CHAPTER 1
Fostering the Development of Numeracy
Selected Challenges
Numeracy is much more than performing operations with numerals. Numeracy canbe defined as the combination of mathematical knowledge, problem solving andcommunication skills required by all persons to function successfully within ourtechnological world. Numerate persons can make sense of mathematical ideas thatare part of everyday experiences and they possess characteristics that are favourablefor lifelong learning about mathematics.
Fostering the development of numeracy or mathematical literacy is the major general goal ofthe new mathematics curriculum. Implementing this curriculum presents challenges that arerelated to:
• Areas of sense making.
• Aspects of cognition.
• Characteristics in students favourable to the learning of mathematics.
Translating the critical components of the mathematics curriculum into action requiresspecial teaching strategies and instructional settings. Assessment strategies arerequired that reflect the learning outcomes related to major goals of the curriculum.Reports to parents need to include information about indicators of sense making,aspects of cognition as well as characteristics favourable to the learning ofmathematics.
A variety of reasons exists for the fact that students arriving in the intermediate gradeswill be at different stages as far as having reached the learning outcomes from theprimary grades is concerned. Diagnostic settings and strategies will be required forsome of these students before effective Individual Educational Plans – IEPs – can bedeveloped and presented.
Since the critical components and the goals of the new curriculum are quite differentfrom the mathematics teaching and learning experiences that teachers and parentshave had, new information needs to be shared, analyzed and assimilated. In orderfor parents to be able to reinforce and supplement what students experience in themathematics classroom, important information needs to be made available to them.
The Purpose and the Parts of the Book
The main purpose of this book is to identify the important components and learningoutcomes of the curriculum for the intermediate grades. Suggestions are made for teachingstrategies and assessment techniques deemed appropriate for reaching the key goalsand major learning outcomes. The suggestions in the book include ideas for:
• Teaching strategies, classroom settings and sample questioning techniques.
• Types of activities, problems and appropriate practice.
• Sample assessment tasks and suggestions for reporting to parents.
• Diagnostic tasks, settings and strategies.
• Reflection or discussion.
Whenever appropriate, discussions will begin with the identification of important prerequisiteideas, procedures and skills. Examples from these discussions are suggestiveof introductory teaching-learning settings and they can also be used for diagnosticpurposes. The responses that are elicited during diagnostic interviews can be used forplanning effective intervention – Individual Educational Plans (IEPs).
The intent of the questions that are included at the end of some sections and at the endof each chapter is to provide ideas for reflection or for initiating discussions.
Theoretical comments will be kept to a minimum. Brief reference will be made to generalguidelines that research provides with respect to teaching, learning and assessment.Suggestions will be made for accommodating selected types of responses from students.
The suggestions that are made and the examples that are cited in the book are of apractical nature since they are based on:
• Experiences with students in classrooms.
• Observations in classrooms of teachers interacting with students.
• Action research conducted with teachers and students in classrooms.
• Responses collected from students during diagnostic interviews.
• Transcripts of diagnostic interviews with students and conversationswith adults.
Challenges Related to Curriculum Content
Aspects of Sense Making and Problem Solving
One of the key goals includes the maintaining and fostering of all aspects of sense makingin mathematics. These aspects include:
• Number sense.
• Spatial sense.
• Measurement sense
• Statistical sense.
• Sense of relationships.
• Developing and applying new mathematical knowledge throughproblem solving.
Problem solving is one of the major goals of teaching students about mathematics.The curriculum includes the statement that, 'learning through problem solving should bethe focus of mathematics at all grade levels' (p.8). It is in these through or via problemsolving settings that students develop their own problem solving strategies. New problemsolving strategies may be encountered when students are given opportunities to discussand compare strategies. An awareness of new strategies may lead to attempting these inthe future.
The key to creating a through problem solving setting lies in how tasks are presentedand how questions are phrased and posed. The onus is put on the students who arerequested to use what they know and try to come up with solutions or suggestions fora solution. The following are examples of types of questions and requests that invitestudents to invent which is one component of a balanced and effective mathematicsprogram:
How would you or could you ...?
Try to think of at least two ways to ...
The ability to respond to these types of requests is dependent upon one or more pre- orco-requisites. These can include: number sense; spatial sense; ability to think flexibly;ability to visualize; ability to generalize; ability to connect; ability to estimate; high self-esteem;willingness to take risks. The accommodation and development of these aspectsof cognition and these favourable characteristics has to be a component of ongoinginstructional settings in the mathematics...
