Instructions:

Write a short (no more than 15 pages, double-spaced, excluding references; 12 point font; 1- margins) literature review that provides background information about a topic/question you are interested in investigating through research; • Include a reference list of all cited work. This may be approximately 10-12 references. While you will not be designing a study, this literature review should provide relevant information about your selected research topic/question. You may think about this as a brief/abbreviated literature review that you would have as 1) part of a research proposal, or 2) part of a publishable manuscript.

The ten articles I have chosen are below. I need to group related/nonrelated articles to come up with a nice literature review. I need a ten-page document, excluding the references.

Introduction and Conclusion

Many students around the world find it difficult in understanding calculus due to many reasons. The following review of literature confirm that students have difficulties in understanding calculus. The review of literature also discusses specific and general solutions to the problem.

1. Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Procedia-Social and Behavioral Sciences, 8, 173-180.

Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010), says that the lack of understanding causes serious obstacle for student globally in learning the concepts of two-variable functions.

The authors presented the obstacles face by the students in learning of two -variable functions through mathematical thinking approach. The data collection in this study was collected from a multivariable calculus for analyses. The data analyses revealed students’ common difficulties were:

Lack of understanding two different symbolic for a concept; selecting appropriate representation of the three worlds of mathematical thinking and met before (previous experience). The authors findings reveal that sketching the graph of two-variable functions in 3- dimensions is the greatest difficulty for majority of students in this method. The authors suggested the mathematical thinking approach for students having difficulties in understanding two-variable functions.

2. Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Studentsâ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2).

Hashemi, N., Abu, M. S., & Kashefi, H. (2019), investigates the reason undergraduate students’ faces difficulties in solving derivative and integral mathematical problems.

The authors provided a test containing derivative and integral problems to sixty-three undergraduate students, and the results was analyzed by qualitative and quantitative methods. The authors provide these as reasons why the students are having difficulties in learning derivatives and integrals:

• Weakness in recalling previous knowledge in entry and attack steps of specialization and generalization

• Weakness in making connection embodied and symbolic worlds of mathematical thinking and using symbolic world rather than embodied world

• Inability to use suitable problem-solving framework.

The authors suggested that there is a need to find suitable mathematical thinking strategy to overcome these difficulties in order to improve students’ abilities in the learning of derivative and integral.

3. Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), 0574.

Sebsibe, A. S., & Feza, N. N. (2019), assessed students’ challenges as it relates to conceptual knowledge in limit of functions. The participants in this study were 238 12th grade students from four different schools in one administrative zone of Ethiopia. An open-ended test about limit of a function at a point and at infinity was administered and analyzed quantitatively and qualitatively. The findings revealed by the authors in this study are:

• The students lack conceptual knowledge in limit of functions

• Lack of procedural knowledge in limit of functions

• Wrong interpretation of symbolic notations

• Lack of coherent and flexibility of reasoning

The authors concluded that, mathematics teachers who teach calculus for beginners should be concerned about the necessary pedagogical content knowledge.

4. Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.

(Hashemi et al., 2015), introduce the modified generalization strategies to improve the undergraduate student’s problem solving in derivative and integral. The authors presented derivatives and integrals with prompts and questions based on mathematical thinking to evaluate the undergraduate students. The authors concluded from this study that these difficulties are due to the followings:

• Weakness in problem solving

• Lack of suitable method

• Weakness of recalling knowledge

• Lack of problem-solving framework

5. Van Dyken, J., & Benson, L. (2019). Precalculus as a Death Sentence for Engineering Majors: A Case Study of How One Student Survived. International Journal of Research in Education and Science, 5(1), 355-373.

Van Dyken, J., & Benson, L. (2019), say precalculus as a death sentence for engineering majors. In this paper, a case study was constructed around a student by the authors using quantitative data from his mathematics and engineering courses, as well as qualitative data in the form of an open-ended survey and interviews. A mathematics instructor, who modeled self-regulation strategies as he served as the student’s mentor, was key to his success in passing the required courses in the calculus sequence. The authors suggested that self-regulated learning strategies and mentors who model them are key for students to pass required courses.

6. Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University).

