Teaching Calculus: Key Knowledge and Skills for VCE Enter Specialisation Unit 2

This article discusses the key knowledge and skills required for VCE Enter Specialisation Unit 2 Calculus. It covers topics such as the interpretation of the variable in graphical format, the purpose of the degree of a polynomial equation, the concept of limit, and the rules for finding derivatives and antiderivatives of simple power functions and polynomial functions. The article also provides teaching strategies and resources to help students understand these concepts.

VCE Enter Specialisation
Unit 2: Calculus
Outcome 1:
Key Knowledge and skills How I would teach the outcomes Reasoning
Key Knowledge:
the sign of the gradient at and near a point
and its interpretation in terms of functions
and polynomial functions
Key Skill:
use Newton’s method to find a numerical
approximation to a root of a cubic
polynomial function
Showing the interpretation of the variable in
graphical format and the purpose of the degree of
a polynomial equation
It will help to understand the interconnection
between moving point in graph and formation
of a polynomial equation as a fundamental
concept of the topic (Moyer-Packenham and
Westenskow 2013)
Showing the near point approximation in a first
degree polynomial equation by graph and
interpret the viability of the gradient
It will help the student to understand the
purpose of the approximation and its
utilisation to solve an equation and engage in
learning experience
Gradient concept and its implementation in a
directional graph through changing the position of
a single point
It will enable the students to develop the clear
concept on gradient function in numerical and
graphical presentation
Showing the Newton’s approximation method and
the approximation from a polynomial function by
using the graphical calculator (Bressoud et al.
2013). Interpret the boundary of a polynomial
function as a foundation of limit theory
It will help to utilise the previous learning
under this key learning in the implementation
of approximation issues through visual
learning and memorisation
Key Knowledge:
informal concepts of limit, continuity and
differentiability
limit definition of the derivative of a
function, and the derivative as the rate of
change or gradient function of a
given function
Key Skill:
evaluate limiting values of a function
use a variety of approaches (numerical,
graphical, first principles and by rule) to
Describe the concept of limit by showing its
implementation in a simple polynomial equation
while examining the changes due to the change of
the degree of the function such as y=2x+1 verses
y=x^2 + x+ 1
It enable student to understand how the
changes occur in a polynomial function and
also to support Supports collaborative learning
(HITS)
Understand the notation of limit operator and its
use in practical problem solving for any equation.
It will enable the student the utilisation of
symbol and notation to promote higher order
thinking and engage in learning experience
The numerical and graphical interpretation of limit
based polynomial equation and calculating the
It will help to visualise the whole equation and
the intervention of limit

find the value of the derivative
of a function at a given point
result. Such as:
limit x->1((x^2 +x+1)/(x+1))
Evaluate the foundation of deferential equation
and the representation in limit by using
It will help to understand the fundamental
concept of differentiation and derivative and
engaging learning experience in VCE
Mathematics study design
Description of the purpose of derivative while
showing the representation method such as
dy/dx,
It will help to understand the utilisation of
derivative in real problems
Key Knowledge:
the rules for finding derivatives and anti-
derivatives of simple power functions and
polynomial functions
Show the solving process of derivative of a
polynomial equation depending on the degree of
the question. Focusing on the changes in the
sufficient and the elimination of constant value
(Arsyad, Rahman and AHMAR 2017)
Describing the a relation between a graph
polynomial equation before and after derivation
and the cause of the changes.
It enable the students to understand the
process of solving the equation and its
implementation and also to support Supports
collaborative learning (HITS)
Key Skill:
use first principles to find by hand the
derivative of simple polynomial functions up
to degree 3
find by hand the derivative function and an
anti-derivative function for a simple power
function, or a polynomial
function of low degree
Describing the derivative method for polynomial
equation of 3rd degree while representing them in
the graphical format
Utilisation of multiple derivative and the reduction
of higher degree to constant for the polynomial
question throughout the process with graphical
representation
Derive real equation and implementing these
process of derivative
It will help to learn cooperatively advanced
utilisation of derivative and its functions in
different equations and to engage in learning
experience
Describing the purpose of anti derivative while
making comparison with the derivative of an
equation
Showing the invasive relation between derivative
It will allow the student to visualise the
relation between derivative and anti
derivative and its reversible property that will
be helpful to memorise (Voigt 2013)

and anti derivative with graphical calculator to
show the graphical representation
References
Moyer-Packenham, P.S. and Westenskow, A., 2013. Effects of virtual manipulatives on student achievement and mathematics learning. International
Journal of Virtual and Personal Learning Environments, 4(3), pp.35-50.
Voigt, J., 2013. Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In Theories of mathematical
learning (pp. 33-62). Routledge.
Arsyad, N., Rahman, A. and AHMAR, A.S., 2017. Developing a self-learning model based on open-ended questions to increase the students’ creativity in
calculus. Global Journal of Engineering Education, 9(2), pp.143-147.
Bressoud, D.M., Carlson, M.P., Mesa, V. and Rasmussen, C., 2013. The calculus student: insights from the Mathematical Association of America national
study. International Journal of Mathematical Education in Science and Technology, 44(5), pp.685-698.