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Sophia Institute online Waldorf Certificate Studies Program

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Waldorf Methods/Reading and Math 3

Introduction

Language is our most important means of mutual understanding and is therefore the primary medium of education. It is also a highly significant formative influence in the child’s psychological and spiritual development and its cultivation is central to the educational tasks of Steiner/Waldorf education. It is the aim of the curriculum to cultivate language skills and awareness in all subjects and teaching settings. Clearly the teaching of the mother tongue has a pivotal role within the whole education.

Mathematics in the Waldorf school is divided into stages. In the first stage, which covers the first five classes, mathematics is developed as an activity intimately connected to the life process of the child, and progresses from the internal towards the external. In the second stage, covering classes 6 to 8, the main emphasis is on the practical.

Course Outlines

Waldorf Methods/Reading and Math 1
Lesson 1: Introduction
Lesson 2: Reading/1st Grade
Lesson 3: Reading/2nd Grade
Lesson 4: Reading/3rd Grade
Lesson 5: Math/1st Grade


Waldorf Methods/Reading and Math 2
Lesson 1: Math/2nd Grade
Lesson 2: Math/3rd Grade
Lesson 3: Reading/4th Grade
Lesson 4: Reading/5th Grade
Lesson 5: Reading/6th Grade


Waldorf Methods/Reading and Math 3
Lesson 1: Math/4th Grade
Lesson 2: Math/5th Grade
Lesson 3: Math/6th Grade
Lesson 4: Reading/7th and 8th Grade
Lesson 5:
Math/7th and 8th Grade
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Tasks and Assignments for Waldorf Methods/Reading and Math 3.2.

Please study and work with the study material provided for this lesson. Then please turn to the following tasks and assignments listed below.

1. Study the material provided and look up other resources as needed and appropriate.
2. Create examples of curriculum that addresses the learning method and content appropriate for the age group in question as follows. Curriculum examples should include outlines and goals, activities, circle/games, stories, and illustrations/drawings:
Create 2 examples for this age group.
3. Additionally submit comments and questions, if any.

Please send your completed assignment via the online form or via email.

Study Material for Waldorf Methods/Reading and Math Lesson 3.2.

Arithmetic and Mathematics/Class 5

General Observations and Guidelines

Classes 4 and 5

Upon reaching their ninth year, children make  a decisive change. Their close relationship to the  world around them becomes different and more  remote. The earlier harmony between outer and  inner worlds is fundamentally broken.

This transformation in their soul is reflected  in the mathematics curriculum when in Class 4  the children begin to work with broken numbers  (fractions). By this means they meet something  in the teaching content which they have also  experienced in themselves.

It is not essential for the children to be able to  manage fractions swiftly. It is much more important  that they can experience these 'external' fractions  very strongly. In connection with this, the historical  development of fraction calculations in Egypt can  give the teacher interesting and Significant teaching ideas. In order to do general justice to the subject  of fractions it is recommended to use the following  three methods as an introduction: To proceed from  the whole to the parts, from the parts to the whole,  and to establish the principle of equivalence. After  this the four rules are practised with fractions, the  same with simplifying, expansion and division of  the denominator into prime factors.

After this, decimal fractions follow as a practical  application. Once the divisibility border is crossed  the children can discover the practicality of  calculations in Class 5.

The aim according to Steiner is as follows: 'in  Class 5 we want to continue with fractions and  decimals and to give the children everything which  will allow them to calculate freely with whole and  fractional numbers,"

In Class 4 form drawing is led into elementary  geometry. Here one can begin again with the basic  linear polarity of circle and straight line. In order  that the pupils get as intensive an image as possible  of these forms, it is recommended that they do not  initially use compasses and ruler, but draw free-  hand.

Although we deal with the most basic elements  in the first geometry lessons, it is important to let  the pupils feel something of that dimension which  is connected with existential questions over and  above the practical and utilitarian. This is made far  easier if the beauty of form and strongly regulated  connections of geometry are felt in addition to the  working rules and methods.

In connection with stories from ancient Egypt  in the history lessons, the Pythagorean rope can be  introduced as a first introduction to Pythagoras'  Theorem.

Class 5

* Constant practice in mental arithmetic * Revision: the four rules with natural numbers
* Combinations of the four rules
* Calculations with fractions: expansion and  reduction of equivalents (division into prime  factors)
* Illustration and comparison of fractions,. Calculation with decimals. Consolidation of  fractions methods
* Table of place values, rhythmically, through  movement, and qualitatively introduced
* Introduction of the relationship of decimals to  place values
* Measurements using decimals
* Recognition of connections between decimal  numbers and decimal fractions

The main new task for Class 5 is learning to use  a pair of compasses with accuracy, though some  teachers prefer to wait until the beginning of Class 6.  The forms previously drawn in Class 4 can now  be accurately constructed. Children will naturally  colour these flower-like forms, and thus make an  obvious link with the botany main-lesson in Class 5.  A set square and ruler can also be used to draw  accurate parallel lines.

* Starting with the construction of a circle,  discovery of the main geometrical figures:  triangle, hexagon, square, rhombus,  parallelogram, octagon
* Division and joints on 24-point circle
* Construction of perpendicular bisector,  angle bisection, perpendicular bisector, angle  bisection, perpendiculars
* Construction of different triangles; equilateral,  isosceles, scalene, right angled
* The various angles; acute, obtuse, reflex.
* Circles touching a triangle; inside (incircle)  and outside (circumcircle)
* Pythagoras' Theorem; visually using knotted  string. (Egyptians used this to construct their  pyramids). Grains covering an area, theorem  drawn using Roman tiles (Isosceles triangle)
* Tessellation (tiling) involving accurate construction of parallel lines
* Exact construction of pentagon/pentagram

Numeracy Checklist for Class 4 to 5

Most children within the normal range of ability  will be able to:

Number
4    carry out all four processes of number  confidently
4    read and understand numbers up to six figures
4    know the multiplication tables up to 12 out  of sequence
4    do long multiplication with numbers up to 122 as multiplier
4    find factors of a given number
4    identify prime numbers less than 100
4/5    answer more complex mental arithmetic  questions involving a mix of processes (e.g.  The 12.38 train to Reading takes 18 minutes.  but left 14 minutes late, when did it arrive? or  I doubled a number and added 8 and got 32,  what was the number?)
4/5    do long division including making use of  remainder and estimating approximate  answers.
4/5    find Lowest Common Multiple or Highest  Common Factors
5    use all four processes with fractions including  mixed numbers and improper fractions
5    understand how to use decimal notation,  decimal fractions and interchange of decimal  with common fractions
5    carry out four processes with decimals
5    use long division and multiplication using  the decimal point
5    apply the Rule of Three (if, then, therefore) to  practical problems

Measurement
4    record information such as height, weight,  volume, etc.
5    work with metric measurement including  estimation
5    work with aspects of time including 24 hour  clock
5/6    calculate average speeds

Geometry
5    draw freehand archetypal geometric shapes:  different kinds of triangle, rectangle,  quadrilaterals, polygons and circles
5    divide circles into 17, 16 or 20 parts, deriving  regular figures like pentagon and hexagon  from them

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