BMTS104
Teaching and Learning Algebra and Geometry

ECTS Value: 6 ECTS

Contact Hours: 30

Self Study Hours: 72

Assessment Hours: 48

 

Overall Objectives and Outcomes

This module prepares course participants in the pedagogy of algebra and geometry. It will familiarise learners with seminal literature about teaching and learning of algebra and geometry, such as those dealing with students’ misconceptions of algebra and with the developmental skills required for students to be able to learn particular geometric concepts. Based on such research evidence, the course participants will be given the opportunity to learn about students’ interpretations and representations of algebraic and geometric concepts and how these could be utilised in favour of the teaching and learning of algebra and geometry. In the process, they will become aware of students’ possible algebraic and geometric misconceptions and learn how these could be addressed. This will form a context within which teaching and assessment techniques for the teaching and learning of algebra and geometry will be studied and practised. 

By the end of this module, the learner will be able to: 

Competences

    • a)Cooperate with the mathematics head of department to determine readiness of school children to learn particular algebraic and geometric concepts;
    • b)Contribute to the development of a school mathematics curriculum with particular emphasis on age- and ability-appropriate algebraic and geometric learning outcomes;
    • c)participate in the evaluation, review, and/or creation of school policies about assessment, particularly of and for  students’ understanding of algebraic and geometric concepts;
    • d)Create a set of student-friendly brief notes aimed at helping students’ understand and revise particular algebraic and geometric concept;
    • e)Create an exercise booklet aimed for students to work out problems including both algebraic and geometric problems, which will enable students to represent their knowledge and skills and to make a self-evaluation, and will also enable the teacher to make formative and summative assessments of those students’ knowledge;
    • f)Create concise student-centred lesson plans which help the teacher to present appropriate algebraic and geometric learning opportunities.
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Knowledge

  • a)Identify pre-algebraic concepts (e.g. the BIDMAS rule) and their importance in the introduction of formal algebra (the introduction of letters);
  • b)List the diverse students’ interpretations letters and expressions with letters (parameter, variable, unknown);
  • c)Identify students’ misconceptions of algebraic notation and concepts;
  • d)Recall Del Grande’s seven spatial perception skills and their relevance in the teaching and learning of geometry;
  • e)Define the Van Hiele levels of geometric thought and the related phases of instruction;
  • f)Identify specific mathematical learning difficulties e.g. ADHD and dyscalculia and the needs of students with such conditions to be able to develop algebraic and geometric skills.
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Skills

    • a)Design a resource pack aimed at facilitating algebra and geometry lessons, which is created around students’ interpretations and representations of algebraic and geometric concepts while minimising student misconceptions;
    • b)Prepare age- and ability-appropriate algebra and geometry lesson plans, including lesson plans which integrate algebraic and geometric concepts;
    • c)Devise a set of activities aimed at assessing both summatively and formatively students’ algebraic and geometric knowledge and skills.
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Assessment Methods

This module will be assessed through: Lesson Plan, Presentation, Resource Pack

Suggested Readings

Core Reading List 

  1. Del Grande, J. (1990). Spatial Sense. The Arithmetic Teacher, 37(6), 14–20. https://doi.org/10.5951/at.37.6.0014. 
  2. Fuys, D. J., Geddes, D., & Tischler, R. W. (2002). The van Hiele model of thinking in geometry among adolescents. National Council of Teachers of Mathematics. 
  3. Kieran, C. (2018). Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. In ICME-13 Monographs. https://doi.org/10.1007/978-3-319-68351-5. 
  4. Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). Macmillan. 
  5. Küchemann, D. E. (1981). Algebra. In K. M. Hart (Ed.), Children’s Understanding of Mathematics, 11-16 (pp. 102-119). John Murray. 
  6. Skemp, R. R. (1987). The psychology of learning mathematics. Routledge. 
  7. Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. University Of Chicago. 
  8. Van Hiele, P. M. (1986). Structure and Insight. A theory of Mathematics Education. Academic Press Inc. 

Supplementary Reading List 

  1. Adeniji, S. M., & Baker, P. (2022). Worked-examples instruction versus Van Hiele teaching phases: A demonstration of students’ procedural and conceptual understanding. Journal on Mathematics Education, 13(2), 337–356. https://doi.org/10.22342/jme.v13i2.pp337-356. 
  2. Bergeson, T., Fitton, R., Bylsma, P., Neitzel, B., & Stine, M. A. (2000). Teaching and Learning Mathematics: Using Research to Shift From the “Yesterday” Mind to the “Tomorrow” Mind. https://www.academia.edu/34830242/Teaching_and_Learning_Mathematics 
  3. Bloomfield, A. and Vertes, B. (2005). People Maths: Hidden Depths. Association of Teachers of Mathematics. 
  4. Kieran, C., Pang, J., Schifter, D., & Ng, S. F. (2016). Early algebra. In ICME-13 Topical Surveys. https://doi.org/10.1007/978-3-319-32258-2. 
  5. Küchemann, D.E. (2019). Algebradabra: Developing a better feel for school algebra. Association of Teachers of Matematics. 
  6. Pia, K. F. (2015). Barriers in Teaching Learning Process of Mathematics at Secondary Level: A Quest for Quality Improvement. American Journal of Educational Research, 3(7), 822–831. https://doi.org/10.12691/education-3-7-5. 
  7. Van Hiele, P. M. (1999). Developing Geometric Thinking through Activities That Begin with Play. Teaching Children Mathematics, 5(6), 310–316. https://doi.org/10.5951/tcm.5.6.0310. 
  8. Wang, X. (2015). The Literature Review of Algebra Learning: Focusing on the Contributions to Students’ Difficulties. Creative Education, 06(02), 144–153. https://doi.org/10.4236/ce.2015.62013
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