Practice Math Using Pictures

This article is about “Teaching Math Using Pictures”

Random pictures from your daily life can be a catalyst for thinking!
Pictures have always been an excellent visual aid for building literacy and vocabulary skills…What Math can you teach using pictures?

Lets explore!  Make Math more engaging sessions from now on…

Quite apparent that some topics in math like Data handling needs pictures or images to build the concept concretely. I personally feel, there is a necessity to involve more pictures in every other session of Math.Find below some of my ideas.

Please feel free to try them out in you classroom as well.I have attached few photographs that are from our daily life.Let’s see how Math can be taught and practiced at primary level using these as resources in Math sessions. 

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1.This picture was taken in Zac’s Zumba class last Saturday.Which child has created an acute angle using his hand and trunk of his body? Identify and circle him.

toy wooden blocks, multicolor building construction bricks 2.In the collection of 3D shapes packet sold in Toys R Us ,which other 3D shapes did the shop keeper forgot to place in?

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3. Anu’s daddy bought this new open shelf to stack formal shoes,sports shoes and organize them.If every slot can have three pairs, how many pairs can this open-shelf accommodate?

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4. This is the picture of Mr. Remo’s house. How many triangles can you spot and how many rectangles can you spot? Turn and Talk to your partner.

Well, I strongly believe by using pictures or ideas from real life Math teaching and solving problems based on them is going to be fun.

                           Pictures might turn out to be a motivation factor too!

Please click on the link for more images and the concepts that can be taught using them.

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Hope you try them and share your thoughts and experiences too!

Awaiting your responses…

Sudha Mahesh,Primary teacher

Authentic Learning

Did he get it?!!!

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Off late, I have been reading and unearthing answers for How an authentic learning takes place? Why does it differ from one child to another?

Soon I realized the cognitive process has to supported and not always the content and procedure to attain the content.So,What plays a major role then?

Is it the teacher’s stimulating plans?  Is it the Style of teaching or is it all about what activities I have chosen?

What If I just give extra time and go according to the learner pace, Am I making a smart move then? OR Is it about the age of learner ?

As teachers in practice, we all would have come across situations in classes where we might want to stop the teaching session and sit with that one child to see how far and how much more I need to help him/her to reveal certain conceptions and unveil misconceptions.

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By nature unknowingly, as facilitators of learning, we might be addressing the topic alone, content or that specific day’s sessions activity.We might fail to address  or consider the bottom of ice berg which is nothing but the aiding the cognitive process of that child.

Despite the best instructional practices and with good language skills in place, we find few of them are left with no choice other than attending remedial, after school hours special classes, focus oriented games and many other possible methods to “ACQUIRE IT”

Our own cognitive structures as adults, that has absorbed a detail using some patterns and connections doesn’t allow us to be empathetic with a 7 or 8 year old and often leaves us puzzled as to why is the child not able to “Get it” that is so obvious?

The onus often lies on the shoulders of educators and the institution. I realize that mediation of awareness and reflection also comes from home front.

The more enriched experience a child gets through addressing their cognitive structures such as,

  • Making the connections
  • Identifying patterns
  • Making sense of rules
  • And abstracting principles the “Getting it” problem solves.

Glad to share that there is one more side to it! 

Here I mean the authentic learning.

Some of the excerpts from the book I have been reading online, Getting to “Got It!”

by Betty K. Garner

I would like to share with all of you, How a thinking is processed for every child and how it differs in each one of them?

As teachers if you are already on the track of planning smart objectives ,if you have given time for reflection, if you give feedback individually or do take out time to give personal touch, If you have combination of small group and large group sessions and activities planned…Do feel contented about it.

You are on the right track.for-blog-nov1

Do not feel dejected or low, brooding over those few occasions when you felt, “Oh! What else have I missed out in making this child “understand”?”

The author Betty K.Garner shares…

….Meanwhile, sitting in the same classroom with the struggling students are the high-achieving students. They thrive on our well-prepared lessons, and secretly we suspect that they could learn from anyone at any time with any kind of method. They can do this because they know how to gather, process, and output information. They have well-developed cognitive structures.

…….Often, neither the struggling students nor their teachers are aware of what lies behind the students’ failure. The teachers get frustrated and conclude that the students need to pay more attention, work harder, or change their attitudes. The students have no idea why they don’t get it; they think that the schoolwork is simply too hard or doesn’t make sense. They may quit trying and become behavior problems, or they may slip through the cracks in the system, passing from grade to grade with minimal competency. Those who do get by typically do so by using memorization or imitation strategies. Although these tricks can help students find right answers, using them gets students no closer to experiencing the joy and excitement of deep understanding. They get no closer to developing metability( the word was coined by the author as meta -change and ability)

The more educators learn about how cognitive structures affect learning, the more causes there are for us to be optimistic. There are two key points to keep in mind:

  1. Each individual has to develop his or her own cognitive structures. However, just as good coaching helps athletes improve their performances; good teaching provides learning opportunities that stimulate students’ reflective awareness and visualization and help them develop their cognitive structures.
  1. It is never too late to develop cognitive structures. From infancy through old age, everyone who has the neurological capacity to communicate, to be reflectively aware, and to use visualization can develop cognitive structures. When I work with students who are struggling in school, I explain that they already have the capability to learn; what they need to do is learn how to use their “mental tools.”

