I asked if the rectangle and square they had got from the pieces were equivalent and isoperimetric. In this case, they all answered correctly. In general, regardless of the number of correct or wrong answers, I noticed that due to what they discovered in this activity pupils were led to reflect more before expressing the position. We got many solutions, although they were not extremely different. It is interesting that nobody thought about copying from their deskmate, as if the object under consideration were something personal.
They certainly collaborated, but in a functional way to their solution needs. In particular a very good pupil female could not solve the problem [to find the area of one of the obtained figures] because she could not think using pieces. Some days later she confessed to me that when she solves a geometrical problem she only draws the figure to make me happy. The teacher thought she could use this tutoring to stimulate pupils to re-elaborate on their notions on a metacognitive level, in order to explain them to younger pupils.
At the end the children drew these figures on their workbooks. Tangrams were glued on cards and then cut out; each child was invited to recompose the figure already constructed and colour it as they fancied. The various pieces of each figure were fixed with adhesive tape, made stiff through bamboo sticks and then wore as masks.
At the end of the work there was a collective discussion in which younger pupils expressed their amazement in discovering that from initially identical Tangram they could make up such different figures. Among the sentences that most convinced young children we report the following, that seem to show an understanding of the work done and a non trivial capacity of verbal re-elaboration:.
After trainees who experimented the activities in the classroom presented their reports, discussion focused on the motivational value of the activity and everybody agreed on that , in particular on its potential to involve also pupils with scarce interest or capacity in mathematics. This prediction was not confirmed, although it was noticed that younger pupils were actually more involved in the construction of fancy figures, whereas older pupils were soon ready to move to work on geometrical figures.
In this phase we also noticed how this work naturally stimulates the acquisition of techniques, methods and terminology linked to geometrical transformations. Hence the proposal was made to consider, in classes after grade 6, the activity as preparatory for a module of laboratory-like geometry, to be located after completing the polygon teaching unit and aiming to a reflection on equal extension and isometries in particular symmetry, translation, rotation , as well as to reach competencies related to visualisation and recognition of geometrical figures in general.
At the end of the concluding discussion two further activities were proposed, one designed and partially already carried out by one of the trainees and the other presented by SSIS lecturers:.
If you digit the word Tangram on any Internet search engine you get the list of a great quantity of web pages, many of them suggesting teaching activities. Some pupils, as well as adults, have strong capacities for spatial view and graphical representation; some others meet difficulties on this ground. And it is well known that these capacities are not necessarily at the same level as other mathematical abilities. This difference in cognitive styles makes it necessary to propose to all students activities involving spatial view and verbal description of solids, so that students can complement their competencies and also weaker students on the computational and algebraic planes, but strong in this other field can perform highly.
To exemplify the mechanism, the following questions were proposed to SSIS students:. Imagine you open up the tetrahedron so that you get its plane unfolding. What is its shape? Is there only one? A boy constructed a figure using squares and equilateral triangles, we do not know how many. We know that this figure has 5 faces, 5 vertices and 8 sides. What figure is it? Video 4. Put the two pyramids on a plane, getting them aside, so that they only share one and only one side of the basis. There is an empty space between these two solids.
Would you be able to describe the solid that can fill in that emptiness, so that a convex solid can be obtained? Picture 7. Two 3D pyramids.
Combine now these 7 pieces to construct a solid as the one shown in Picture 8. Putting two of these solids aside what regular solid do we get? Picture 8. Our solid figure with 7 faces. The answers to questions B. Represent then this solid from the different possible perspectives frontally, from the right side, from the left side, from the top using a given dotted grid. Conversely, given its representations, reconstruct the solid. Of course in this type of activity, the main difficulty lies in having representations on different planes, some of which hidden to sight, and thus requiring a great effort for spatial representation.
However this activity is also suitable for creating links to other disciplines like Technical education and Arts, beyond offering a good support to a rational description of what is actually achieved each time. Gardner , M. Mathematics, Magic and Mistery. Dover Pub. Kanizsa, G. Firenze : Giunti-Barbera. Jaglom, I. Le isometrie. Bologna : Zanichelli. Pellegrino, C. Prospettiva: Il punto di vista della Geometria. Bologna : Pitagora Ed. The general aim of the proposal Tangram piloted in Slovakia was to make the teacher trainees think of the importance that problem activities of measuring can bring into the mathematics formation of the pupils.
We used the game of Tangram in seminars for the teacher trainees in their preparation for teaching static and metric geometry to pupils aged 11—14, that is, at lower secondary school. The main goal was the development of creative thinking and geometric imagination of pupils via using Tangram at school.
