- Based Learning Context: Initial Teacher Knowledge and Perceived Needs”, is collaboratively authored by Kim Beswick, Rosemary Callingham and Tracey Muir. This paper attempted to unearth teachers' initial knowledge (pedagogical content knowledge), skills and confidence to teach in a project-based learning context. The data were collected qualitatively, using the conceptual understanding test as an instrument. The conceptual understanding focused on teachers' mathematical content knowledge (quantitative reasoning) and pedagogical content knowledge. Results indicate that most teachers had a reasonable level of mathematical competence and pedagogical content knowledge, however, some of them were skeptical about their in-depth mathematical content knowledge to teach in a project-based learning context.

Project-based learning, a teaching methodology that utilizes student-centered projects to facilitate student learning is touted as superior to traditional teaching methods in improving problem solving and thinking skills, and engaging students in their learning (Berends,Boersma &Weggemann, 2003; Scarborough, Bresnen, Edelmann, Laurent, Newell & Swann, 2004; Tsang, 1997). This learning system enhances students' creativity, thinking ability, connectivity, communication skills, and ability to work collaboratively to solve problems, and then to discuss and reflect on what they learned.

The conventional teaching and learning of the mathematics begin with symbols and notations, are top choices in mathematics instruction for decades. These lead students failing to understand the key concepts of mathematics. Teachers focus more on the procedures rather than underlying concepts (Zachariades, 2007). It has become merely a list of procedures to follow and results only in usual routine in algebraic manipulations. As a result, students develop the skills of algebraic manipulation and memorizing the formulae instead of conceptual understanding. Students acquired an instrumental knowledge, an ability to apply rules without really understanding what they are doing. Thus, it’s paramount for a significant paradigm shift from the conventional teaching and learning approaches to contemporary teaching and approaches to meet the demand of 21st-century education.

Teaching in the context of project-based learning needs not only in-depth relevant content knowledge but also how students learn, understand and make the knowledge accessible to learners with the integration of technology. Moreover, in the transit from conventional teaching and learning to contemporary approach (project-based learning), teachers' philosophy of teaching should change. The article explicitly stated teacher should be a facilitator instead of instead of teaching. He /she should be confident to facilitate learning mathematics in a project-based learning context. Thus, the transition to project-based learning requires an increase in teachers’ mathematics content knowledge, pedagogical content knowledge and technological pedagogical content knowledge and self-efficacy and confidence while facilitating project-based learning.

The researchers used different instruments like questionnaires and conceptual understanding test to unearth teachers’ mathematics content knowledge, pedagogical content knowledge and their confidence in facilitating the project-based learning and its desired outcomes. Researchers asserted that to facilitate project-based learning, the teacher must possess strong content knowledge, pedagogical content knowledge and beliefs system compatible with a constructivist approach to teaching and learning. Most of the aforementioned requirements are easily not met.

In the project-based learning contexts, the teacher needs to understand the relevant content knowledge and relational understanding of the content to apply the knowledge. However, the research finding revealed that most of the teachers of that particular school lacked the conceptual/relational understanding of the content. None of the teachers had any qualification for teaching secondary mathematics. Moreover, some of them hold alternative or incomplete conceptions of subject matter. Their knowledge of the concepts and the process skills addressed by a project may not be sufficient to distill the concepts the project addresses, identify possible links between the central ideas in the project and other concepts in the subject area covered in the curriculum, or recognize ways other disciplines can be incorporated into projects. Thus, the implementation of project-based learning in our context also requires an increase in content knowledge, focusing more on enhancing the relational knowledge instead of instrumental knowledge.

Teachers may have sufficient understanding of the concepts, but may not have pedagogical content knowledge of probable alternatives; possible misconceptions of students; or activities, explanations, demonstrations, and analogies that can provide powerful illustrations of the concepts. Also, they may not be adept at modeling thinking and problem-solving strategies or scaffolding instruction in ways that progressively release responsibilities to students. Moreover, the finding indicated that most of the teachers lack the pedagogical content knowledge to teach quantitative reasoning in the project-based learning context. Most teachers expressed a need for professional development to enhance their pedagogical content knowledge in relation to quantitative reasoning to facilitate project-based learning. Thus, the transition to project-based learning requires an increase in teachers’ pedagogical content knowledge on different mathematical topics and another discipline.

Teachers' beliefs regarding their role, the goals of schooling, and how students learn are frequently antithetical to the assumptions underlying project-based instructional approaches. Teachers often view learning as a process of obtaining information rather than an active process of knowledge construction; they often view motivation simply as a problem of developing positive attitudes rather than enhancing cognitive engagement. Thus, they often select tasks with the goal of providing something interesting for students to do and give less attention to achieving cognitive goals. The researchers also articulated that teacher will take a longer time to develop the confidence to teach in the context of project-based learning as most of them are at the verge of transforming their beliefs from traditional content and text-booked oriented to project-based learning. The project-based learning can be instituted in our education system provided; teachers work zealously and re-conceptualize theirs as a facilitator of individual students' learning process.

