Numerical Literacy and Problem Solving
Target Audience: Teachers from years 3-10 (Stages 2, 3, 4 & 5)
This workshop addresses Professional Teaching Standards 1.2.2, 1.2.3 & 2.2.3.
This workshop will examine the literacy issues that apply to mathematics and will develop classroom strategies to overcome them. It will encourage student engagement in more complex and interesting mathematical investigations.
During the workshop participants will:
· Examine data that supports Newman’s five hurdles concept
· Critically examine three of the hurdles (Comprehension, Transformation and Encoding)
· Examine and participate in activities that support improved student outcomes
At the end of the workshop participants will have:
· An understanding of Newman’s five hurdles to problem solving
· A process for identifying which of the hurdles is preventing a student from successfully completing a word problems.
· Explore some approaches to problem solving: such as ‘acting it out’, ‘making a systematic list’, ‘drawing a diagram’ and many others
Fractions and Decimals
Target Audience: Teachers from years 1- 8 (Stages 1, 2, 3 & 4)
This workshop addresses Professional Teaching Standards 1.2.1-1.2.4, 2.2.2-2.2.4, 3.2.1-3.2.5.
This workshop will cover effective techniques and provide teachers with a sequence for teaching fractions, decimals and percentages to students. Practical hands on examples that are ‘classroom ready’ and sample lesson plans will be provided in the workshop.
During the workshop participants will:
· Examine student misconceptions about fractions, decimals and percentages
· Look at effective ways of overcoming them
· Experience and trial various techniques that allow students to understand the concepts of fractions, decimals and percentages
At the end of the workshop participants will have:
· An understanding of fractions, decimals and percentages from a students point of view
· A toolbox of strategies that they can use in the classroom to assist and encourage students to make sense of fractions decimals and percentages
Alternate Assessment Techniques
Target Audience: Teachers from K- 8 (Stages ES1,1 2, 3 & 4)
This workshop addresses Professional Teaching Standards 3.2.4, 3.2.5, 3.2.6 & 3.2.7.
This workshop will examine practical ways of assessing the Mathematics Syllabus without killing students’ desire for knowledge.
During the workshop participants will:
· Develop assessment techniques that will foster a learning approach based on student needs and learning styles
· Adapt tasks and develop rubrics that will allow their students to demonstrate “Extensive (A), Thorough (B), Sound (C), Basic (D) and Elementary (E)” levels of understanding
· Examine different types of feedback to students and feedback strategies
At the end of the workshop participants will have:
· A bank of assessment tasks and rubrics that will allow them to efficiently assess their students
· The ability to develop further tasks in collaboration with other teachers which in turn creates “Consistent Teacher Judgement” (CTJ)
Algebra for Yrs 5-10
Target Audience: Teachers from 6-10 (Stages 3 to 5) also suitable for new teachers and teachers teaching mathematics out of field.
This workshop addresses Professional Teaching Standards 1.2.1, 1.2.2, 1.2.3, 3.2.2 & 3.2.4.
The Workshop will be presented by Dr Heather McMaster from Macquarie University
The workshops will demonstrate simple and effective ways to make algebra more accessible to students by making it practicable and relevant to today.
At the end of the workshops, teachers will have an understanding of the P&A strand and a knowledge of how to teach this most interesting strand in a simple, effective and non threatening fashion. They will have access to a bank of relevant and fun activities and will be in a position to facilitate Patterns and Algebra in their school.
The workshop looks at ways to develop a student’s understanding of Patterns and Algebra (P&A) from Stage 3 to Stage 5.3. The workshop will address areas such as developing and describing number patterns, algebraic techniques, linear relationships, applying basic coordinate geometry techniques to linear, quadratic, and exponential functions.
Understanding, Fluency, Problem Solving and Reasoning in Mathematics
Teaching Mathematics: Addressing the proficiency Strands.
Turning our students into Mathematicians
Target Audience: Teachers from K-9 (Stages ES1 to 5)
This workshop addresses Professional Teaching Standards 1.2.1, 1.2.4, 3.2.1, 3.2.2 & 3.2.4.
This workshop goes beyond Working Mathematically with the inclusion of the 4 proficiency strands from the national curriculum and how to apply them in a practical way that addresses the needs of NSW teachers and students.
The workshop will look at ways to encourage students to make connections between related concepts and develop the confidence to use the familiar to develop new ideas. It will look at the “Why” as well as the “How” of mathematics ie “Understanding”.
The workshop will address “Fluency” which is the skill in choosing appropriate procedures and then choosing the most appropriate procedure and so develop a flexible efficient and appropriate use of mathematical skills, knowledge and concepts.
Problem Solving, the third proficiency strand which involves making choices, interpreting, investigating, and communicating will also be part of the workshop
And
Reasoning, the workshop will investigate ways of developing in our students the capacity for logical thought and actions including analysing, generalising, inferring and justifying.
Participants will experience a range of activities suitable for students from early K to 8 and examine how these can be applied to the Syllabus outcomes. Participants will have a bank of activities and teaching strategies that are relevant to the syllabus and the ideals of the national curriculum and they will be able to present this workshop to teachers at their school.
Introduction and Applications of Calculus
Target Audience: Teachers of stage 6 Mathematics and Mathematics Ext 1 This workshop addresses Professional Teaching Standards 1.2.1, 1.2.2, 1.2.3, 2.2.3, 3.2.1, 3.2.3
This workshop will take participants from basic definitions to geometrical applications of calculus including curve sketching, areas and volumes.
