Pure Science and Maths

#Mathematics – Mistake versus Misconception

First things first – before we start discussing different strategies in remedial teaching, in my opinion, it would be a great idea to walk through some common mistakes and misconceptions related to mathematics. As we agreed in our previous post, that every child has its own way of learning; in this post, we shall see how each child makes mistakes differently. 🙂 And yes, mistakes are different from misconceptions. This is where a teacher needs to be sensitive and sharp enough to differentiate between the two. Let us begin the diagnosis!

The Difference Between a Mistake and Misconception:

Here is a Grade 2 student’s response to a given set of questions: try to identify the misconception in the following two problems.

a. Use < as ‘is less than’ and > as ‘is greater than’ signs to compare and order numbers:

  1. 73 < 79
  2. 25 = 25
  3. 45 < 56
  4. 51 < 49

b. Add two digit numbers:

Add

By now you would have understood the learner’s misconception; somewhere s/he is struggling with the basic concept of place value, isn’t it?

Just look at the a.4. (51 < 49), the learner seems to have compared the one’s place values; 1 in 51 with the 9 in 49 and thus, we see the alligator’s mouth open towards 49 instead of 51. A similar mistake due to misconception can be seen in b.2. (28 + 56 = 714), wherein the one’s place has been added to get 14 and the ten’s place adds up to 7 – instead of carrying 1 for addition in the ten’s place, it remains below, and hence, getting a result of 714 instead of 84. If you have observed something else too, please do mention in the comment below.

As a teacher correcting tons of pages daily and beginning to get insensitive over a period of time, the teacher would not mind putting a big cross to the above answers. With good intent, s/he would also give additional worksheets to solve (most of the time downloaded from the internet). Here is another thing about ready made stuff: the beautifully designed mark sheet or score card may even say that the learner’s understanding in ‘comparing and ordering numbers’ is 75% and is likely to be promoted to next level. Now as s/he progresses to the next grade, the learner has to deal with 3 to 4 digit numbers. And the new errors would look like this ‘1105 < 999’. In this case, the ready made stuff didn’t help in learning but surely in the promotion (of error). The learner is likely to continue to get such answers unless someone takes a little moment to reflect as to how is s/he arriving at the incorrect answer consistently. Which according to the learner is the correct answer but there is no iota of doubt in the learner’s mind!

Here is the fine line between the two… Remember mistakes are usually one-off. If the problem is shown again to the learner, s/he may figure out the mistake because mistakes are usually done due to carelessness. But if the learner continues to make similar error confidently then it has to do with misconception.

I love understanding things this way – ‘All misconceptions lead to mistakes but all mistakes are not misconceptions’.

Check out some interesting examples on misconception from math4teaching.com by author Erlina. Couple of them given below:

Did we not learn that the greater the opening of an angle, the bigger it is? So, angle A is less than angle B in the figure below.

angle-300x138

Isn’t it that the base is the one lying on the ground?

area

Whether you are a maths teacher or not, in life we all make mistakes. So if we keep making mistakes, we keep learning from them. But remember, they get serious if hidden or done consistently and consciously.

Here is an interesting idea about multiplication – ‘If we multiply two numbers, we get a bigger number’. Tell us if this is a true fact or a misconception and do justify your answer in the comment section below.

I am eagerly waiting to discuss ‘Remedial Teaching Strategies’ in our next post.

 

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#Mathematics – Remedial Teaching

Having discussed the issue of Maths Anxiety in our earlier posts, I would like to get on a soapbox and talk about Remedial Teaching in Mathematics.

Initially, I didn’t believe in remedial teaching; for me, a good maths teacher was the one who could make students understand every concept in the textbook (fun included) in a given amount of time (as prescribed by the school) with a very marginal delta between student’s performance (Either A or A* ). After failing to do so in last three years of teaching, I have realized that either I am not a ‘good’ maths teacher or I need to change my definition and accept the ground reality.

Here is what I think now, based on real experience and facts – irrespective of how good a teacher is; in almost every classroom, there will be at least one student that needs remediation in maths. And if the classroom strength is more than 30, then the numbers only multiply. As an educator who believes in good learning for every child, I feel it is very important to accept the fact and carve out a plan to deal with the situation that we are in. The problem is not as traumatic as the word ‘remedial teaching’ may sound it to be. Actually, remedial teaching is nothing but helping a student who is experiencing difficulties so that they can understand and master the concept with which they are struggling. In fact, that is fundamental to teaching.