As noted, students develop cognitive structures by being reflectively aware of sensory input and by visualizing information for processing. It’s often the case that many so-called “smart” students are those who have received the most effective mediation at home. Encouraged to visualize and reflect from an early age, they come to school with well-developed cognitive structures. Students who appear “slow” due to underdeveloped cognitive structures may have grown up with little mediation or encouragement for reflection and visualization. 

Well, I felt personally, on reading these excerpts that we can be rest assured that well planned instructional lay out does have effect and aids learning authentically.

One more important take away for me after reading the book was, “What does this mean to me?” and “How would I explain this to someone in my own words?” When any learner begins to ask themselves these questions, they become their own teachers.

It differs from each and every child when the complex cognitive process falls in place where hypothetical thinking and making cause and effect relationships, all of these takes a shape and a concrete form. It’s always  through making connections, identifying patterns, following certain rules and ideating abstract things.

To put in in simple way, unless the rules of Mathematical operation is followed it is going to be tough for any child to master it. This is our perspective.

But, does the child understand ‘RULE’ as a convenient tool to classify the right from the wrong and helps elucidate learning.

They might presume any rule as some absurd statement that makes no sense to him/her personally. Unless this is unveiled it is going to be a boredom session of Math making no impact in learning space.

As educators we must try and attempt to get closer to learners through simple questioning. Once the right chord strikes, there up on the identification pattern and making connections takes over.

I am sharing form the book one such conversation the author had with a primary child , “What is rule and why it is followed?”

Greg: Exploring the Meaning of Rules

I started our exploration by asking Greg, “What is a rule anyway?”

He responded, “Something you can’t do.”

“Give me an example,” I prompted.

“Don’t run in the hall. Don’t fight. Don’t talk out in class.”

“Those are school rules. Do you have any rules at home?”

“I have to be in at a certain time,” he said. “I have to clean my room.”

“Do adults have rules?” I asked.

“No, they can do whatever they want. I will too, when I get big.”

“Do adults have to be at work at a certain time or do what their boss tells them?”

“Well, yeah!”

“What about laws? Are laws like rules that we all have to follow?” I asked.

“Yeah.”

“Where else do you have rules?”

“At restaurants you have to pay for your food and act a certain way. Don’t steal.”

“OK,” I said, nodding. Then I prompted Greg to think beyond the negative constraints. “Have you ever thought of rules as being there to help you and keep you safe?”

“Not really.”

“What about games? Could you win a game if there were no rules?”

“Sure! You can cheat!”

“How would you know if you were cheating if there were no rules? How would you know if you had any points, or won or lost?”

“Oh,” he said and then paused. “I never thought of it like that.”

“What if you thought about rules as being there to help you win, to make learning easier?” I suggested.

“What do you mean?”

“In math, for example, if you know the rules for multiplying and dividing, it’s a lot easier to do the work,” I explained. “In language arts, if you know the rules for punctuation or how to spell a word, you don’t have to look it up each time.” Through our interaction, Greg realized that a rule was a guide you could count on to be the same in most cases.

When working with rules, the ability to automatically predict builds confidence and enables students to quickly process more difficult and complex information. We cannot assume that knowing a rule is the same as knowing when and how to use that rule.

 Most teachers are trained to first teach rules and then have students apply these rules by making connections with content. I recommend instead inviting students to make connections and find patterns and relationships before asking them to formulate rules. For example, rather than teaching rules about punctuation and quotation marks, give students texts and have them work together to identify when, where, and why punctuation is used. When they identify patterns and formulate rules, they can test these rules with other texts. In addition, students are more likely to remember these rules because they created them. Does this approach take more time? Yes. Is it more effective, and will it save time in the long run? Yes.

Please find time to check out this book to gain more insight in to meaningful transactions that lifts up the morale of educators which in turn will benefit the learners as well.

The Space In Classrooms,Not The Physical But The Cognitive

Few days back I was wondering and pondering over a thought on ‘creativity and prior knowledge’.I had posed this question to my fellow people,”Prior Knowledge –Does it rule creativity?”.Today I am sharing with my readers on what I have perceived as zone for originality and how it can be nourished by us as educators.

