Didactics of Mathematics I

Code:

DID4008

Acronym:

DID4008

Keywords
Classification	Keyword
OFICIAL	Didactics

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Science Education Unit
Course/CS Responsible:	Master in Mathematics Teacher Education for Middle and Secondary Schools

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENSM	19	Plano de Estudos M:ENSMAT_2015_2016	1	-	6	56	162

Teaching language

Portuguese

Objectives

The main goal of the course is to create a discussion and reflection forum around fundamental issues concerning the teaching and learning of mathematics. Among these issues we find: mathematics curricula, the teacher's role in the classroom and recommendations from research in mathematics education to classroom practice.
The discussion forum should allow future teachers to build a tool box for constructing, conducting and analisying mathematics teaching and learning situations, and for developing cooperative and autonomous work skills, as well as a life long learning attitude towards the teaching profession.

Learning outcomes and competences

At the end of the course, future teachers should know the main theoretical and methodological principles guiding the mathematics curricular orientations for basic and secondary education, understand the main differences between direct teaching and an inquiry-based approach, distinguish various types of mathematical tasks and analyzing them with a critical stance, analyse and criticize methodological recommendations of sequences of learning tasks, identify forms of organizing students' work in the classroom, their advantages and limitations, and start to understand the teacher's role in the exploration of learning tasks of varied nature and and beyond the classroom.
Future teachers should also show evidences of developing skills in terms of cooperative and autonomous work, communicating their ideas and perspectives (orally and in written form) in a coherent and clear manner, and with the support of research in mathematics education

Working method

Presencial

Program

1) Curricular orientations for mathematics teaching in basic and secondary education
1.1) curricular evolution in Portugal and in the world
1.2) brief analysis of theoretical perspectives guiding the methodological suggestions for the teaching of mathematics, in light of research in mathematics education, with an emphasis on the core standards in mathematics for basic education
1.3) mathematical tasks: types of tasks, mathematically rich tasks; need for diversification of tasks
1.4) creation and analysis of tasks for classroom usage 
2) The teacher's role in the classroom
2.1) forms of organizing students' work in the classroom
2.2) exploration of tasks of different nature in and beyondd the classroom

Mandatory literature

National Council of Teachers of Mathematics 050; Princípios e normas para a matemática escolar. ISBN: 978-972-8768-24-9
National Council of Teachers of Mathematics; Princípios para a ação: Assegurar a todos o sucesso em matemática, APM, 2014

Teaching methods and learning activities

Class sessions will work mainly in a climate of interaction between the teacher and the students; thus, students' participation is of outmost importance. During the class sessions, students will engage in various assignments, mainly in small groups or pairs but also individually, supprting their work on texts, teaching and learning situations (episodes and classroom tasks, multimedia cases, observations in schools, etc.). Almost all assignments will involve components of oral discussion, mostly in class. The proposed assignments are based in research in mathematics education, always focusing on the challenges teachers face when involving students in working on mathematically rich tasks under an inquiry-based approach to teaching and learning. All assignments proposed are elements of assessment, which is distributed along the semester and has no final exame, following a formative approach.

keywords

Physical sciences > Mathematics
Social sciences > Educational sciences > Education > Teacher training
Social sciences > Educational sciences > Teaching methods
Social sciences > Educational sciences > Education

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	5,00
Teste	20,00
Trabalho de campo	35,00
Trabalho escrito	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	98,00
Frequência das aulas	52,00
Trabalho de campo	12,00
Total:	162,00

Eligibility for exams

Participating in class sessions of Didactics of Mathematics I is mandatory for the students who have not the status of student workers. Once the legal limit of absences plus one is reached, the students are excluded from the course and loose approval (the course has no evaluation by exame, in no case). Students' participation in class sessions is not mandatory for the students who have the status of student workers. However, they should develop all efforts towards participating in class sessions due to the nature of this course. Student workers who do not participate in class (or those who exceed the legal limit of absences as if they were regular students) have to complete a set of assignments, designed specifically for them (although many of those assignments might be very similar to those proposed to their classmates who are regular students) and they have to complete a final global assignment, mandatory. Student workers who do not achieve at least six points in a total of twelve points relative to the assignments they have to complete throughout the semester (see details regarding assessment in special cases, particularly student workers) automatically loose approval in Didactics of Mathematics I. Student workers who wish to be assessed as regular students should inform the instructors via moodle or e-mail. Student workers who exceed the legal limit of absences allowed to the regular counterparts are immediately subject to the specific assessment regime aimed at student workers (whether they wish to be assessed like the regular students or not).

Calculation formula of final grade

All students are assessed continuously. If students exceed the allowed number of absences in class, they will fail the course.
continuous assessment is focused on
1) several assignments of exposition, discussion, analysis and reflection on various topics and texts, made by the students, during class sessions mainly (these assignments involve, in general, an oral component); if possible, one of these assignments will be focused on classroom observations and it might also include an oral component.
2) at least, 2 written assignments, with or without the uspport of materials, and with a certain time limit. students accomplish these assignments in groups, pairs, or individually - these assignments are mainly accomplished in class but can be also done at home. there may be an oral component in these assignments; the number of written assignments may be changed depending in the students' needs;
3) field work aiming at constructing teaching materials.
4) a final assignment, written, individual and global, during up to 2 hours

students' oral participation is assessed according to its quality, relevance, and pertinence.
The classification is the weighted average ot the assignments accomplished according to the formula

FC=A1+A2+MT+FT+OP, where 
A1 (written assignment(s) on specific content or transversal skills)=4 points
A2 (written assignment(s) on mathematical tasks and curricular materials)=4 points
MT (construction of a mathematical trail)=7 points
FT (final test)=4 points
OP (oral participation)=1 point

The final test usually happens until the last day of the first exam period. Whenever a student does not submit an assignment which constitutes an explicit assessment component, its classification is obviously null. 

Any student ou pair/group of students (including student workers) may be called to orally discuss any written assginment thtat explicitly constitutes an assessment component.

Student workers have a slightly different assessment formula once their oral participation cannot be considered.

Examinations or Special Assignments

There are no special assignments or tests except with deals with the assessment of the student-workers who cannot or do not want to attend classes with the same periodicity demanded of regular students.

Classification improvement

No students can improve the grade obtained in a completed assessment component, being a regular or a student worker, unless the assessment is explicitly proposed as a two-phase task. In this case, students have the opportunity fo improve their productions based on the feedback received - the grade will be the highest grade between the grades obtained in the first and ssecond phases.