We aimed at preparing a school activity in which we could deal with the concepts of perimeter and area in different contexts. We wanted to use Tangram to demonstrate isometric transformations in measuring perimeter and area, too. Partners in Florence Italy , who co-piloted the project Tangram, provided us with the following feedback their view of the project :.
It is planned as a laboratory activity, so that pupils have to use their perceptive, manual and logical skills, starting from concrete objects to achieve geometrical and graphical competences. Pupils, at the end of activity, are expected. They provided us with the following variation of project aims:. The main aim was to define concepts, to develop creative thinking and geometric imagination and to make the student teachers aware of related didactical difficulties.
The aims of all three participants of the project Tangram have been essentially identical. The pupils could develop their geometrical imagination via a didactical game and to strengthen their knowledge from isometric and metric geometry. The teacher trainees prepared differentiated classes.
They studied the problem of mapping in metric geometry via a priori analysis. They could see the theme of modelling in geometry from a new perspective via a posteriori analysis. Most crucially, perhaps, is the change of perspective of maths being something boring to becoming a creative and fun activity, leading to a desire to tackle more advanced maths.
In fact, using Tangrams is one of the primary recommendations I make to improve the mathematical and thinking skills of the children who come to see me for assessment. It is easy to make your own Tangrams by downloading and printing one of the many Tangram templates available free online. Alternatively, inexpensive plastic and wooden Tangrams are readily available. While I have some plastic sets and many homemade ones, I am a recent convert to using Tangram apps.
An easy way to incorporate Tangrams into your child's day is to make up a Tangram box at the kitchen table and give your child the option of solving a Tangram puzzle while eating breakfast. I also know of some excellent teachers who have a Tangram table in their classrooms where children can go to work on a puzzle if they finish their activities before their classmates.
I am using them myself and I find them quite tricky! I have yet to find the perfect one for young children so I am using physical Tangrams with my toddler. What age group are you looking for? Identifiers publons. Navigate Abstract. Pre-publication review final round Decision letter, Nov Reviewer report, Nov Author response, Sep Decision letter, Sep Reviewer report, Sep Reviewer report, Aug Publication History.
Dec in Journal of Computer Assisted Learning. Effects of tangrams on learning engagement and achievement: Case of preschool learners Published in Journal of Computer Assisted Learning in Abstract The purpose of this research was to compare the effectiveness of physical and virtual tangrams on preschool children's learning engagement and achievement.
Contributors on Publons 1 reviewer. Metrics Publons score from 0 scores? Score publication. Add review. Otanga: JCAL R1 "Effects of tangrams on learning engagement and achievement: Case of pre-School learners" Thank you for this resubmission.
I am therefore very pleased to accept the manuscript for publication in JCAL. Thank you again for submitting your work to JCAL. We look forward to seeing it in print shortly. Best wishes Prof. Reviewer: 2 Comments to the Author This paper has already been well-revised based on two reviewers' comments. Decision letter by. Cite this decision letter. Reviewed by. Cite this review.
The authors have done a good job responding to most reviewer queries. However, some issues should be addressed first as the follows: Engagement is very important in this paper. Our response We have added paragraphs on engagement in the introduction and literature review sections. Our response We have explained why the learning achievement test was designed this way. Our response The reviewer may have thought the black colour in the paper outline is part of the tangram pieces. Our response We have deleted this suggestion.
Our response This was a citation according to the authors who made the comparison. Our response We have provided the theoretical background for the use of manipulatives in learning. Our response We have given a rationale for the relatively small sample size.
Our response We have explained this in the manuscript. Did the authors develop the learning test on their own, or is it from somewhere else? Our response We have indicated this in the manuscript.
Our response We have explained how the participants were assigned to groups to ensure the groups were equivalent.
Author response by. Cite this author response. A simple concept with powerful, brain growth positive results. Tangrams are a fantastic addition to your classroom learning centers or home lessons. Disclaimer: This article may contain commission or affiliate links. As an Amazon Associate I earn from qualifying purchases. Not seeing our videos? Turn off any adblockers to ensure our video feed can be seen.
Like building blocks or Lego, Tangrams are wonderful for teaching about spatial relationships. In addition, they are a powerful tool in mathematics. Students learn geometric vocabulary and strong communicators in math concepts. They also become capable problem solvers, confident in their critical thinking skills.
There are even indications that working on Tangram puzzles can increase achievements in math. Recently, we talked about Math Anxiety and how to tackle anxiety around numbers. One of the techniques we discussed was building foundational skills for math using games. Tangrams are a fantastic tool for helping tackle math anxiety.
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