Exploring understanding
In the first post in the series, I explained, through 4 cases, the ways that my students think about understanding. Not surprisingly, educators themselves have diverse views on the meaning of the word understand (Folk, 2006). In this essay, I shall explore my journey towards making meaning of understanding. I start with my time in middle school (around the age of 12) because that was when I began to question the how/why of what I was learning in school.
Middle school (grades 7 to 10)
One day, when I was in 7th standard, I returned from school and asked my mother, "What is the point of all these marks that my teachers give me?" Up until that point, my primary indicator on whether I was doing "well" in school was marks; out of the blue, something (I cannot pinpoint exactly what) was motivating me to question the foundations of that metric.
My mother wasn't too concerned with marks and more keen on me seeing value in the knowledge/skills that I was picking up at school. She encouraged me to consult the Arthur Mee set of encyclopedias at home to supplement textbooks in science, history and geography while reassuring me that the marks would take care of themselves. In addition, we had just bought our first desktop computer; one of the CDs that came with it was Encarta Encyclopedia which became an engaging, colourful and visual source of information that enhanced my learning experience.
Middle school (grades 7 to 10)
One day, when I was in 7th standard, I returned from school and asked my mother, "What is the point of all these marks that my teachers give me?" Up until that point, my primary indicator on whether I was doing "well" in school was marks; out of the blue, something (I cannot pinpoint exactly what) was motivating me to question the foundations of that metric.
My mother wasn't too concerned with marks and more keen on me seeing value in the knowledge/skills that I was picking up at school. She encouraged me to consult the Arthur Mee set of encyclopedias at home to supplement textbooks in science, history and geography while reassuring me that the marks would take care of themselves. In addition, we had just bought our first desktop computer; one of the CDs that came with it was Encarta Encyclopedia which became an engaging, colourful and visual source of information that enhanced my learning experience.
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| Encarta Encyclopedia 99 was my first brush with digital content |
The internet was novel, exciting and gaining a foothold at the time. Exploring topics and seeking explanations for questions became easier than ever before and the very notion of what "studying" meant underwent a significant change.
With these practical changes in my approach to studying came invaluable shifts in mindsets. I started to enjoy reading and learning material that extended beyond the textbook. Being exposed to content put forth in a manner quite different from what I was used to pushed me to think for myself and frame answers independently. This helped me tremendously in high school when I was faced with a vast curriculum and intimidatingly thick volumes of books! Perhaps, most importantly, the seeds of reading, writing and learning for their intrinsic value were planted in my mind and has continued to play a key role in how I approach all facets of my life.
With these practical changes in my approach to studying came invaluable shifts in mindsets. I started to enjoy reading and learning material that extended beyond the textbook. Being exposed to content put forth in a manner quite different from what I was used to pushed me to think for myself and frame answers independently. This helped me tremendously in high school when I was faced with a vast curriculum and intimidatingly thick volumes of books! Perhaps, most importantly, the seeds of reading, writing and learning for their intrinsic value were planted in my mind and has continued to play a key role in how I approach all facets of my life.
High school (grades 11 and 12)
For a teenager preparing for engineering college entrance exams in India, the stakes in grades 11 and 12 are extremely high. Two years of intense studying and sacrifices come down to how one performs during the few hours of the entrance exams. Questions are tough coupled with the knowledge that one is competing with 10,00,000+ peers for a handful of seats in India's top engineering colleges. Besides learning test-taking techniques, keeping a cool head under this kind of pressure required a student to efficiently and thoroughly understand a plethora of concepts in mathematics, physics and chemistry.
Up to the 10th grade, each subject had one textbook and we would have a good sense of the kind of questions we could expect in the exam. Grade 11 brought that idyllic existence to an abrupt and painful end. Now, my shelves were loaded with books on topics in math-physics-chemistry; in fact, in the case of physics and math, there were entire textbooks devoted to single topics. The situation shifted from looking up additional sources to supplement the textbook to having way too many textbooks to handle!
My view of understanding took on an added dimension during these two years. I began to realise how glibly my friends and I used the phrase in middle school. I lost count of how often a teacher asked us, "Children, did you understand?" to which we would give a chorus reply of "Yes Ma'am!". In grades 11/12, concepts that appeared innocent enough would be effortlessly twisted by teachers into convoluted problems that resembled the Greek Hydra. Grasping the meaning of the concept was one thing but knowing how to apply that understanding to new problems was an entirely different ball game.
My biggest takeaway about understanding from these two years was valuing the role of practice and being exposed to different problems that pushed me to apply my learning and cement understanding. It made me respect the fact that thoroughly understanding any topic (not just restricted to math-physics-chemistry) required effort and going through the roller coaster of eureka moments and times of sheer frustration!
Up to the 10th grade, each subject had one textbook and we would have a good sense of the kind of questions we could expect in the exam. Grade 11 brought that idyllic existence to an abrupt and painful end. Now, my shelves were loaded with books on topics in math-physics-chemistry; in fact, in the case of physics and math, there were entire textbooks devoted to single topics. The situation shifted from looking up additional sources to supplement the textbook to having way too many textbooks to handle!
