Main Page -> Working Seminars -> Children 7-9 years old
Guided by M. Hejný, D. Jirotková, J. Slezáková
Charles University in Prague, Faculty of Education

Acknowledgement: The research was supported by VZ MSM 002 162 0862

Scheme is understood as the memory structure that incorporates clusters of information relevant to comprehension. Scheme-oriented mathematics education on the primary level is described and illustrated in M. Hejn's plenary.
The aim of working seminar is to familiarise participants with schema-oriented education of mathematics via dealing with several semantic environments.

The guides of this working seminar are authors of textbooks for grade 1 and 2 for Czech pupils. The textbook for grade 3 is in progress. The textbooks with the guide for teachers will be available during our working seminar.

Seminar schedule:
 17.08.2008 Introducing ourselves and topic introduction
 18.08.2008 WalkCreating language for given process, improvement of the short-term memory, number as address and operator, negative numbers, minus of minus, system of equations, absolute value, statistics, stochastics
 19.08.2008 BusCreating language enhancing procept of number, improvement of the short-term memory, number as state and operator, analysis of more-parametric situation, decomposition a set of realition with respect to two parameters
 20.08.2008 Farther WoodlandGetting familiarity with the iconic language of small numbers, equations (including Diophantus's), unequalities, partition, divisibility, understanding of combinatoric
 21.08.2008 Cube buildingsFormalisation of existing experiences with cube blocks, pictorial, iconic, processual and conceptual languages for the description of 3D-objects, spatial ability
 22.08.2008 Presentation of participants' results and discussion

Structure of four working seminars (August 18, 19, 20, 21)
  1. Introduction to the environment (5 - 15 minutes)
  2. Participants solve given problems with the aim to get familiarity with the environment. (15 - 20 minutes)
  3. Primary teachers: J. Michnová and L. Kalčíková present their class experiences. (10 minutes)
  4. Participants create sets of problems for pupils, prepare scenario for a particular lesson or even prepare conception of a given topic. (30 - 40 minutes)
Commentary to Issue 2. Two of the problems which will be given to participants are presented below.
Problem 1 (to the environment Walk): Fill in six arrows to the three empty boxes to fulfill both equations:

Find all solutions. Remark: In each box arrows only of the same direction are allowed.

Problem 2 (to the environment Bus): Fill in numbers to the table recording Bus-performance. You know that the numbers of passengers entering the bus at each stop A, B, C, D are same.

Commentary to issue 4. Our understanding of the challenge prepare conception of a given topic is illustrated by "Conception of environment Walk for grade 1".
The conception is described by a set of nine stages, some of them ellaborated:
  1. Walk as a process. (preschool kids) A three-year old can already walk. By interconnecting this action with clapping, a song, a riddle,... - the child subconsciously synchronises the two actions, achieving "process".
  2. Walk as a figure. (1st grade) The steps are now accompanied by a specific singsong: "One, two, three...", recited by the teacher or the child. The singsong refers to certain objects in various real-life contexts. The child does not yet see the connection between the word "three" as three apples on a plate and "three" as three steps.
  3. Social aspect of Walk. (1st grade) Climate in the class, collaboration of pupils.
  4. Walk on command. (1st grade). Once the pupils have mastered the Walk, the teacher adds another element - commands. The teacher appoints a pupil-figurant and gives him/her a command: "Five steps forward, go!" The pupil is marching, with the class counting in rhythm with his steps. "One, two, three, four, five."
  5. Standardising the steps. (1st grade) In order to keep the lengths of pupils' steps the teacher places a sequence of marks on the floor.
  6. Compound Walk. (1st grade) The teacher introduces two-part commands consisting of two numbers, e.g. "3 steps, then 2 steps, go!"
  7. Walk backwards. (1st grade) Commnads like "Two steps backward, go!" are introduced and performed.
  8. Taking records of Walk. (1st grade) As the commands grow longer, some pupils find it difficult to remember them. The way of recording Walk performance is needed. Pupils will create different languages and the teacher will choose that one which uses arrows.
  9. Addition and subtraction. (1st grade) The teacher starts to use this environment for adding and subtracting numbers as operators.
We hope that our collaboration will produce valuable results which will be elaborated as a monography.

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