15 research outputs found
Review: arrow cards
No full textArrow cards are a simple manipulative to grasp place value or more generally the base-ten number-writing system that we use. Dr Maria Montessori invented the static cards. These cards are used along with proportional material like static beads (unit = single bead, ten = 10 beads strung together forming a line, hundred = 10 tens strung together to form a square and thousand = 10 hundreds strung to form a cube) to gain a sense of numbers – the quantities they indicate and the numerals that represent them and how they are linked. When these cards are superimposed, they form the multi-digit number. When these transitioned to regular schools, an arrow got added so that the cards can be held up for an entire class to see. The cards are supposed to be held only by one hand holding the arrows together. This ensures that a number like 327 can’t be made with 300, 2 and 7. Even if a child tries to do that and succeeds thanks to friction, one flick of the hand would send the 2 flying out! So, the only way to make 327 would be to use the cards 300, 20 and 7 which is essentially a self-corrective feature, common to many Montessori materials
Triangles to Tetrahedrons and beyond…
No full textThe seed-idea of this article came from an activity from
an upper primary math textbook and the modification
in a subsequent edition. Students were asked to find the
midpoints of the sides of an acute isosceles triangle and join them
to form four smaller triangles, and then fold the triangles up to a
tetrahedron. An equilateral triangle replaced the isosceles one in
the subsequent edition. What caused this change? Wouldn’t any
triangle generate a tetrahedron? This initial exploration revealed
something unexpected and the findings had an eerie resemblance
to a known result. Further discussions with more math-friendly
minds watered and added subsequent layers to this exploration
and took it to a newer dimension – figuratively and literally! If a
perpendicular is dropped from the apex (which is the top vertex
of the tetrahedron where all three vertices of the triangle meet)
to the base, where will the foot of this perpendicular be? For an
equilateral triangle, it is the centre of the base but would it ever
be coincident with any of the triangle centres, i.e., centroid,
circumcentre, incentre or orthocentre of the base for other
triangles? We will investigate these
Low floor high ceiling tasks : Summing v
No full textThe Thinking Skills Pullout continues to be our favorite as it packs a lot of food for thought.
It has already generated a series of two articles including a LFHC (Dotted Squares) and a
TearOut. Here is another LFHC (which we have tried with a group of children from Class
3-4 in Pokhrama, Bihar, and with government school teachers from Telengana)
Assessing mathematical proficiency at the secondary stage – I
No full textThe National Education Policy 2020 emphasizes that “Mathematical thinking, problem solving, recreational mathematics, connecting classroom mathematics with ‘real life mathematics’ will be incorporated throughout the school curriculum …. in order to excite children about mathematics and develop the logical skills that are critical throughout school years and indeed throughout life.” The shift towards competency-based teaching and learning in the National Education Policy 2020 will be an important basis for curricular and pedagogical transformation in schools. In keeping with the thrust on competency-based teachinglearning proposed in the National Education Policy 2020, Azim Premji University has supported the Central Board of Secondary Education to develop a ‘Learning Framework.’ The learning framework is a comprehensive package which provides learning outcomes, assessment frameworks, samples of pedagogical processes, assessment items and marking schemes
Review : counters
No full textSimply put, anything that can be counted may be
considered to be counters. So, pebbles, chalk pieces,
bottle caps, seeds, buttons – all these are familiar
objects which can be utilised as counters. Square counters
can be made easily from (corrugated) cardboard boxes by
drawing a square grid with squares of side at least 2cm and
then cutting it up. Cutters (with steel scales) work much
faster for corrugated cardboard than scissors. Making round
counters from cardboard is more tedious but not impossible
(with difficulty decreasing as size increases). Carrom coins,
bottle caps (ideally of the same size), tooth paste caps are
great as round counters. It is advisable to paint the counters
in bright colours especially for younger children
Review: spinner
No full textData Handling, Statistics and Probability have gained prominence in school mathematics over the last 5-6 years and thanks to the pandemic we all understand how crucial it is to have a basic understanding of probability. This topic is included in Classes 7 and 8 according to the NCERT syllabus and is part of the respective data handling chapters. However, the probability portions of these two chapters seem very disjoint from the rest of the data handling parts. The integration happens later in Class 9 when chapter-wise statistics and probability are separated! However, one does not need to wait that long. Spinners provide an excellent way to integrate probability within the rest of data handling along with many other benefits
Manipulative Review: Geoboard
No full textUnlike many other teaching-learning materials (TLM) for
math, which we would like to call mat(h)erials, geoboard
is very well known among teachers and referred to in
teacher education programs, pre-service in particular. It is a board
– wooden or plastic, with many pegs or nails stuck on it. One can
stretch a rubber band along some of these pegs to create many
polygons
Manipulative Review: Ten-frames
No full textTen-frames are not well known in India. But they do have certain advantages and can be made very easily. There are also virtual ten-frames in several websites. A ten-frame is a 2 × 5 frame with slots on which counters have to be put, to represent various numbers up to ten
Integers: Extending the Number line with Coloured Counters
No full textThis article is intended for students – as hands-on play with integers by extending the number line and combining it with coloured counters. For this activity, rectangular dot sheets are better than square grid sheets since the dots can be joined by horizontal lines to form number lines and will not get mixed up with existing lines. We also recommend a sketch pen/crayon/colour pencil of two contrasting colours to draw the counters
2D Base-10 Blocks : (also known as Flats-Longs-Units)
No full textMany teaching- learning aids help one understand the base-10 structure and how we conceptualise and use whole numbers. Several of these also aid in introducing and exploring the four operations. We found that the best of these is 2D base-10 blocks popularly known as Flats-Longs-Units (FLU). The unit is a small square or a 1. The long is ten times the unit and therefore a 10. Finally, the flat is a bigger square, a hundred times the unit and ten times the long, therefore a 100. Figure 1 illustrates these basic blocks. All three types of blocks should be of the same colour for the reason explained below