In the article, researcher though intensively investigated the mathematical content, pedagogical content knowledge and their beliefs and confidence to facilitate project-based learning; however they fail to investigate the teachers’ technological pedagogical content knowledge. The 21st-century learners are digital natives, so it’s paramount for the facilitator to possessed required technological pedagogical content knowledge.TPACK emphasizes the connections among technologies, curriculum content, and specific pedagogical approaches, demonstrating how teachers’ understandings of technology, pedagogy, and content can interact with one another to produce effective discipline-based teaching. The technology can help develop an understanding of abstract mathematical concepts through visualization. Moreover, technology often reveals mathematical results simply and clearly. Bert Waits, co-founder of T3 (Teachers Teaching with Technology) mention that technology is a great pedagogical tool as it offers the multi-representational approaches in teaching and learning of mathematics. Tiwari (2007) also found that students who were taught with technology are more like likely to achieve a conceptual/relational understanding. Thus, PACK one of the important pre-requisite for teachers to facilitate project-based learning.

In nutshell, teaching mathematics in project-based context required strong content knowledge, pedagogical content knowledge, technological pedagogical content knowledge, and beliefs and confidence to facilitate project-based learning. Though, many studies supported that project-based learning is an effective means of reaching student mastery of curricular content and greater gains in content knowledge, skills than their traditionally taught peer, however failure to possess all the aforementioned skills and knowledge by the facilitator may result in failing the project-based learning. Thus, teachers need to work extra mile to acquire the aforementioned skills and knowledge, so that we can bring visible and quality change in our education system.

 

 

References

Parrot, M. A. S., & Eu, K. L. (2014). Teaching and Learning Calculus in Secondary Schools with the TI-Nspire. The Malaysian Online Journal of Educational Science (MOJES), 2(1), 27–33. Retrieved from http://files.eric.ed.gov/fulltext/EJ1086249.pdf

 

Zachariades, T., Pamfilos, P., Christou, C., Maleev, R., & Jones, K. (2007). Teaching Introductory Calculus: approaching key ideas with dynamic software. CETL–MSOR Conference 2007 on Excellence in the Teaching & Learning of Maths, Stats & OR, (September), 9. Retrieved from https://eprints.soton.ac.uk/50741/1/Jones-etc_teach_calculus_software_2007.pdf

The article titled, “Teaching Mathematics in Project- Based Learning Context: Initial Teacher Knowledge and Perceived Needs”, is collaboratively authored by Kim Beswick, Rosemary Callingham and Tracey Muir. This paper attempted to unearth teachers' initial knowledge (pedagogical content knowledge), skills and confidence to teach in a project-based learning context. The data were collected qualitatively, using the conceptual understanding test as an instrument. The conceptual understanding focused on teachers' mathematical content knowledge (quantitative reasoning) and pedagogical content knowledge. Results indicate that most teachers had a reasonable level of mathematical competence and pedagogical content knowledge, however, some of them were skeptical about their in-depth mathematical content knowledge to teach in a project-based learning context.

Project-based learning, a teaching methodology that utilizes student-centered projects to facilitate student learning is touted as superior to traditional teaching methods in improving problem solving and thinking skills, and engaging students in their learning (Berends,Boersma &Weggemann, 2003; Scarborough, Bresnen, Edelmann, Laurent, Newell & Swann, 2004; Tsang, 1997). This learning system enhances students' creativity, thinking ability, connectivity, communication skills, and ability to work collaboratively to solve problems, and then to discuss and reflect on what they learned.

The conventional teaching and learning of the mathematics begin with symbols and notations, are top choices in mathematics instruction for decades. These lead students failing to understand the key concepts of mathematics. Teachers focus more on the procedures rather than underlying concepts (Zachariades, 2007). It has become merely a list of procedures to follow and results only in usual routine in algebraic manipulations. As a result, students develop the skills of algebraic manipulation and memorizing the formulae instead of conceptual understanding. Students acquired an instrumental knowledge, an ability to apply rules without really understanding what they are doing. Thus, it’s paramount for a significant paradigm shift from the conventional teaching and learning approaches to contemporary teaching and approaches to meet the demand of 21st-century education.

Teaching in the context of project-based learning needs not only in-depth relevant content knowledge but also how students learn, understand and make the knowledge accessible to learners with the integration of technology. Moreover, in the transit from conventional teaching and learning to contemporary approach (project-based learning), teachers' philosophy of teaching should change. The article explicitly stated teacher should be a facilitator instead of instead of teaching. He /she should be confident to facilitate learning mathematics in a project-based learning context. Thus, the transition to project-based learning requires an increase in teachers’ mathematics content knowledge, pedagogical content knowledge and technological pedagogical content knowledge and self-efficacy and confidence while facilitating project-based learning.