My view of understanding took on an added dimension during these two years. I began to realise how glibly my friends and I used the phrase in middle school. I lost count of how often a teacher asked us, "Children, did you understand?" to which we would give a chorus reply of "Yes Ma'am!". In grades 11/12, concepts that appeared innocent enough would be effortlessly twisted by teachers into convoluted problems that resembled the Greek Hydra. Grasping the meaning of the concept was one thing but knowing how to apply that understanding to new problems was an entirely different ball game.
My biggest takeaway about understanding from these two years was valuing the role of practice and being exposed to different problems that pushed me to apply my learning and cement understanding. It made me respect the fact that thoroughly understanding any topic (not just restricted to math-physics-chemistry) required effort and going through the roller coaster of eureka moments and times of sheer frustration!
College
Courses in college proved to be a mixed bag - some professors structured their courses to be stimulating and demanding while others modelled their courses along the lines of my middle school experiences where there was a textbook and a fairly well known set of potential written exam questions. This heterogeneity among approaches made me realise the immense influence that a teacher has over what students understand from a course.
On an average, we had to enroll in 6-8 courses per semester (one semester was 4.5 months long). Paired with sports, extracurricular pursuits and learning how to wisely use our new found independence away from home, such a course distribution led to us skimming the surface of content. I recall this being the first instance in life where I began to question the "quality vs. quantity" aspect of my education (I bring this up later as well in the concluding portion of this essay). For instance, would it have been preferable to have lesser "general" courses and more "discipline-specific" courses (in my case, electronics) distributed over the 4 year program? Could the number of courses per semester be reduced to 4 while making them more intensive through projects and research components? Could less focus be given to "written exams" and higher weight be given to "practical work"?
My university, BITS Pilani, believed in connecting students to industry through a mandatory 5 month internship in a company during the final year of the bachelor's program. I had the opportunity to work on a project at an analog electronics design company. Quickly, I recognised the gulf between the theoretical understanding gained in college and the practical understanding required to meaningfully contribute to the work of the company that I was placed at. Having sound understanding of the principles that govern electronics was essential but served purely as a first step into the labyrinth of practical design. There was so much to learn on the job!
On an average, we had to enroll in 6-8 courses per semester (one semester was 4.5 months long). Paired with sports, extracurricular pursuits and learning how to wisely use our new found independence away from home, such a course distribution led to us skimming the surface of content. I recall this being the first instance in life where I began to question the "quality vs. quantity" aspect of my education (I bring this up later as well in the concluding portion of this essay). For instance, would it have been preferable to have lesser "general" courses and more "discipline-specific" courses (in my case, electronics) distributed over the 4 year program? Could the number of courses per semester be reduced to 4 while making them more intensive through projects and research components? Could less focus be given to "written exams" and higher weight be given to "practical work"?
My university, BITS Pilani, believed in connecting students to industry through a mandatory 5 month internship in a company during the final year of the bachelor's program. I had the opportunity to work on a project at an analog electronics design company. Quickly, I recognised the gulf between the theoretical understanding gained in college and the practical understanding required to meaningfully contribute to the work of the company that I was placed at. Having sound understanding of the principles that govern electronics was essential but served purely as a first step into the labyrinth of practical design. There was so much to learn on the job!
Graduate school
A geode is a hollow, vaguely circular rock in which masses of mineral matter (may include crystals) are formed, layer by layer (refer image below). One insightful analogy that I came across in graduate school was comparing the process of understanding to a geode. In fact, I have structured this essay along those lines by illustrating how my views of understanding have built up over time, layer by layer. Let me elaborate...
First, the surface similarities among different geodes can obscure the fact that each geode is unique on the inside ⇔ each child is unique and makes connections in his/her own special way even though, on the outside, children look and behave very similarly at times!
Second, a geode is built up, one layer at a time over years ⇔ a child comes in with prior knowledge and experiences that are then built upon over years. No child is a blank slate and there are pre-existing layers to every child.
Third, the minerals and crystals create a structure that lends integrity and form to the geode ⇔ the connections that we make between prior knowledge/skills and new knowledge/skills lend integrity and form to our understanding.
I would like to conclude with a dilemma (or question?) that educators often have to grapple with and which I stumbled upon as an undergraduate - should we teach for deep understanding of content OR for a broad coverage of content (Grotzer, 1996) in schools? This is something I touched upon in the "College" section of this essay too. Broad coverage has the benefit of giving children a flavour of subjects that deal with different facets of language, science, math, nature and society which should ideally help them in learning about their interests and career inclinations in the long run. On the downside, students might be exposed to vast amounts of information that they learn by rote, quickly forget post the exam and never think about or use again in life! Deep understanding aids children in making connections between their learning experiences and meaningfully store and use information. However, developing deep understanding is quite time-consuming, specific and requires quality teachers and pedagogy. I see the balancing act required to draw the best from both schools of thought as central to the goals that schools and universities aim to achieve with their students.
As you can see, my own views have evolved a lot over the years! If I was to condense my current view of understanding, it is this:
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| Image Source: https://www.flickr.com/photos/58827557@N06/37917281042 |
First, the surface similarities among different geodes can obscure the fact that each geode is unique on the inside ⇔ each child is unique and makes connections in his/her own special way even though, on the outside, children look and behave very similarly at times!
