Introduction to Workshop 10
Choosing Learning and
Teaching Approaches and
Strategies
Guiding Principles for Workshop 10:
a rationale for the effective learning and teaching
of mathematics
 Knowledge: can be procedural and
conceptual
 Learning: the process and the learning
outcomes in the syllabus – strong procedural
skills and problem solving are of equal
importance.
 Setting clear learning targets is essential for
teachers and students.
 Teaching for Understanding: enabling students
to think flexibly and inquire critically.
Guiding Principles for Workshop 10:
A rationale for the effective learning and teaching
of mathematics
 Prior knowledge
 A wide range of pedagogies: many strategies




complement each other.
Quality interaction: effective questioning and
feedback guide the learning process.
Teaching for independent learning: this should be
nurtured.
Feedback and assessment: not confined to
giving a grade, but a wide range of strengths
and weaknesses where learning can be
improved.
Resources: make use of a wide variety
Guiding Principles for Workshop 10:
A rationale for the effective learning and teaching
of mathematics
 Engagement of students: they
participate actively, collaborate
closely, express themselves openly,
treat suggestions positively.
 Learner Diversity
 Literacy and Numeracy
Effective delivery of the syllabus:
Common Pedagogical Approaches:
1. using an understanding of basic rules and skills
approach
2. using an enquiry approach
3. using a co-construction approach
4. using a problem- solving approach.
A single approach is rarely adopted, effective
teachers integrate various strategies when
teaching a topic
Workshop 10
Choosing Learning and Teaching Approaches and Strategies
 Session A: 9.30 – 10.15
 Introduction & Lesson Study as a form of professional





development
Session B: 10.15 – 11.00
Cultivating skills for problem solving
Tea & Coffee 11.00 – 11.15
Session C: 11.15 – 1.00
Teaching as co-construction
1.00-2.00 Lunch
Session D : 2.00 – 2.45
Teaching as enquiry
Session D: 2.45 – 3.30
Problem-solving learning
Summary Workshops 1-10
 have highlighted the underlying principles of an
effective mathematics classroom that is applicable
to all levels at Junior and Senior Cycle.
 have set the direction for the teaching, learning and
assessment (formative) of mathematics.
 have emphasised mathematical problem solving as
being central to the learning of mathematics,
involving
A. the acquisition and application of mathematics
concepts and skills in a wide range of situations,
including closed, open-ended and real-world
problems
B. the development of mathematical problemsolving ability, which is dependent on five interrelated components – 1.Concepts, 2.Skills,
3.Processes, 5.Attitudes and 5.Metacognition
1. Concepts
 Mathematical Concepts cover numerical,
algebraic, geometrical, statistical, probabilistic
and analytical concepts.
 Students should develop and explore
mathematical ideas in depth and see that
mathematics is an integrated whole, not merely
isolated pieces of knowledge.
 Students should be given a variety of learning
experiences to help them develop a deep
understanding of concepts, to make sense of
ideas as well as their connections and
applications.
 Use of concrete materials, practical work and ICT
should be part of the learning experience.
2. Skills
 Includes procedural skills for numerical
calculation, algebraic manipulation, spatial
visualisation, data analysis, measurement, use
of mathematical tools, technology and
estimation.
 Development of skill proficiencies in students is
essential in the learning and application of
mathematics.
 Students should become competent in the
various skills; over-emphasising skills without
understanding the underlying principles should
be avoided.
 It is also important to incorporate the use of
thinking skills in the process of the development
of skill proficiencies.
3. Processes
 ‘Mathematical Processes’ refers to the
knowledge skills involved in acquiring and
applying mathematics. It includes
reasoning, communication (using
mathematical language to express ideas
precisely, concisely and logically) and
connections (seeing and making linkages
among mathematical ideas, between
maths and other subjects and between
maths and everyday life), thinking skills and
heuristics (giving a representation, looking
for patterns, working backwards, solving a
problem), application and modelling.
4. Attitudes
Affective aspects of maths learning:
 beliefs about maths and its usefulness
 interest and enjoyment in learning maths
 appreciation of the beauty and power
of maths
 confidence in using maths
 perseverance in solving a problem.
These are shaped by their learning
experiences.
5. Metacognition
 In particular, the selection and use of problem-solving strategies
 Experience is necessary to develop students’ problem-solving
abilities
Activities used to enrich metacognitive experience
 Expose students to general problem-solving skills and how these
skills can be used to solve problems.
 Encourage students to think aloud about the strategies and
methods they use to solve problems.
 Provide students with problems that require planning (before
solving) and evaluation (after solving).
 Encourage students to seek alternative ways of solving the
same problem and check the reasonableness of their answer.
 Allow students to discuss how to solve a particular problem and
to explain the different methods that they use for solving a
problem.