The researchers used different instruments like questionnaires and conceptual understanding test to unearth teachers’ mathematics content knowledge, pedagogical content knowledge and their confidence in facilitating the project-based learning and its desired outcomes. Researchers asserted that to facilitate project-based learning, the teacher must possess strong content knowledge, pedagogical content knowledge and beliefs system compatible with a constructivist approach to teaching and learning. Most of the aforementioned requirements are easily not met.

In the project-based learning contexts, the teacher needs to understand the relevant content knowledge and relational understanding of the content to apply the knowledge. However, the research finding revealed that most of the teachers of that particular school lacked the conceptual/relational understanding of the content. None of the teachers had any qualification for teaching secondary mathematics. Moreover, some of them hold alternative or incomplete conceptions of subject matter. Their knowledge of the concepts and the process skills addressed by a project may not be sufficient to distill the concepts the project addresses, identify possible links between the central ideas in the project and other concepts in the subject area covered in the curriculum, or recognize ways other disciplines can be incorporated into projects. Thus, the implementation of project-based learning in our context also requires an increase in content knowledge, focusing more on enhancing the relational knowledge instead of instrumental knowledge.

Teachers may have sufficient understanding of the concepts, but may not have pedagogical content knowledge of probable alternatives; possible misconceptions of students; or activities, explanations, demonstrations, and analogies that can provide powerful illustrations of the concepts. Also, they may not be adept at modeling thinking and problem-solving strategies or scaffolding instruction in ways that progressively release responsibilities to students. Moreover, the finding indicated that most of the teachers lack the pedagogical content knowledge to teach quantitative reasoning in the project-based learning context. Most teachers expressed a need for professional development to enhance their pedagogical content knowledge in relation to quantitative reasoning to facilitate project-based learning. Thus, the transition to project-based learning requires an increase in teachers’ pedagogical content knowledge on different mathematical topics and another discipline.

Teachers' beliefs regarding their role, the goals of schooling, and how students learn are frequently antithetical to the assumptions underlying project-based instructional approaches. Teachers often view learning as a process of obtaining information rather than an active process of knowledge construction; they often view motivation simply as a problem of developing positive attitudes rather than enhancing cognitive engagement. Thus, they often select tasks with the goal of providing something interesting for students to do and give less attention to achieving cognitive goals. The researchers also articulated that teacher will take a longer time to develop the confidence to teach in the context of project-based learning as most of them are at the verge of transforming their beliefs from traditional content and text-booked oriented to project-based learning. The project-based learning can be instituted in our education system provided; teachers work zealously and re-conceptualize theirs as a facilitator of individual students' learning process.

In the article, researcher though intensively investigated the mathematical content, pedagogical content knowledge and their beliefs and confidence to facilitate project-based learning; however they fail to investigate the teachers’ technological pedagogical content knowledge. The 21st-century learners are digital natives, so it’s paramount for the facilitator to possessed required technological pedagogical content knowledge.TPACK emphasizes the connections among technologies, curriculum content, and specific pedagogical approaches, demonstrating how teachers’ understandings of technology, pedagogy, and content can interact with one another to produce effective discipline-based teaching. The technology can help develop an understanding of abstract mathematical concepts through visualization. Moreover, technology often reveals mathematical results simply and clearly. Bert Waits, co-founder of T3 (Teachers Teaching with Technology) mention that technology is a great pedagogical tool as it offers the multi-representational approaches in teaching and learning of mathematics. Tiwari (2007) also found that students who were taught with technology are more like likely to achieve a conceptual/relational understanding. Thus, PACK one of the important pre-requisite for teachers to facilitate project-based learning.

In nutshell, teaching mathematics in project-based context required strong content knowledge, pedagogical content knowledge, technological pedagogical content knowledge, and beliefs and confidence to facilitate project-based learning. Though, many studies supported that project-based learning is an effective means of reaching student mastery of curricular content and greater gains in content knowledge, skills than their traditionally taught peer, however failure to possess all the aforementioned skills and knowledge by the facilitator may result in failing the project-based learning. Thus, teachers need to work extra mile to acquire the aforementioned skills and knowledge, so that we can bring visible and quality change in our education system.

 

Parrot, M. A. S., & Eu, K. L. (2014). Teaching and Learning Calculus in Secondary Schools with the TI-Nspire. The Malaysian Online Journal of Educational Science (MOJES), 2(1), 27–33. Retrieved from http://files.eric.ed.gov/fulltext/EJ1086249.pdf

 

Zachariades, T., Pamfilos, P., Christou, C., Maleev, R., & Jones, K. (2007). Teaching Introductory Calculus: approaching key ideas with dynamic software. CETL–MSOR Conference 2007 on Excellence in the Teaching & Learning of Maths, Stats & OR, (September), 9. Retrieved from https://eprints.soton.ac.uk/50741/1/Jones-etc_teach_calculus_software_2007.pdf