‘Think Out of the box’-The moment a teacher tells this to the learner, somewhere unknowingly it subdues the child’s risk taking factor in thought process.By defining a boundary called  ‘box’ and then thrusting saying ‘to go out of the box’ there is ambiguity as to where to start and what is acceptable!

Why define a boundary in first place? Creating an imaginary boundary that cannot be internalized and on top of  that provoking them to move out of it!

There isn’t any box. It’s all “in there or out there”. Any reply that has never been told by others in a group or in a classroom. An answer that never came out so far, a word being replaced by its synonym,an illustration that has something different from others OR any two pictures that are not same…Doesn’t it mean creativity has surfaced? An expression that says a lot more than words…Won’t we accept them as creativity?

As teachers we have always learnt pedagogical approaches that are proven to establish sound connections and lays foundation for knowledge gained. It is indeed essential. Does it stop there? In case it does, then the child is definitely ‘successful’ at the end of formal education obtained, but seldom turns himself or herself in to a decision maker later in life. It is apparent because throughout out the formal education time he/she has always perceived something out of what existed already and what will happen next lies in the predictable  horizon. At times during academic sessions of Science or performing Arts, the inherent quality of not being rationale, emerges out but again in a safe zone of predictability.

We raise our chin saying we are always rationale. Being rationale means building our own ideas based on what we observe /heard previously and to create our own perceptions about something. Being rationale falls in safe zone. No one can point out our errors. That’s because it has foundation.

What is more difficult is to prove something that has no foundation. And to develop that sense in learner, it needs practice for the mind, an urge and spontaneity to overlook prior knowledge sense and yet define the unknown.

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This ability to create and nurture the same to certain/marginal extent lies in our hands as an educator.

It is extremely crucial for educators to “Exploit the learner Potential” as I would term it to be. It is known that as educators we find that fear of failure is reduced or never exist in the young minds. So why not exploit their potential then, Rather than cribbing about learner not being creative enough in later years!

To avoid this I personally feel educators at class room level should avoid defining or proclaiming… ‘The correct answer is’. During last week, post my experience in setting assessment paper and answer key to that, I was sharing my views to one of my colleague on answer keys created.

I realized off-late, the vast and expanded our answer keys are prepared, we are practicing being a risk-taker and in turn it would reflect in the mind set of learners we handle.

As teachers we always believe that any reply that is given by or told by learners has had a thinking process and it reflects later. So unless we take the initiative to figure that process behind every reply we are unknowingly curbing creativity.

Coming to prior knowledge’s role in grooming creativity…it is purely in the hands of teacher who handles to transform and translate the prior knowledge as a base for creativity. It doesn’t have to be a clean canvas for new painting to be created. The existing painting can be modified or redesigned too.

It is not that easy to connect abstract ideas and henceforth develop new ideas.It becomes imperative to support the foundation with some amount of knowledge. We need to be conscious that we limit it to an extent and thereafter proceed the further sessions towards instilling problem solving skills and critical thinking  ability.

Of course, an airplane came in to existence looking at the flight of bird.

Can we deny that? Don’t we enjoy remixes of popular tunes? 

As teacher we need inputs, training and exposure on “Questioning Skills” practiced in class room to make our classroom transaction more enriched.

Check out my previous article on ‘Questioning skills’ that enhances academic sessions.Questioning, A skill to acquire

Please find below few more ways to kindle diversified replies from the learners.

Keep them ignited.

I always believe in the quote, “I have not failed 10,000 times but found 10,000 ways it won’t work”-Einstein

  Using Precise Terminology to Encourage Thinking

Instead of Saying: Say:
‘Let’s look at these two pictures.’ ‘Let’s compare the two pictures’
‘What do you think will happen when …’ ‘What do you predict will happen when …’
‘What do you think of this story?’ ‘What conclusions can you draw about this story?’
‘How can you explain …?’ ‘What evidence do you have to support …?’
‘Let’s work this problem.’ ‘Let’s analyze this problem.’

Adapted from: Costa & Marzano (1987)

Courtesy: http://iteslj.org

Encouraging Learners to Think About Thinking

When Learners Say Teachers Say:
‘The verdict is, guilty as charged.’ ‘Describe the steps you took to arrive at that answer.’
‘I don’t know how to solve this question.’ ‘What can you do to get started?’
‘I am ready to begin.’ ‘Describe your plan of action.’
‘I like the large one the best.’ ‘What criteria are you using to make your choice?’
‘I am finished.’ ‘How do you know you’re correct?’

Adapted from: Costa & Marzano (1987)

Please find below a link from ted.com.It’s need of the hour in education system across the globe.The speaker shares what lies in future and why  there is a necessity to change the entire outlook of public education.

Questioning, A skill to acquire

In my last blog I had discussed about the important skill a student needs to develop which is reading.Here I am going to share my thoughts on one of the effective strategy in teaching that is ‘Questioning’.

