BMTS206
Functions and Graphs

MQF Level: 6

ECTS Value: 5 ECTS

Self-Study Hours: 60

Duration: 10 Sessions

Contact Hours: 25

Mode of Delivery: Blended

Assessment Hours: 40

Entry Requirements

Applicants applying for the module are to be in possession of the following: 

1  An MQF Level 3 (minimum Grade 5 or C) in Maltese, English Language and Mathematics awarded by MATSEC or an equivalent examination body recognised by the IfE

AND

  1. A minimum of one of the following: 
  2. a) An awarded MATSEC Certificate or equivalent (MQF Level 4) with a Grade C or better in Mathematics at Advanced Level; OR
  3. b) Three subjects at advanced level (MQF Level 4) including a Grade C or better in Mathematics and another subject, and at least a Grade D in a third subject; OR
  4. c) Two subjects at Advanced Level (MQF Level 4) at Grade C or better including Mathematics, and three intermediate subjects with a minimum Grade D. 

Overall Objectives and Outcomes

This module provides an in-depth exploration of functions and graphical representations to acquire the necessary knowledge and pedagogical skills, to understand and be prepared to teach functions and graphs at various educational levels.  The module covers a range of topics including polynomials, exponentials, logarithmic, trigonometric, rationals, Polar functions as well as transformations, composite and inverses of functions along with their graphical representations.  Course participants will explore the principles of graphing, analysing key features such as intercepts, turning points, and behaviour of function as it is approaching zero, infinity or any other values. Through a blend of theoretical understanding and practical application, course participants will develop the skills to effectively teach these concepts, using technology and graphical tools to enhance learning.  The module also integrates strategies for teaching these concepts effectively in the classrooms, focusing on developing students` conceptual understanding and problem-solving skills. This module emphasises conceptual understanding, procedural fluency, and problem-solving techniques.  Learning will occur through collaborative discussions, hands-on problem-solving sessions connecting theory to practice with interactive teaching, quizzes, reflections on teaching practices with a focus on practical teaching strategies, rigorous mathematical reasoning and formative assessment techniques. Course participants will also learn how to explain Functions and graphs concepts clearly, solve problems both in writing and orally and understand the need to include resources to make graphical applications more accessible and engaging for oneself and for future students.

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

  • Represent functions namely algebraically, graphically, verbally and numerically;
  • Present functions graphically and explain key features of function graphs, also by using graphing calculators and software, such as Geogebra and Desmos, and online platforms to teach and explore functions interactively;
  • Ensure collaborative experiences to explore and solve problems related to functions and graphs;
  • Deal with functions in various contexts and foster critical thinking skills;
  • Interpret, represent, and communicate functional relationships using multiple representations and apply these skills to real-world contexts and pedagogical practices;
  • Identify, discuss and address common students` misconceptions and errors related to functions and graphs;
  • Perform operations on functions, such as addition, subtraction, multiplication, division and composite functions;
  • Plot graphs accurately, and draw proper sketches from properties and learnt behaviours of graphs;
  • Interpret and analyse graphs extracting important information namely the maximum and minimum points, intercepts, increasing and decreasing behaviour and points of inflection;
  • Apply and recognise transformations such as translation, reflection, stretches and compressions on the graph of a function.
  • Represent functions namely algebraically, graphically, verbally and numerically;
  • Present functions graphically and explain key features of function graphs, also by using graphing calculators and software, such as Geogebra and Desmos, and online platforms to teach and explore functions interactively;
  • Ensure collaborative experiences to explore and solve problems related to functions and graphs;
  • Deal with functions in various contexts and foster critical thinking skills;
  • Interpret, represent, and communicate functional relationships using multiple representations and apply these skills to real-world contexts and pedagogical practices;
  • Identify, discuss and address common students` misconceptions and errors related to functions and graphs;
  • Perform operations on functions, such as addition, subtraction, multiplication, division and composite functions;
  • Plot graphs accurately, and draw proper sketches from properties and learnt behaviours of graphs;
  • Interpret and analyse graphs extracting important information namely the maximum and minimum points, intercepts, increasing and decreasing behaviour and points of inflection;
  • Apply and recognise transformations such as translation, reflection, stretches and compressions on the graph of a function.
  • Show and explain clearly the concepts related to functions and graphs using appropriate teaching methods and tools;
  • Analyse and interpret graphs; explain how changes in equations change the graph including shifts, stretches and reflections;
  • Solve equations involving functions, finding roots and evaluate the significance of these solutions in various contexts;
  • Perform and describe transformations such as translations, scaling, and rotations on functions and their corresponding graphs;
  • Show proficiency in using graph calculators, and/or educational software, and other digital tools to explain and teach functions and their graphs;
  • Develop precise mathematical language to describe and explain functions and their graphs;
  • Create and use visual aids effectively to support teaching and the knowledge;
  • Show how to interpret and analyse graphical data such as trends, making predictions and explaining the relationship between variables;
  • Discuss, draw and manipulate the concepts discussed;
  • Use online resources and platforms confidently so that mathematics can be visualised better.

This module will be assessed through: Presentation, Assignment.

Core Reading List

  1. Curmi F. Spiteri J.E, Vassallo C, (2006). Pure Mathematics 1B.   ISBN: 9789993286950,  Miller Prod.
  2. Curmi F. Spiteri J, E, Vassallo C, (2008). Pure Mathematics 2A .  BDL Books, ISBN: 978-99909-211-5-1.
  3. Buhagiar Karl, Advanced Level Pure Mathematics Basic Algebra and Graphs(2002). PEG Ltd.  ISBN:99932-0-198-7.

Supplementary Reading List

  1. Muscat Rianne, (2017; Author and Publisher). Pure Mathematics Exercises, ISBN 9789995711634
  2. Muscat Rianne, (2017; Author and Publisher). Further Pure Mathematics Exercises, ISBN:9789995711665
  3. John Bird, (2021). Engineering Mathematics, 9th Edition ISBN: 9780367643782.
  4. Khan Academy functions course https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions
  1. Khan Academy Parametric and Polar course: https://www.khanacademy.org/math/calculus-2/cs2-parametric-equations-polar-coordinates-and-vector-valued-functions
  1. Paul`s online Notes on functions: https://tutorial.math.lamar.edu/classes/calci/Functions.aspx
  1. Paul`s online Notes on Polar Graphs: http://tutorial-math.wip.lamar.edu/Classes/CalcII/PolarCoordinates.aspx
 
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