Issues of assessment of educational results in mathematics (primary school)

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Issues of assessment of educational results in
mathematics(primary school)

• S. Gorbov

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Presentation abstract

• Issues of math education.
• Configuring math content in test. Content
  domains.
• Test construction. Levels. Level indicators. How
  the test tasks are made.
• Teachers professional development.
• Securing of focus of pedagogical influence.

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Whats measured by SAM

• Concept as a means of action
• Constructs of meaning vs skills

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Object-Related Content of the Test in Mathematics
Proficiency
Content Area Means of Mathematical Operations (Concepts, Representations) Mathematical Operations
Numbers and Calculations Positional principle (multiplace numbers) Arithmetic operations properties Order of operations Comparing multiplace numbers Arithmetical operations with multiplace numbers Determining the order of operations in an expression Estimation
Measurement of Values Relation between number, value and unit Relation between the whole and its parts Formula for the rectangle area Direct measurement of the length of lines and of figure areas (direct fitting-in of the unit, also unit fitting-in with preliminary rearrangement of the object parts) Indirect measurement (using measuring devices, formula calculations)
Regularities Induction step Recurrence (periodicity) Determining regularities in numerical and geometrical sequences as well as in other structured objects Calculating the number of elements in a structured object
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Object-Related Content of the Test in Mathematics
Proficiency
Dependencies Relations between like quantities (equality, inequality, multiplicity, difference, whole and parts) Direct proportionality between values Derived quantities velocity, labor productivity, etc. Relationship between units Solving text tasks Describing associations between variables using different mathematical languages (presenting such associations through drawings, diagrams and formulae) Operations with concrete numbers
Elements of Geometry Form and other qualities of figures (main types of geometrical figures) Spatial relations between geometric figures Symmetry Recognition of geometrical figures Determining relative positions of geometric figures
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Items block sample
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Items block sample
3. It is known that the area of a square with a
side equaling b is 4 times larger than the area a
square with a side equaling a (see the drawing).
Find the value of a.
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Items block sample
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Items block sample

1. Put a dot inside the square and the triangle, but
   outside of the circle.

2. Which of the figures below are
rectangles? Mark the correct answers.
3. In this drawing there are 4 circles and a
point B. Draw a line through the point B so that
it would have one point of intersection with two
circles and two points of intersection with the
other two circles.
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Items block sample
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Levels

• assimilation of concept mastering general
  mode of action
• Level 1 (formal) orientation to the form of
  the pattern of action. This level means that
  students have the ability to act per sample in
  standard conditions.
• Level 2 (object-related) orientation to a
  substantial relationship in the basis of the mode
  of action. This level means that students have
  the ability to determine the mode of action
  taking into account significant (object-related)
  relations lying at the basis of the task
  situation rather than its external
  characteristics.
• Level 3 (functional) orientation to the limits
  of the mode of action. This level assumes that
  students can freely apply the mode of action. An
  indicator for achieving this level will be their
  ability to resolve tasks in which it is necessary
  to transform (reinvent) a situation in a way that
  will either make it possible to see an option of
  using some known method or to create a new method
  using the old ones, applying it to the particular
  situation.

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Items block sample (Levels)
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Item block sample (Levels)
1. A rectangle is combined of three equal
squares. Determine the area of the rectangle if
the side of the square equals 10 cm.
2. A rectangle is combined of four equal squares.
A jogged line was drawn through it (see the
drawing). Determine the area of this rectangle if
it is known that the length on the jogged line is
20 cm.
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Item block sample (Levels)

• .

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Item block sample (Levels)
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Item block sample (Levels)
1. In which drawing the line intersects the
rectangle?
2. Put the dot in an area where it would be
inside two squares, but outside of both the
triangle and the circle.
3. The drawing shows a jogged line and several
dots. How many times will the AB line intersect
with the jogged line?
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Thank you for your attention!