The art of questioning and powerful questioning methods dates back to Vedic ages, probably Mughal period and medieval periods too in the East, and to ages of Socrates in western culture. Socrates asked questions to his fellow Athenians in a dialectic method (the Socratic Method) which compelled the audience to think through a problem to a logical conclusion. Wherever used, questioning skills always leads a scholar to win over their opponents and to spread their ideologies and philosophies on a particular concept.

Their questioning patterns brought out the insight and deep knowledge they had. It also showcased the vast knowledge they had gained in their life time through education and experiences.

Questioning -Is it an art?  Does questioning involve a bit of science?

I think it has both in the process. I believe ‘Questioning’ has lead to clarity and wisdom. It has challenged assumptions, exposed contradictions, has paved path for new knowledge and theories.

As teachers,licensed person who gets the authority to spread knowledge and expel darkness from young minds, don’t they need to train themselves to use this powerful tool efficiently?

For instance if I were to ask you at the end of this article,

Did you understand what is questioning skill?(I may get these replies )

Yes I understood,

Some what I understood

 May be its important skill but still not clear.

There could be no response from few of you. You may not want to extend your replies more than the yes/no or just keep mum and wait for others to reply that.

Instead if I were to ask you…

Given that there are many ways to question students in class such as verbal/written/multiple choices or a subjective question, which questioning method would you prefer for your students and why?  

The moment you read the above question…

  • You will start processing in your mind and try to answer this by considering the age group of your learners, recalling your experiences in class, connect it with your peers experiences if they had shared it with you and many others factors.
  • You will also think of your recent classes where you had tried any of these and you will start justifying which worked better for you.
  • Your brain makes connections spontaneously without any external motivation to answer.
  • You are self motivated to answer this because you link it to yourself and your experience.

The way I inquire should make you recall/Identify/classify/justify your replies.It should make you speak few more words than a simple chorus yes/no

This was just an example for close ended and open ended questioning.

There has to be methodical approach in questioning too. This technique can be arrived based on Bloom’s taxonomy verbs. Renowned educational psychologist Benjamin Bloom’s had researched in 20th century on the classification of learning objectives and created purposeful verbs that a teacher can use while making her lesson plans. These verbs would guide her to be clear and specific about the objective of a particular session.

The complexity of questions should move from lower order questions to higher order questions.Here is why I consider ‘Questioning skill’ also involves scientific approach.

Of course there needs to be questions like…

What is the name of author? Who wrote this book? What book you read yesterday?

A good teacher should slowly shift this to divergent questions that will make them think and answer. Here we can make use of Bloom’s taxonomy verbs to make the shift from Lower order to Higher order thinking through questions.

It is imperative that a teacher must give importance to lower order questions and then move on to higher order.No where in studies and researches it is mentioned that teacher needs to rule out lower order questions.

Bloom’s Taxonomy provides a structure for developing questions that encourage students to think on different levels.  In order, from lower to higher the levels are:

  • Knowledge (facts, recall, recognition)
  • Comprehension (translation, interpretation, extrapolation)
  • Application (to new or unfamiliar situations)
  • Analysis (break into parts)
  • Synthesis (combine elements into a new pattern)
  • Evaluation (apply criteria to defend the conclusion)

 

Check out this link for more insights in to Bloom’s https://tlc.iitm.ac.in/PDF/Blooms%20Tax.pdf

It is essential that a teacher enters the classroom with planned questions and possible replies. At the same time, as she plans to ask open ended questions she also needs to have an in-depth knowledge on the topic to be discussed in the class. Many a times I have observed that if a teacher fails to sustain that interest of ‘probing by questioning’ method from a student’s end then the students slowly lose interest in the topic.

Here are few questions that can be asked to invite multiple replies and delve on discussions for enriched experience in a class room

  1. Is the boy happy or sad? Instead you can ask…

What kind of expression do you see on the boy’s face?

  1. Can you sort these objects in to big and small? Instead you can ask…

In what all ways you think these objects can be sorted?

  1. What is the name of our national bird? Instead you can ask…

A bird that can sense rain seeing dark clouds and can dance beautifully is our national bird. Can you guess the name?

 Any indirect clues that will make students imagine, relate to their learning, make connections, in turn even ask you back a question to verify and answer…

Training students to ask value added questions in a class  empowers them and makes them accountable for their own learning.Reward a student and acknowledge them if their question provokes a thought process in class discussion.

 Isn’t questioning skill a must for a teacher?

This is a close ended question. From here I should move on to higher order thinking questions…

Create few questions for your next session and classify them as closed ones and open ended ones.

Frame questions in such a way that brings out the best from a child. Plan your questions! Do expect a surprise and an ‘Aaha’ moment in your class.

(courtesy-wikipedia About bloom’s and classification of bloom’s)