🐼️ 🍅️ = 10 ; 🐼️ 🦋️ = 20 ; 🦋️ 🍅️ = 24 ; 🐼️ 🦋️ 🍅️ = ❓️
Back in โจทย์เลข สำหรับครูสมัยนี้ https://www.gotoknow.org/posts/702642 I posted a quiz without explanation or instruction but a clue that it was (is) a ‘math’ problem for children.
The points I am trying to raise are that
- if we can present math problems in a language that children can understand ('picture' is one such language that encourage curiosity and imagination), we can rouse children interests and help them ‘explore’ their mathematical thinking
- if we can hold children's interests, we can show them many essence and concepts of mathematics and allow them to work out practical applications of math.
- if we can use simple languages that children have already learned rather the more precise mathematical language that children have to learn at the same time as learning math, children may learn the essence of math now and later learn to refine what they learn in more precise language
- Teachers would, in the process of ‘visualizing’ math problems in children's languages, develop clear and demonstrable teaching tools that can help accelerate children learning at large
- I'll let you fill in more of ‘pro’ and ‘con’ (or ‘for’ and ‘against’) you would have many better ideas than I have had experienced ;-)
Let us go back to the picture quiz:
Do we need to explain the quiz and what the question is? (I found a 10 year old kid can ‘understand’ and solve the quiz in 15 minutes.
Now let us change what it looks like to demonstrate ‘transformation’ (in math) and to make it easier (for us) to type out. (Using ‘emoji’ rather than ‘image’ also helps to save data load by quite a few bytes.)
🔵️ 🔲️ | 10kg 🔵️ 🔺️ | 20kg
🔺️ 🔲️ | 24kg 🔵️ 🔺️ 🔲️ | ❓️
and then re-arrange into 1 line with a comma (;) between two given ‘facts’ (or 'math statements')
🔵️ 🔲️ | 10kg; 🔵️ 🔺️ | 20kg; 🔺️ 🔲️ | 24kg; 🔵️ 🔺️ 🔲️ | ?
Would you say (or convince the class) that we still have the same quiz but in a different form?
Let us show a slightly different quiz
🔵️ 🔲️ | 10m; 🔵️ 🔺️ | 20m; 🔺️ 🔲️ | 24m; 🔵️ 🔺️ 🔲️ | ?
Do you see the change fro 10kg to 10m, 20kg to 20m, …? So we have changed the context of the quiz from weight to distance (measure). But we have not changed the essence of the math problem at all.
🔵️ 🔲️ | 10%; 🔵️ 🔺️ | 20%; 🔺️ 🔲️ | 24%; 🔵️ 🔺️ 🔲️ | ?
What would you say about the change from kg or m to %? Have we change the essence of the quiz?
Now read carefully:
🔵️+🔲️ = 10; 🔵️+🔺️ = 20; 🔺️+🔲️ = 24; 🔵️+🔺️+🔲️ = ?
We have removed reference to ‘unit’ in the quiz, and voila it becomes a quiz in ‘pure’ number in math.
To go a little further
🐼️+🍅️ = 10; 🐼️+🦋️ = 20; 🦋️+🍅️ = 24; 🐼️+🦋️+🍅️ = ? ❓️
Have we changed the mathematical essence of the quiz? or do we have to write this out as
X+Y=10; X+Z=20; Z+Y=24; X+Z+Y = ?
to make it an ‘algebra’ quiz?
Can we prove ‘the commutative law’ that : Z+Y = Y+Z; and that X+Z+Y = X+Y+Z
I hope you enjoy this little excursion into a simple language for learning math in 'emoji'. ;-)
[I use Google's Noto-color-emoji font here. A lot more can be found at https://emojipedia.org/ ]
[We can solve the problem of the given 3 facts or equations in 3 variables in a standard Algebra substitution method or
by observing that there are 2 of each ‘object’ in the 3 given equations, so that by adding the 3 given equations up we get 2X + 2Y +2Z = 54 and X+Y+Z =54/2=27.
The value for each variable follows by observing its absence in 1 of the 3 given equations. – intuition can be powerful and simple ;-)
Would you like to share your emoji quizzes? We may have a good collection before the end of this term.]
[*Aside* There is a talk about ธนาคารหน่วยกิต for university students, so they can choose and study their own course at whichever ‘unit’ provider; and without losing credits of study they have attained. There are also examples of ‘examination questions’ (data)banks (or databases) which can generate ‘examination papers’ (or test papers). A number of websites operate on some models along this idea. Math questions (in text) are abundant, but in many different languages (some translations/renderings) may not be easy for Thai-speaking kids. (There are also issues of different ‘grade’ curricula among countries that for examples quizzes for 5th grade in USA may not be suitable for ป.5 in Thailand.)
A consolidated ‘open’ ‘questions’ (attributed by subject area, levels, dependencies, .. ) databanks can serve as examination/test (papers) generators for both students and teachers and also serve as a tool for managing education standards by editing questions and their attributes.
If the number of questions for each subject area has grow over a certain size, there is no need for ‘secrecy’ of the questions. Any one can draw and study any question. Only shortly before a 'formal' test or examination begins, the test papers can be generated, printed and secured for distribution. Modern technologies in (distributed) printing can reduce time to generate test papers before tests and thus can reduce value and incidence of ‘leaks’.
Those who study the open questions would have more chances to do well. And that is the aim of education.]
ความเห็น (2)
ANSWER… 27
Thank you GD. Your answer is absolutely correct.
Would you like to share ‘how’ you work this out?
I am sure as teachers we would be interested in the ‘process’ (logical steps before arriving at the solution or conclusion) more than just a correct answer.
We can quote a well-known proverb about teaching ‘how to fish’ because a gift is merely a temporary help. The children should learn not just remember answers.