Rabadi, N. (2015) identified the misconceptions and difficulties in the concepts of function, limits, continuity, and derivatives through existing literature. There were 21 students that partook in this research. Based on the theoretical framework, a collection of problems was created to help students overcome their misconceptions and difficulties. Nazar Rabadi said that the students had these difficulties due to the lack of mathematical knowledge to investigate functions, limits, and derivatives. The author concluded that these students showed improvement in their difficulties and misconceptions and found the collection of problems helpful in overcoming their difficulties and misconceptions.

7. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81-91.

Klymchuk et al., (2010) investigates the difficulties in solving application problems in calculus faced by engineering students. An observational parallel study was conducted simultaneously at two universities located in New Zealand and Germany by the authors. Two groups of students (54 in New Zealand and 50 in Germany) completed a questionnaire about their difficulties in solving the problem which was set as part of a mid-semester test. The authors found out that most of these students had difficulties in solving application problems due to the following reason:

a. The students did not know how to convert the real-life problem into one to solve mathematically b. They were unable to identify the unknown variable c. Difficulties in the identification and usage of the formula d. The students did not know how to do mathematical modelling. Finally, the authors suggested that teachers should teach the students the basic skills in solving application problems from the beginning of a calculus course.

8. Muzangwa, J., & Chifamba, P. (2012). Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students. Acta Didactica Napocensia, 5(2), 1-10.

Muzangwa, J., & Chifamba, P. (2012) analyze errors and misconceptions in an undergraduate course in calculus. The study was based on a group of 10 BEd Mathematics students at Great Zimbabwe University. The authors gathered data using two exercises on calculus 1&2. The analysis of the results from the tests showed that many of the errors were due to knowledge gaps in basic algebra. Besides, the authors also noted that errors and misconceptions in calculus were related to learners’ lack of advanced mathematical thinking since concepts in calculus are intertwined. The authors concluded that analytic concepts should be developed early in a calculus course to overcome the analysis of errors and misconceptions in the learning of calculus.

9. Pierce, V. U., & Kypuros, J. A. (2015). Utilizing an emporium course design to improve calculus readiness of engineering students. American Society for Engineering Education.

Pierce, V. U., & Kypuros, J. A. (2015) introduce utilizing an emporium course design to improve calculus readiness of engineering students. The authors targeted incoming students in engineering and computer science degrees at the University of Texas. Participating students were selected based on a record of participation in pre-calculus classes in high school, but who had not demonstrated their readiness to take calculus, as measured by placement tests and existing credit. According to the authors, the course design uses an emporium method, specially the assessment and learning in knowledge spaces (ALEKS) software. The results in this research conducted by the authors show that calculus placement for most students improve and were significantly more successful at doing so than a traditional pre-calculus class. The authors suggested that calculus 1 instructors need to be improved. The course content heavily emphasized algebra and symbolic manipulation techniques as instructors identified this as a need.

10. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia-Social and Behavioral Sciences, 8, 142-151.

Tambychik, T., & Meerah, T. S. M. (2010) investigate the major mathematics skills and cognitive abilities in learning that caused the difficulties in mathematics problems -solving among students from students’ point of view. According to the authors, the study was carried out on three focused group samples that were selected through purposeful sampling. A mixed qualitative and quantitative approach was used to have a clearer understanding. The authors said that their data findings showed that respondents lacked in many mathematics skills such as number-fact, visual-spatial and information skills. According to the authors, the deficiency of these mathematics skills and of cognitive abilities in learning inhibits the mathematics problem-solving. Finally, the authors recommended that for the students to over come these challenges, the understanding of the difficulties faced by students in any particular area and phase is the strategy to respond to this issue. Based on the understanding, it could provide a guideline for teachers or researchers to plan better approaches and effective teaching methods.

References

1. Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Procedia-Social and Behavioral Sciences, 8, 173-180

2. Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Studentsâ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2).

3. Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), 0574.

4. Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.

5. Van Dyken, J., & Benson, L. (2019). Precalculus as a Death Sentence for Engineering Majors: A Case Study of How One Student Survived. International Journal of Research in Education and Science, 5(1), 355-373.

6. Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University).

7. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81-91.

8. Muzangwa, J., & Chifamba, P. (2012). Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students. Acta Didactica Napocensia, 5(2), 1-10.

9. Pierce, V. U., & Kypuros, J. A. (2015). Utilizing an emporium course design to improve calculus readiness of engineering students. American Society for Engineering Education.

10. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia-Social and Behavioral Sciences, 8, 142-151.