Why Remedial Teaching is often associated with Maths?

Sequence in MathsDoes that make Maths a difficult subject? Certainly not! Mathematics has this special characteristic of being sequential in nature. In maths, each concept is the foundation for next new learning, and when a student has not mastered one concept they are unable to move on to the other concept.

As the class progresses, the student who struggled to understand the basics develops low self-confidence which may lead to fear, dislike or discomfort with the subject resulting in ‘Maths Anxiety‘. In such cases, remediation helps to get the student back on track so they can continue their learning on the maths continuum. We would not list the learning difficulties associated with these type of learners; instead look at the objectives of remedial teaching.

Objectives of Remedial Teaching

Each student is different in terms of learning ability, academic standards, classroom discipline, academic performance, and even choosing a tuition teacher (in Asian context). Yes, each student has his own way of learning. The aim of remedial teaching is to provide learning support to students who lag far behind their counterparts in school performance. By adapting school curricula and teaching strategies, teachers can provide learning activities and practical experiences to students according to their abilities and needs. In simple words, we need to ‘customize our lesson plans for a particular student‘, in order to help him/her consolidate the basic knowledge in the subject: master the learning methods, strengthen the confidence and enhance the effectiveness of learning. Do everything to get them back on track.Everest_kalapatthar_crop

For those who worry too much about rigid Academic Standards,  we have to ask them: “Do every mountaineer have to climb Mt. Everest?” or “Do we really need to be a mountaineer to derive pleasure from walking up a hill?” It need not have to be the Everest all the time!

Enjoying something means being able to participate with confidence and take pleasure from the experience. Letting the students enjoy according to their strengths and conquer each of the little hills is an Everest in itself.

I am sure we all would have come across different strategies for ‘remedial teaching’! In my next post, we shall explore and discuss some good ones. Stay tuned and be on track!

#3 Fixing Science – 6 Principles of GH

In our previous post, we got to know about Genius Hour, in this post after briefly discussing why GH we shall discuss the 6 principles of GH.

Why students need Genius Hour?

In essence, high school students have spent most of their academic lives being told what to do. Their grades are then dependent on how well they completed the assigned tasks. Most teenagers spend their free time doing things they are “not told to do”. For example, most parents aren’t yelling at their son to play video games, or at their daughter to spend three hours on Facebook. These actions are done because teenagers want to do them (and in part because they are told many times not to do this). My class agreed that most teenagers “want to do what they want to do, and not what others tell them”.

Imagine one project that will teach:

  • Goal Setting
  • Implementing Goals
  • Reflecting and Redirecting Goals
  • Showcasing Goals

Genius Hour can do all of the above.  By allowing students to choose any goal, accomplishment, project of their choice, and then guide the students through the process, we can give them the foundation of successful autonomous learning.

I found this interesting post on 6 principles of GH by Terry Heick on teachthought.com; thought to share it with you guys…enjoy the post!

6 principles of GH

  1. Sense of Purpose

Students must find their own sense of purpose in what they study, make sense of, and create. The context and motivation are no longer entirely academic, which forces both the student and teachers to make adjustments.

  1. Design

Without teachers “packaging” content that frames and scaffold content, students are left to design their own learning experiences.

  1. Inquiry & Navigation

Through surveying possibility, navigation of unfiltered content, gathering information, and narrowed research, students make sense of ideas important to them. This navigation and survey of possibility then leads to more narrow inquiry and research. In this way, inquiry-based learning has significant overlap with Genius Hour.

  1. Create

Whether students “make,” publish, design, act, or do, “creating” is core to Genius Hour. There is always a visible product or function of the learning.

  1. Socialization

Students connect with teachers to plan, peers to produce, and experts and community members to establish a sense of purpose for their work.

  1. 80/20 Rule

The 80/20 rule is important, as it provides the only structure of most Genius Hour learning. Whether it’s an “hour,” one day per week, or something else, it provides a kind of schedule while contrasting usefully with traditional academic “training.”

About the author:

Sahil Sayed is an Educator, Teacher, and Learner. An engineer who understood science and mathematics little better after teaching primary grades for almost 4 years now. Currently heading Science, Mathematics and ICT department at Red Camel International School, India.

