Teacher notes

Dynamic calculus is a web-based, multimedia resource focusing on the introductory calculus topics of the Stage 6 Mathematics syllabus (Board of Studies NSW, 1982) and Stage 6 Mathematics Advanced syllabus (Board of Studies NSW, 2008).

The resource addresses the key competency of using technology by exploiting the functionality of dynamic mathematics software. It comprises 35 dynamic html worksheets, each exploring a different concept in differential and integral calculus. Student understanding is guided and assisted by accompanying directions and points for discussion. The dynamic worksheets can be opened on any computer with a web browser and Java and are particularly well suited to use with an interactive whiteboard.

The positive influence of dynamic geometry software and computer algebra systems on teaching mathematics has been widely researched and reported. Both as a tool for demonstration and as a vehicle for discovery learning, Dynamic calculus aims to enrich and supplement students’ learning of concepts in calculus.

Syllabus links

The resource covers three syllabus topics:

Topic	Syllabus outcomes
The tangent to a curve and the derivative of a function	8.1 to 8.7
Geometrical applications of differentiation	10.1 to 10.8
Integration	11.1 to 11.4

Topic

Syllabus outcomes

The tangent to a curve and the derivative of a function

8.1 to 8.7

Geometrical applications of differentiation

10.1 to 10.8

Integration

11.1 to 11.4

Quality teaching framework

By incorporating these resources into the lesson, teachers can provide opportunities for student learning within the context of the quality teaching framework.

Intellectual quality

Element	Evidence
1.1 Deep knowledge	Throughout the resource, focus is sustained on key ideas and concepts and the content is structured to bring coherence and a clearly defined purpose to each activity. Students are required to articulate relatively complex relationships between central concepts and their application.
1.2 Deep understanding	Students are given the opportunity to demonstrate deep understanding of complex ideas and concepts as they explore relationships, solve problems, construct explanations and draw conclusions. The functionality of the applets gives students the means to explore the syllabus content to a depth that may not otherwise be possible.
1.3 Problematic knowledge	Students are confronted with real-life problems that require critical analysis of the appropriateness of a solution in a given context.
1.4 Higher-order thinking	Interaction with the activities enables non-routine questions to be explored and ‘problem-solved’.
1.5 Metalanguage	Opportunities exist for students to discuss how the symbolic systems of calculus function and how they relate to the underlying mathematics.
1.6 Substantive communication	In the classroom setting, the scope and range of activities provides many opportunities for initiating extended dialogue on the topic.

Element

Evidence

1.1 Deep knowledge

Throughout the resource, focus is sustained on key ideas and concepts and the content is structured to bring coherence and a clearly defined purpose to each activity. Students are required to articulate relatively complex relationships between central concepts and their application.

1.2 Deep understanding

Students are given the opportunity to demonstrate deep understanding of complex ideas and concepts as they explore relationships, solve problems, construct explanations and draw conclusions. The functionality of the applets gives students the means to explore the syllabus content to a depth that may not otherwise be possible.

1.3 Problematic knowledge

Students are confronted with real-life problems that require critical analysis of the appropriateness of a solution in a given context.

1.4 Higher-order thinking

Interaction with the activities enables non-routine questions to be explored and ‘problem-solved’.

1.5 Metalanguage

Opportunities exist for students to discuss how the symbolic systems of calculus function and how they relate to the underlying mathematics.

1.6 Substantive communication

In the classroom setting, the scope and range of activities provides many opportunities for initiating extended dialogue on the topic.

Quality learning environment

Element	Evidence
2.2 Engagement	Students have the opportunity to be active learners as they explore the dynamic functionality of the applets and use their theoretical knowledge in practical applications. The activities throughout the resource demonstrate the relevance of mathematics to real-world applications and engage the students in learning.
2.4 Social support	Used in a classroom setting, the learning activities encourage group and class discussion which may be used to foster supportive behaviours.
2.6 Student direction	The interactive nature of the resource gives students the opportunity to be motivated and self-directed learners with the autonomy to explore their own learning pathway.

Element

Evidence

2.2 Engagement

Students have the opportunity to be active learners as they explore the dynamic functionality of the applets and use their theoretical knowledge in practical applications. The activities throughout the resource demonstrate the relevance of mathematics to real-world applications and engage the students in learning.

2.4 Social support

Used in a classroom setting, the learning activities encourage group and class discussion which may be used to foster supportive behaviours.

2.6 Student direction

The interactive nature of the resource gives students the opportunity to be motivated and self-directed learners with the autonomy to explore their own learning pathway.

Significance

Element	Evidence
3.1 Background knowledge	Students’ background knowledge is consistently incorporated into the activities and there is substantial connection to out-of-school background knowledge.
3.3 Knowledge integration	The broad range of resources ensures that meaningful connections are achieved between topics. Students have the opportunity to integrate the key competencies of using mathematical ideas and techniques, using technology and solving problems.
3.5 Connectedness	The opportunities provided by this learning will assist students to connect their learning in mathematics to real-world applications and to find solutions for a potentially broad range of problems in work beyond school.

Element

Evidence

3.1 Background knowledge

Students’ background knowledge is consistently incorporated into the activities and there is substantial connection to out-of-school background knowledge.

3.3 Knowledge integration

The broad range of resources ensures that meaningful connections are achieved between topics. Students have the opportunity to integrate the key competencies of using mathematical ideas and techniques, using technology and solving problems.

3.5 Connectedness

The opportunities provided by this learning will assist students to connect their learning in mathematics to real-world applications and to find solutions for a potentially broad range of problems in work beyond school.