Write a short (no more than 15 pages, double-spaced, excluding references; 12 point font; 1- margins) literature review that provides background information about a topic/question you are interested in investigating through research; • Include a reference list of all cited work. This may be approximately 10-12 references. While you will not be designing a study, this literature review should provide relevant information about your selected research topic/question. You may think about this as a brief/abbreviated literature review that you would have as 1) part of a research proposal, or 2) part of a publishable manuscript.

The ten articles I have chosen are below. I need to group related/nonrelated articles to come up with a nice literature review. I need a ten-page document, excluding the references.

Introduction and Conclusion

Many students around the world find it difficult in understanding calculus due to many reasons. The following review of literature confirm that students have difficulties in understanding calculus. The review of literature also discusses specific and general solutions to the problem.

1. Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Procedia-Social and Behavioral Sciences, 8, 173-180.

Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010), says that the lack of understanding causes serious obstacle for student globally in learning the concepts of two-variable functions.

The authors presented the obstacles face by the students in learning of two -variable functions through mathematical thinking approach. The data collection in this study was collected from a multivariable calculus for analyses. The data analyses revealed students’ common difficulties were:

Lack of understanding two different symbolic for a concept; selecting appropriate representation of the three worlds of mathematical thinking and met before (previous experience). The authors findings reveal that sketching the graph of two-variable functions in 3- dimensions is the greatest difficulty for majority of students in this method. The authors suggested the mathematical thinking approach for students having difficulties in understanding two-variable functions.

2. Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Studentsâ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2).

Hashemi, N., Abu, M. S., & Kashefi, H. (2019), investigates the reason undergraduate students’ faces difficulties in solving derivative and integral mathematical problems.

The authors provided a test containing derivative and integral problems to sixty-three undergraduate students, and the results was analyzed by qualitative and quantitative methods. The authors provide these as reasons why the students are having difficulties in learning derivatives and integrals:

• Weakness in recalling previous knowledge in entry and attack steps of specialization and generalization

• Weakness in making connection embodied and symbolic worlds of mathematical thinking and using symbolic world rather than embodied world

• Inability to use suitable problem-solving framework.

The authors suggested that there is a need to find suitable mathematical thinking strategy to overcome these difficulties in order to improve students’ abilities in the learning of derivative and integral.

3. Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), 0574.

Sebsibe, A. S., & Feza, N. N. (2019), assessed students’ challenges as it relates to conceptual knowledge in limit of functions. The participants in this study were 238 12th grade students from four different schools in one administrative zone of Ethiopia. An open-ended test about limit of a function at a point and at infinity was administered and analyzed quantitatively and qualitatively. The findings revealed by the authors in this study are:

• The students lack conceptual knowledge in limit of functions

• Lack of procedural knowledge in limit of functions

• Wrong interpretation of symbolic notations

• Lack of coherent and flexibility of reasoning

The authors concluded that, mathematics teachers who teach calculus for beginners should be concerned about the necessary pedagogical content knowledge.

4. Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.

(Hashemi et al., 2015), introduce the modified generalization strategies to improve the undergraduate student’s problem solving in derivative and integral. The authors presented derivatives and integrals with prompts and questions based on mathematical thinking to evaluate the undergraduate students. The authors concluded from this study that these difficulties are due to the followings:

• Weakness in problem solving

• Lack of suitable method

• Weakness of recalling knowledge

• Lack of problem-solving framework

5. Van Dyken, J., & Benson, L. (2019). Precalculus as a Death Sentence for Engineering Majors: A Case Study of How One Student Survived. International Journal of Research in Education and Science, 5(1), 355-373.

Van Dyken, J., & Benson, L. (2019), say precalculus as a death sentence for engineering majors. In this paper, a case study was constructed around a student by the authors using quantitative data from his mathematics and engineering courses, as well as qualitative data in the form of an open-ended survey and interviews. A mathematics instructor, who modeled self-regulation strategies as he served as the student’s mentor, was key to his success in passing the required courses in the calculus sequence. The authors suggested that self-regulated learning strategies and mentors who model them are key for students to pass required courses.

6. Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University).

Rabadi, N. (2015) identified the misconceptions and difficulties in the concepts of function, limits, continuity, and derivatives through existing literature. There were 21 students that partook in this research. Based on the theoretical framework, a collection of problems was created to help students overcome their misconceptions and difficulties. Nazar Rabadi said that the students had these difficulties due to the lack of mathematical knowledge to investigate functions, limits, and derivatives. The author concluded that these students showed improvement in their difficulties and misconceptions and found the collection of problems helpful in overcoming their difficulties and misconceptions.

7. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81-91.

Klymchuk et al., (2010) investigates the difficulties in solving application problems in calculus faced by engineering students. An observational parallel study was conducted simultaneously at two universities located in New Zealand and Germany by the authors. Two groups of students (54 in New Zealand and 50 in Germany) completed a questionnaire about their difficulties in solving the problem which was set as part of a mid-semester test. The authors found out that most of these students had difficulties in solving application problems due to the following reason:

a. The students did not know how to convert the real-life problem into one to solve mathematically b. They were unable to identify the unknown variable c. Difficulties in the identification and usage of the formula d. The students did not know how to do mathematical modelling. Finally, the authors suggested that teachers should teach the students the basic skills in solving application problems from the beginning of a calculus course.

8. Muzangwa, J., & Chifamba, P. (2012). Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students. Acta Didactica Napocensia, 5(2), 1-10.

Muzangwa, J., & Chifamba, P. (2012) analyze errors and misconceptions in an undergraduate course in calculus. The study was based on a group of 10 BEd Mathematics students at Great Zimbabwe University. The authors gathered data using two exercises on calculus 1&2. The analysis of the results from the tests showed that many of the errors were due to knowledge gaps in basic algebra. Besides, the authors also noted that errors and misconceptions in calculus were related to learners’ lack of advanced mathematical thinking since concepts in calculus are intertwined. The authors concluded that analytic concepts should be developed early in a calculus course to overcome the analysis of errors and misconceptions in the learning of calculus.

9. Pierce, V. U., & Kypuros, J. A. (2015). Utilizing an emporium course design to improve calculus readiness of engineering students. American Society for Engineering Education.

Pierce, V. U., & Kypuros, J. A. (2015) introduce utilizing an emporium course design to improve calculus readiness of engineering students. The authors targeted incoming students in engineering and computer science degrees at the University of Texas. Participating students were selected based on a record of participation in pre-calculus classes in high school, but who had not demonstrated their readiness to take calculus, as measured by placement tests and existing credit. According to the authors, the course design uses an emporium method, specially the assessment and learning in knowledge spaces (ALEKS) software. The results in this research conducted by the authors show that calculus placement for most students improve and were significantly more successful at doing so than a traditional pre-calculus class. The authors suggested that calculus 1 instructors need to be improved. The course content heavily emphasized algebra and symbolic manipulation techniques as instructors identified this as a need.

10. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia-Social and Behavioral Sciences, 8, 142-151.

Tambychik, T., & Meerah, T. S. M. (2010) investigate the major mathematics skills and cognitive abilities in learning that caused the difficulties in mathematics problems -solving among students from students’ point of view. According to the authors, the study was carried out on three focused group samples that were selected through purposeful sampling. A mixed qualitative and quantitative approach was used to have a clearer understanding. The authors said that their data findings showed that respondents lacked in many mathematics skills such as number-fact, visual-spatial and information skills. According to the authors, the deficiency of these mathematics skills and of cognitive abilities in learning inhibits the mathematics problem-solving. Finally, the authors recommended that for the students to over come these challenges, the understanding of the difficulties faced by students in any particular area and phase is the strategy to respond to this issue. Based on the understanding, it could provide a guideline for teachers or researchers to plan better approaches and effective teaching methods.

References

1. Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Procedia-Social and Behavioral Sciences, 8, 173-180

2. Hashemi, N., Abu, M. S., & Kashefi, H. (2019). Undergraduate Studentsâ Difficulties in Solving Derivative and Integral Mathematical Problems. Sains Humanika, 11(2).

3. Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), 0574.

4. Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.

5. Van Dyken, J., & Benson, L. (2019). Precalculus as a Death Sentence for Engineering Majors: A Case Study of How One Student Survived. International Journal of Research in Education and Science, 5(1), 355-373.

6. Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University).

7. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81-91.

8. Muzangwa, J., & Chifamba, P. (2012). Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students. Acta Didactica Napocensia, 5(2), 1-10.

9. Pierce, V. U., & Kypuros, J. A. (2015). Utilizing an emporium course design to improve calculus readiness of engineering students. American Society for Engineering Education.

10. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia-Social and Behavioral Sciences, 8, 142-151.

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