#2 Fixing Science – Genius Hour

It is strange to hear students complaining of boredom in their science class. What really students want? What do they look forward to? I think its freedom; Freedom to explore and do what they like to do. Science to me is all about exploring with your free mind. The entire space is open to gaze and search for meaning. Why restrict students to the four walls? What makes us hold them to few pages of a textbook; perhaps this is what makes them feel bored. Genius hour is a student-centered approach to engaging students in a way they enjoy and learn.

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What is Genius Hour?

Genius hour is a movement that allows students to explore their own passions and encourages creativity in the classroom.  It provides students a choice in what they learn during a set period of time during school. Let say every Friday in my science class we form group of students with similar interests and allow them to make or do a project they wish. Out of 5 science periods or sessions we dedicate 1 period or session to Genius Hour. The amount of time dedicated to GH may vary but roughly it comes to 20%. And there is a reason why it comes to 20% when we know it’s origin. It’s not easy to determine where the idea was originally created, but there are at least two events that have impacted genius hour.

Genius Hour Origins

The search-engine giant, Google, allows its engineers to spend 20% of their time to work on any pet project that they want.  The idea is very simple.  Allow people to work on

something that interests them, and productivity will go up.  Google’s policy has worked so well that it has been said that 50% of Google’s projects have been created during this creative time period.  Ever heard of Gmail or Google News?  These projects are creations by passionate developers that blossomed from their 20-time projects.

Another origin of genius hour projects came from the book Drive by best-selling author, Daniel Pink.  In a blog post, he writes about how the Google-time projects are also used in other corporations.

Genius Hour in Education

The same genius hour principles apply in the classroom as they do in the corporate environment.  The teacher provides a set amount of time for the students to work on their passion projects.  Students are then challenged to explore something to do a project over that they want to learn about.  They spend several weeks researching the topic before they start creating a product that will be shared with the class/school/world.  Deadlines are limited and creativity is encouraged.  Throughout the process, the teacher facilitates the student projects to ensure that they are on task.

In our next post, we will see how to implement Genius Hour in your classroom. Till then you may wish to read a book about Genius Hour and 20% Time in education by A.J. Juliani.

About the author:

Sahil Sayed is an Educator, Teacher, and Learner. An engineer who understood science and mathematics little better after teaching primary grades for almost 4 years now. Currently heading Science, Mathematics and ICT department at Red Camel International School, India.

#1 Fixing Science – The STEM bubble

Today we are starting a new series of articles under ‘Fixing Science‘. I believe there is a lot to be fixed when it comes to teaching science. Our articles would include current trends in science education as we focus primarily on three major areas:

  • 1. Content (What are we trying to teach?)
  • 2. Methodology (How are we trying to teach?)
  • 3. Assessment (What are we trying to assess?)

Fixing Science ppt front page

Before picking any one of the above we shall talk about the new buzz word called STEM. You may have noticed the term STEM has been used often in education circles and conferences. The acronym is even making headlines. Be it the Chief Scientist, Prime Minister of Australia or the President of the United States, all over the world STEM (Science, Technology, Engineering, and Mathematics) is being publicized as one of the most essential elements for any society moving forward.

What is STEM?

  • STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling the development of STEM literacy and with it the ability to compete in the new economy.(Tsupros, 2009)

scissors-clipart-scissors_clip_art

Indeed a precise definition, isn’t it? But let me simplify it further by giving an example, a scissor is a form of technology, and for industrial purposes, they really are. They were engineered to solve a problem: how to cut something more precisely. Science will help me decide which element or alloy to use by telling the material properties. Mathematics, on the other hand will help me in the process of making it from size to shape.

Unfortunately, most of the time the new terms are first picked up by the commercial entities. Yes! I mean, the startup companies, the publishers, and the salesman in the world of education. They come up with a product (a kit, software or even a book) and keep associating it with fancy labels. Beware of the robotic companies selling themselves in the name of STEM. Remember using an electronic whiteboard during a lesson or allowing devices in the classroom has nothing to do with STEM unless they are used conceptually.

It would be great if our educators would teach things encompassing all these elements, interconnecting subjects, performing hands-on activities or working on real models and projects. But are we ready to do the extra work? Do we have the expertise? Or we are waiting for our governing boards to force upon us? are some of the questions one has to answer before moving ahead. If you still wish to walk the extra mile start reading about ‘Genius Hours’ or wait for the next post.

About the author:

Sahil Sayed is an Educator, Teacher, and Learner. An engineer who understood science and mathematics little better after teaching primary grades for almost 4 years now. Currently heading Science, Mathematics and ICT department at Red Camel International School, India.

