Teaching Maths I

Objectives

This course aims to prepare the students for the acquisition of the necessary basic knowledge for the teaching of early number concepts, addition, subtraction and base ten concepts in pre-kindergarten, kindergarten and primary school.

The main goals are:

1. Knowing how children learn basic number concepts.
2. Knowing how children learn to add and subtract.
3. Knowing how children learn base ten concepts.
4. Knowing how to use manipulatives to support children's learning.
5. Knowing how to design activities to learn early number concepts, addition, subtraction and base ten concepts.

Note: As the subject is taught in English, the students will develop the necessary skills and strategies to teach Maths in English (CLIL).

Learning outcomes

Learning outcomes for Early Childhood Education (MEI)

• Identifies the bases of knowledge construction in the mathematical field as well as the main methodological and cognitive strategies that support this construction (LO1).
• Elaborates and designs pedagogical materials for mathematics learning in the classroom, also with the support of ICT. (LO4)
• Correctly applies the basic knowledge of mathematics. (LO5)
• Solves problems and situations of professional development with entrepreneurial and innovative attitudes. (LO7)
• Adequately applies knowledge in solving problems in competitive or professional and specialized work environments that require the use of creative and innovative ideas. (LO9)

Learning outcomes for Primary School Teaching (MEP)

• Identifies the bases of knowledge construction in the mathematical field as well as the main methodological and cognitive strategies that support this construction. (LO1)
• Analyzes the teaching and learning processes and evaluation that are developed in mathematics in primary education. (LO2)
• Identifies the main indicators of mathematical competence and proposes appropriate learning sequences for its acquisition. (LO3)
• Elaborates and designs pedagogical materials for mathematics learning in the classroom, also with the support of ICT. (LO4)
• Correctly applies the basic knowledge of mathematics. (LO5)
• Identifies the main diversity factors in mathematics learning, the resulting needs and the educational response required. (LO6)

Competencies

General skills

• Establish systemic connections between fields of knowledge.

Specific skills

• Acquire basic notions of the construction of knowledge in order to integrate them into educational activities that promote meaningful learning processes.
• Design, plan and assess teaching proposals for different areas of the curriculum, consistent with theories of learning and encouraging cooperative work.
• Develop and adapt educational resources for different curricular purposes, using information and communication technology as basic tools for learning.
• Develop processes for assessment of learning, individually and in groups, through techniques and strategies of teaching observation and documentation.
• Know about methodological and didactic principles of mathematics to promote the acquisition of skills in this area.
• Manage learning spaces in contexts of diversity and inclusion, taking into account the needs arising from disorders and learning difficulties, in order to establish appropriate guidelines for intervention in collaboration with other services, professionals and families.

Basic skills

• Students can apply their knowledge to their work or vocation in a professional manner and have competencies typically demonstrated through drafting and defending arguments and solving problems in their field of study.

Core skills

• Display professional skills in complex multidisciplinary contexts, working in networked teams, whether face-to-face or online, through use of information and communication technology.
• Project the values of entrepreneurship and innovation in one's academic and professional career, through contact with a variety of practical contexts and motivation for professional development.

Content

1. Intuitive, informal and formal number knowledge
2. Early number concepts
   1. What does count mean?
   2. How children acquire number words
   3. The development of counting skills
3. Number concept
   1. Which skills are necessary to develop number concepts?
   2. Number concept is related to counting? Two points of view
4. Informal and formal arithmetic
5. The role of basic facts in arithmetic
   1. Why children need to acquire basic facts?
   2. Helping children master and acquire the basic facts
   3. Manipulatives for helping children acquire basic facts
6. Developing meanings for mathematical operations
   1. Addition and subtraction problem structures
   2. Teaching addition and subtraction
7. Whole number place-value development
   1. Pre-base ten concepts
   2. Basic ideas for place value
   3. Models for place value
8. Strategies or whole-number computation
   1. Toward computational fluency
   2. Invented strategies versus traditional algorism for addition and subtraction

Evaluation

Assessment process

Students will be regularly assessed to track their learning. For this purpose there will be tutorial group sessions and a review of classroom activities.

Final evaluation

The final mark of the subject will be the result of the following four partial marks:

• Final exam (40%)
• Activities during or before class sessions (25%)
• A written work that involves designing a sequence of activities (35%)

To pass in the subject, students have to pass in the exam and the written work.

Activities performed during or before class sessions are not retakeable.

There's an assigned week for a second sitting exam and to repeat the written work if necessary.

Methodology

The subject has a participative approach. Students will have to read articles and book chapters before plenary class sessions. The content of the readings will be reviewed and discussed through activities to resolve all doubts. These activities are designed to link theory and practice, and to encourage student participation in an active way.

In addition, students participating in small group seminars will work in cooperative groups, discussing video clips of children and designing activities for pre-kindergarten, kindergarten and primary school.

In order to achieve the objectives, it is very important to attend all the class sessions regularly.

Bibliography

Bibliography

• Baroody, A. J. (1987). Children's Mathematical Thinking: A Developmental Framework for Preschool, Primary, and Special Education Teachers. Teachers College Press.
• Carpenter, T. P., Fennema, E., Loef Franke, M.; Levi, L.; Empson, S. B. (1999). Children’s Mathematics Cognitively Guided Instruction. Heinemann.
• Cockburn, A.D., Littler, G. (2008). Mathematical misconceptions. Sage Publications Ltd.
• Parrish, S (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies Grades k-5. Math Solutions Publications.
• Van de Walle, J. A., Karp, K. S. i Bay-Williams, J. M. (2008). Elementary and middle schoolmathematics: Teaching Developmentally. Pearson Education.

Reading

Teachers will provide complementary bibliography and compulsory reading throughout the course via the Virtual Campus.