scholarly journals Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

2021 ◽  
Author(s):  
◽  
Farzad Radmehr
Keyword(s):  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Metacognitive Knowledge ◽  
First Year ◽  
Tertiary Level ◽  
Integral Calculus ◽  
Fundamental Theorem Of Calculus ◽  
Revised Bloom's Taxonomy ◽  
First Year University ◽  
Metacognitive Experiences

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus.  A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study.  The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

scholarly journals Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

2021 ◽  
Author(s):  
◽  
Farzad Radmehr
Keyword(s):  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Metacognitive Knowledge ◽  
First Year ◽  
Tertiary Level ◽  
Integral Calculus ◽  
Fundamental Theorem Of Calculus ◽  
Revised Bloom's Taxonomy ◽  
First Year University ◽  
Metacognitive Experiences

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus.  A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study.  The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

scholarly journals Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus

2020 ◽  
Vol 10 (3) ◽  
pp. 55
Author(s):  
Farzad Radmehr ◽  
Michael Drake
Keyword(s):  
Problem Solving ◽  
Procedural Knowledge ◽  
Bloom's Taxonomy ◽  
Metacognitive Knowledge ◽  
First Year ◽  
Integral Calculus ◽  
Revised Bloom's Taxonomy ◽  
Bloom’S Taxonomy ◽  
First Year University ◽  
Developing Strategies

Previous studies of integral calculus have mainly explored students’ conceptual and procedural knowledge; only a few have focused on students’ metacognition in relation to integral calculus. The study reported here explored students’ metacognitive knowledge of integral calculus by interviewing nine first-year university and eight Year 13 students. The design of the interview questions was based on the structure of metacognitive knowledge in Revised Bloom’s Taxonomy. The findings suggest there are differences between students’ metacognitive knowledge at Year 13 and the first year of university. In particular, the importance of knowing the rationale behind the theorems and formulas was not obvious for Year 13 students. Moreover, students’ metacognitive knowledge could be developed further at both levels, particularly in terms of developing strategies to identify how integral calculus questions could be solved and to check the outcome of problem-solving.

scholarly journals A Teaching Experience through the use of Tasks: Limits and possibilities for learning Mathematics in a university context

2020 ◽  
Vol 22 (2) ◽  
Author(s):  
Alessandro Ribeiro ◽  
Juliana Paulin
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Teaching Experience ◽  
Analysis Data ◽  
University Teaching ◽  
Mathematical Tasks ◽  
Integral Calculus ◽  
Mathematical Concepts ◽  
Fundamental Theorem Of Calculus ◽  
The University

Context: Rethinking mathematics teaching practices in a university context is an emerging research theme. Objectives: In this article, we aim to discuss the limits and possibilities of using mathematical tasks in the teaching and learning processes of the concepts of Derivative, Integral and the Fundamental Theorem of Calculus. Design: The study is based on a qualitative-interpretative perspective of research, with methodological procedures inspired by a Design-Based Research. Environment and participants: The research was developed with students attending a Functions of a Variable class in a public university in the state of São Paulo. Data collection and analysis: Data were collected through mathematical tasks on Differential and Integral Calculus solved by students. The protocols produced were analysed, pointing out the main aspects identified, which led us to organize categories of analysis and dimensions (i) knowledges mobilized and developed by students in relation to mathematical concepts; (ii) main errors and difficulties presented by students in the development of tasks; (iii) limits and possibilities of the practice of exploratory teaching in the university context. Results: The results reveal aspects that characterize a process of resignifying the mathematical concepts discussed with the students and a deepening of their knowledge about the concepts of the DIC. Conclusions: As future notes, we suggest rethinking university teaching practice, since the study indicated possibilities and potentialities of the use of exploratory tasks in the teaching of Differential and Integral Calculus.

scholarly journals Creative teaching design in STEM: Using graduate learning outcomes to distribute students' existing knowledge in first-year biology practical work groups

2019 ◽  
Vol 16 (3) ◽  
pp. 4-17 ◽  
Author(s):  
Julia Savage ◽  
◽  
Jillian Healy ◽  
Keyword(s):  
Learning Outcomes ◽  
Inclusive Education ◽  
Teaching And Learning ◽  
Work Groups ◽  
Practical Work ◽  
First Year ◽  
Education Practice ◽  
Science Technology ◽  
New Learning ◽  
First Year University