How to overcome Maths Anxiety?

Analysing and discussing a problem is so much easier than chalking out a solution for it. A solution may not be the only right answer but solutions do get us close to 1.

Here are 5 ways to overcome Maths Anxiety:

  1. Do EASIEST problem first: Simple problems helps in clarifying basic operations and concepts in mathematics. Doing easy problems first gives a lot of confidence. Initial success can help you tackle “harder” problems later. Keep winning!
  2. Look at the answer: Practically, looking at the right answer reduces the anxiety to almost zero. It also gives a clear message that understanding a maths problem and thinking how to solve it is more important than just getting the right answer. Maybe that is the reason why – Most of the textbooks give answers at the back or at the end of an exercise.
  3. Make it a challenge: Does referring word problem as puzzle or riddle really help? Yes, it does. From my personal teaching experience, I have found it helpful. To make students understand time in the 24hours format I created an investigation scene. I was working with 3rd graders, a curious and inquisitive bunch. Our job as a class was to find a thief who stole a Queen’s necklace from a museum. We had 3 suspects and one concrete information – The theft took place at 14:30. We also had other data like the train timings and bus timings of the nearby station. Most of the students were so engaged in identifying the thief that they completely forgot that they are actually doing maths. It was fun! some took it in the true sense and were asking me to get the CCTV footage of the area 🙂
  4. Take care of yourself: There is a psychological aspect here as well. Combat negative thinking. Imagine yourself being relaxed and confident while solving a maths problem just like what an athlete does before a big game (Visualisation). Reward yourself for attempting a difficult problem or for practicing maths daily. If you feel you are good at concepts but lack in calculating answers quickly, use a calculator. Make yourself feel easy because maths is indeed easy.
  5. Go online: Literally, there is an ample amount of resources available online. Why restrict yourself to textbooks and some 30-minute session inside your school. Take your own time to understand any concept and revisit the videos THOUSAND times. Most of them are free, for example, the Khan Academy is a great resource.

Time to reflect on the quote by a great scientist Albert Einstein. By the way, Maths and science are related. Our next post would be on Fixing Science, so stay tuned. Oh! here is the quote: “It’s not that I’m so smart. It’s just that I stay with problems longer”

About the author:

Sahil Sayed is an Educator, Teacher, and Learner. An engineer who understood science and mathematics little better after teaching primary grades for almost 4 years now. Currently heading Science, Mathematics and ICT department at Red Camel International School, India.

Check your level of Maths Anxiety

“Do not worry about your difficulties in mathematics; I assure you that mine are greater.” -Albert Einstein

As we have seen earlier in our post, 360-degree view at Maths Anxiety some major causes of Maths Anxiety. In this post, we would like to check our or our children’s level of Maths Anxiety. So here is a simple questionnaire:

Put a number from 1 to 5 next to each of these statements according to whether it is…

Never true (Disagree) 1
Sometimes true 2
Usually true 3
Almost always true 4
Always true (Strongly Agree) 5
1. I am afraid to ask questions in maths class.
2. When maths starts I get a physical reaction in my body, like a headache.
3. I’m not sure I can trust my answers, even on simple problems.
4. I’m afraid I won’t be able to keep up with the rest of the class.
5. It’s clear to me in maths class, but when I go home it’s like I was never there.
6. Being asked to “go to the board” to explain a maths idea in a class – even for maths I am able to do at desk – scares me.
7. When I meet students who love maths or do it well, I either think they are little weird or I envy them.
8. Maths never seems to stick, and after I learn it or even get a good grade on it, I still don’t think I know it.
9. I don’t know how to study for a maths test.
10. I understand maths now, but I worry that it’s going to get really difficult soon.

Now add up all of the numbers : _________

Here are your math anxiety estimates:

Less than 20: Wow! possibly you can get a major in mathematics.

20 – 25: You are not too far to be called a mathematician.

26 – 30 Some maths discomfort.

31 – 40 Quite a bit of fear, anxiety, and discomfort with maths.

41 – 50 Very anxious about maths. Talking about and working on this with your teacher, and may be with another adult you trust will help you a lot.

Above 50:  Death by numbers. The Einstein’s quote mentioned above doesn’t apply to you. You are just about paralyzed by maths, yet still alive!

Stay tuned, solutions ‘How to overcome Maths Anxiety’ coming soon!

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Image courtesy – Brainy Quote

Interesting posts every wednesday

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