Program outline:
History
- The need for Calculus and the concept of a limit
- Differentiation by first principles and the gradient of a curve
- Rules for differentiation: - Derivative of x to the power of n
- Product Rule
- Quotient Rule
- Function of a Function Rule
- Equation of a tangent & normal to a curve
- Geometrical significance of f '(x) & f "(x)
Geometrical Applications:
- Geometrical significance of f '(x) & f "(x)
- Finding stationary points and methods for determining their nature
- Points of inflexion & the importance of testing
- Problems involving graphs of f '(x) & f "(x)
Problem Solving Using Maxima & Minima
- The importance of Generalised Arithmetic for writing algebraic expressions which represent physical quantities
under a given set of conditions.
- Determining the domain for the problem
- Confirmation of max / min using the appropriate method
- Stationary points & points of inflexion, and their application to Curve Sketching [ including Rational Functions (Ext 1)]
- Maximisation / Minimisation problems
- Integration: - Primitive Functions
- The Fundamental Theorem of Calculus
- Methods of Substitution ( Ext 1 )
- Areas & Volumes
- Special Cases
Binomial Expansion and Parametric Equations
Target Audience: Teachers of stage 6 Mathematics, Mathematics Ext 1 and Ext 2.
This workshop addresses Professional Teaching Standards 1.2.1, 1.2.2, 1.2.3, 2.2.3, 3.2.1, 3.2.3
The first part of this workshop is designed to help teachers develop an understanding of binomial expansions in their students by starting from the basics of permutations and combinations and moving to the point where they can manipulate binomial expressions.
The second part examines parametric equations and how to apply them to locus problems.
Program outline:
Permutations and Combinations
Multiplication Principal
Factorials
Understanding Permutations and Combinations
Binomial Expansions
Pascal’s triangle and its relationship to nCk
Expansion of (a + b)n
Manipulation of expressions including expressions with factorials
Parametrics
Definition of a parameter/why use parameters
Simple parametric equations
x2 = 4ay in parametric form
Locus problems with single and double parameters
Questions
If time permits Ian will answer questions about the Mathematics, Mathematics Extension 1 and Mathematics Extension 2 course and HSC papers
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APPLICATION OF CALCULUS TO THE PHYSICAL WORLD
Target Audience: Teachers of stage 6 Mathematics Ext 1 and Mathematics Ext 2This workshop addresses Professional Teaching Standards 1.2.1, 1.2.2, 1.2.3, 2.2.3, 3.2.1, 3.2.3
Workshop Outline
Gradient as a Rate Measurer
Exponential Growth & Decay
- Solving problems where rates of change are proportional to the quantity present
The Concepts of Velocity and Acceleration
Velocity and acceleration as derivatives
- Solving problems using differentiation and integration
Related rates
- Relating rates of change to each other via the chain rule
Acceleration as a function of x or v
- Redefining acceleration and choosing the appropriate form to solve various problems
Simple Harmonic Motion
- Solving problems (i.e. finding amplitude, period, velocity, etc) where initial conditions are expressed as functions of time (t) or position (x)
Projectile Motion
- Concept of resolution of vectors into vertical and horizontal components
- Deriving the equations of motion in both x & y directions
- Deriving formulae for max. height, range, max. range, etc.
- Cartesian equation of the particle path
Newton’s Laws of Motion
- Inertia
- Definition of Force
- Action & Reaction
Resisted Motion
- Solving problems where a body experiences a resistive force which is proportional to v or v2
Circular Motion
- The definition of angular velocity and its relationship to linear velocity
Acceleration of a particle moving in a circle
- Centripetal Force and Centrifugal Force
- Using the definition of centripetal force to solve problems involving the conical pendulum and banked tracks
Graphs and Curve Sketching
- Standard graphs ( quadratics, cubics, logs, exponentials, etc )
- Absolute value graphs
- Applications of calculus – sketching degree 3 & 4 polynomial functions
- Sketching from the sketch of ( & vice versa )
- Velocity / Displacement graphs
- Trig graphs
- Sketching polynomials without calculus
- Graphs of inverse functions
- Sketching rational functions ( using asymptotes, symmetry, etc )
- Sketching , , , , etc
- Sketching functions in the form , , etc
Trigonometry
- Basic right-angled trig
- Non-right angled trig and its applications.
- Co-ratios & reciprocal ratios
- Pythagorean identities and their applications
- Calculus of trig functions
- Graphs of trig functions &
- Graphical solutions of transcendental equations e.g.
- Three-dimensional trig
- Compound angle formulae , ,
- Double angle formulae
- substitution
- Trig equations – restricted domain & general solutions
- Auxiliary angle formulae e.g.
- Inverse trig functions
- Trig integrals
Activities to support The Senior Mathematics Program
- This workshop demonstrates a number of practical activities that give some meaning to the mathematics we teach our students. The activities are primarily aimed at the Mathematics and Mathematics Ext 1 courses however they can be extended/modified to address both Ext 2 and General.
- The activities are hands on experiments from which we attempt to draw conclusions.which We then model the results using the “GeoGebra” program and participants are advised to bring a computer or tablet loaded with GeoGebra 4 or higher. Please note, it is not necessary to be familiar with the GeoGebra Program.