In Australia, a significant number of students enrol in first-year university biology without the benefit of high school biology. In order to help students support each other, the authors of this paper (a central unit academic developer and a biology coordinator of first-year biology) created a classroom activity that facilitated the distribution of the more experienced students of biology throughout the practical work groups. An important feature of this creative design for forming groups, called the GLO Activity in this paper, was the embedding of two of the University’s key teaching and learning priorities within the activity. These were the University’s eight graduate learning outcomes (GLOs) and, inclusive education practice. We discuss creative pedagogies in STEM (Science, Technology, Engineering and Maths) and their link to supporting students in their first year of university study. We explain our scholarly thinking behind the GLO Activity and evaluate its impact. Finally, we reflect on how we, the educators, found satisfaction in thinking deeply to create a new learning structure for a biology practical class that solved one teaching challenge but also met a number of the University’s curriculum principles.

scholarly journals Bridging conceptual gaps for smooth teaching and learning

2019 ◽  
Vol 24 (1-2) ◽  
pp. 126-146
Author(s):  
Haris C. Adhikari
Keyword(s):  
Teaching And Learning ◽  
Professional Communication ◽  
First Year ◽  
Reader Response Theory ◽  
Technical Problems ◽  
Communication Course ◽  
First Semester ◽  
Holistic Approaches ◽  
Revised Bloom's Taxonomy ◽  
Level Of Analysis

This paper primarily aims to reflect on the majority of my students’ inadequacies of using ‘remembering’, ‘understanding’, ‘analyzing’ and ‘evaluating’, four major levels of the Revised Bloom’s Taxonomy (2001), a helpful reading and writing technique included in Kathmandu University’s first year first semester undergraduate compulsory English and professional communication course, of course for the benefit of all the concerned ones—especially for those from the Asian regions whose communication in English reveals a number of linguistic and technical problems. The focus is more on the level of analysis, because the students had more problems regarding this level. My purpose is to make the level of analysis simpler, more systematic and practical, outlining its nature and various forms, and the inadequacies involved on the part of(the) students, analyzing alongside an analysis part of an assignment submitted by one of my students and a short, well known-about text taken from elsewhere. In doing so, I resort to certain assumptions of a body of theories, namely that of social support theory, reader response theory, and Gestalt theory, apart from my (experimental) experiences of teaching the Taxonomy. These assumptions and experiences gave me insights into how contextually analytical responses are safer when compared to shallow critical responses. I found that shorter texts are more helpful in introducing students to the Taxonomy. I also came across realizations about the importance of balance between textual contexts and extensions of mind, about the effectiveness and beauty of heuristic as well as holistic approaches with emphasis on bridging upon the basic conceptual gaps because of which inadequacies and difficulties arise.

scholarly journals A case study: Do discipline-based programmes improve student learning outcomes?

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Robert Kennelly ◽  
Anna Maldoni ◽  
Doug Davies
Keyword(s):  
Learning Strategies ◽  
Teaching And Learning ◽  
English Language ◽  
Language Skills ◽  
Student Assessment ◽  
First Year ◽  
Unique Contribution ◽  
Domestic Students ◽  
Models Of Teaching ◽  
First Year University

This paper contributes to the growing body of knowledge that supports a disciplinebased approach to academic and language development. To address the academic literacy needs of both international English as an Additional Language (EAL) and domestic students, universities are moving from generic to embedded models of teaching. This project was motivated by the realisation that students had unmet needs in terms of the academic competence required for successful tertiary study. This demonstrates a lack of educational integrity on behalf of the universities to ensure that students gain sufficient academic and language skills for success in firstyear university study. This paper reports on the use of a teaching and learning model which demonstrates the effectiveness of embedding the development of academic and language skills within a particular discipline for EAL students and others. The unique contribution of this paper is that it uses a team-taught approach across two disciplines. It shows that discipline management specialists working in conjunction with English language specialists provide a reconsideration of teaching and learning strategies and modes of assessment that lead to better outcomes for both students and staff. Success of the programme was indicated by student assessment, attendance data, student evaluations, and reflection of peer teaching practices. Finally, the paper makes recommendations for the inclusion of embedded programmes in first-year university study using a diagnostic tool to determine specific student needs. Longitudinal studies need to be undertaken to ascertain specifically whether the benefits of discipline-based programmes are sustained in the longer term and additionally why many “at risk” students do not participate in the programme.

scholarly journals Community, Connections and Innovation in Emergency Remote Teaching and Learning

2021 ◽  
pp. 141-168
Author(s):  
Sandra Healy ◽  
Keyword(s):  
Foreign Language ◽  
University Students ◽  
Teaching And Learning ◽  
Online Courses ◽  
Tertiary Education ◽  
First Year ◽  
Academic English ◽  
Community Connections ◽  
First Year University ◽  
The Impact

The emergence of the Covid-19 virus had an enormous impact on all of our lives and significantly affected the lives of first-year university students in Japan who began their tertiary education during the initial lockdown. This chapter examines the impact the move online had on these students by analysing videos created by them as part of their academic English as a Foreign Language (EFL) coursework. The videos were analysed, and 12 themes emerged which were used as a foundation for new practices focusing on the development of community and connections in online courses, particularly the use of e-mentors.

scholarly journals The use of photogrammetric fossil models in palaeontology education

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
John A. Cunningham
Keyword(s):  
University Students ◽  
Teaching And Learning ◽  
Online Survey ◽  
Three Dimensional ◽  
Physical Models ◽  
First Year ◽  
Digital Models ◽  
First Year University

AbstractPhotogrammetry allows overlapping photographs of fossils to be taken and converted into photo-realistic three-dimensional (3-D) digital models. These models offer potential advantages in teaching palaeontology: they are cheap to produce, can be easily shared and allow the study of rare and delicate specimens. Here I describe approaches for using photogrammetric models in the teaching and learning of palaeontology. Little is known about how students perceive these models and whether they find them valuable in their learning. To address this, first-year university students taught using both fossil specimens and digital models were surveyed about their experience through an anonymous online survey. Most students found that the digital models were easy to use, helped them understand anatomy and were more useful than studying photographs. However, most did not see the models as a substitute for studying real fossils and felt they could learn more from physical models. Digital models are a useful addition to palaeontological education that can supplement real fossils and allow palaeontological education to take place in circumstances where handling of specimens is not possible.

scholarly journals Co-constructing a rubric checklist with first year university students

2017 ◽  
Vol 11 (4) ◽  
pp. 35-55 ◽  
Author(s):  
Sharita Bharuthram ◽  
Mahmoud Patel
Keyword(s):  
Design Process ◽  
Teaching And Learning ◽  
Assessment Tool ◽  
Academic Career ◽  
First Year ◽  
Self Assessment ◽  
Guided Practice ◽  
Student Questionnaire ◽  
First Year University

This paper reports on a study in which students co-constructed a rubric checklist with their lecturer and which they used to assess themselves. Data were collected by means of a student questionnaire, tutor feedback, as well as tutors’ and lecturers’ observations to ascertain students’ experiences and opinions of the design process and of using the tool to self-assess. The findings show that co-designing the rubric checklist with students increased their motivation and enhanced students’ confidence in completing the task. In addition, students gained enormous benefits from using the rubric checklist as a self-assessment tool. Reflecting critically on the feedback received from students and tutors the authors argue that for enhanced student engagement in the teaching and learning process they should be involved as active participants in the assessment processes. In addition, students need to learn to assess the quality of their own work early in their academic career with continuous guided practice throughout their studies with the intention of making the practice of self-assessment a norm rather than an exception, thereby creating independent reflective learners.

scholarly journals The impact of Teacher Fellows on teaching and assessment at tertiary level

2016 ◽  
pp. 77-78
Author(s):  
Tim G Harrison ◽  
Dudley E Shallcross
Keyword(s):  
Learning Strategies ◽  
Teaching And Learning ◽  
Teaching Practice ◽  
Secondary School Teachers ◽  
First Year ◽  
Tertiary Level ◽  
Teaching And Learning Strategies ◽  
The Subject ◽  
The Impact ◽  
Insight Into

It is perceived that Outreach activities are primarily conducted to raise the profile of the department and the subject with a view to recruitment. However, we highlight a range of benefits to teaching practice and assessment of practical teaching at tertiary level that can arise from such activities. In particular, engaging with secondary school teachers can provide invaluable insight into successful teaching and learning strategies in particular for first year undergraduates.

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