Second, a geode is built up, one layer at a time over years ⇔ a child comes in with prior knowledge and experiences that are then built upon over years. No child is a blank slate and there are pre-existing layers to every child.
Third, the minerals and crystals create a structure that lends integrity and form to the geode ⇔ the connections that we make between prior knowledge/skills and new knowledge/skills lend integrity and form to our understanding.
I would like to conclude with a dilemma (or question?) that educators often have to grapple with and which I stumbled upon as an undergraduate - should we teach for deep understanding of content OR for a broad coverage of content (Grotzer, 1996) in schools? This is something I touched upon in the "College" section of this essay too. Broad coverage has the benefit of giving children a flavour of subjects that deal with different facets of language, science, math, nature and society which should ideally help them in learning about their interests and career inclinations in the long run. On the downside, students might be exposed to vast amounts of information that they learn by rote, quickly forget post the exam and never think about or use again in life! Deep understanding aids children in making connections between their learning experiences and meaningfully store and use information. However, developing deep understanding is quite time-consuming, specific and requires quality teachers and pedagogy. I see the balancing act required to draw the best from both schools of thought as central to the goals that schools and universities aim to achieve with their students.
As you can see, my own views have evolved a lot over the years! If I was to condense my current view of understanding, it is this:
- the ability to create a model of cognitive connections between prior and newly acquired knowledge/skills;
- the ability to recognise relationships and patterns within those webs of connections through practice and effort;
- the ability to apply these models and relationships to new situations/problems.
In the next post, I shall discuss a framework that I studied in graduate school which could be used to teach towards such kinds of understanding.
References
Folk, N. (2006). Understanding understanding: A review of the literature. In K.A. Leithwood, P. McAdie, N. Bascia, & A. Rodrigue (Eds.) Teaching for Deep Understanding: What Every Educator Should Know. NY: Corwin Press, pp. 26-29.
Grotzer, T.A. (1996). Understanding counts! Teaching for depth in math and science: Cognitive issues that affect math and science learning. Cambridge, MA: Harvard Project on Schooling and Children/ Exxon Education Foundation, pp. 1-17.
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I read the articles quoted in this essay as part of the course EDU T543 Applying Cognitive Science Research to Learning and Teaching at the Harvard Graduate School of Education. The course was intended for those who wanted to develop thoughtful instructional designs for learning. These designs could be in the form of traditional lesson plans or in forms for a variety of other contexts, formal or informal, including massive open online courses (MOOCs), online learning, computer programs and so on. Many of the course examples were drawn from a K-12 context, but the principles apply broadly to life-long learning.
Very well written, Shreyas. Like you, we all have these levels and layers of understanding and I saw myself drawing parallels to my own life at each image of the circles.
ReplyDeleteThanks for the lovely read.
Hi Bhaiya,
ReplyDeleteI really liked this! I think about depth vs. breadth in the context of my own education a lot. I think I'm on the side of depth for English and a middle ground (like you advocate for) for stats. With English and other subjects that require interpretive work, depth of understanding is transferrable. Learning to dig deep into one text equips you to do the same for another, in a way that interacting with them both on a surface level in the time you would devote to just one doesn't.
I haven't thought as hard about it with stats i.e. quantitative, practical, calculation-related disciplines, but I do feel like a breadth of knowledge is more important since one would need to use multiple techniques in combination to statistically analyze data, for example. How do you feel about which approach favors (applied) STEM and which favors humanities, if those are distinctions you consider relevant?
Hi Simran,
DeleteYour comment brings in a perspective that I hadn't considered before; I appreciate you raising it and adding another "layer" to my thought process! :-) I had not thought about depth vs. breadth and how this debate might play out in college and different specialisations.
I found myself wholeheartedly agreeing with the points you raised in the first paragraph of your comment. I taught English for 3 years to grades 4, 5, 8 and 9 and the core skills (character analysis, setting, theme, main idea, inferences etc.) remained the same but the depth to which my children were expected to apply and hone their skills increased as they moved through middle and high school. In addition, these skills could be transferred (with some adaptation) to poetry, prose, plays etc.
Regarding your second point, I agree to some extent. It is important to know a wide range of statistical techniques but knowing how to use those techniques smartly will require a person to go into some depth about the technique, right?
Think about a person who wants to go into research (Ph.D., academia etc.) in a STEM field. Wouldn't that person need to go into depth into his/her chosen area of research? Same holds true for the humanities. Maybe, it is not so much about the field but the extent to which one wishes to engage with the field?
Perhaps, a person who excels in his/her field (whichever it may be) is one who not only knows a wide range of techniques/skills but also when/how to go deep if necessary. I think about table tennis - if I was to only develop a forehand and become truly exceptional at that stroke, I would still be handicapped if someone targets my backhand. However, if I am able to be competent with both strokes and then focus on refining my skills in both strokes over time, I might become a more balanced player and someone tougher to beat. Knowing both strokes to some degree is better than knowing only one stroke to a larger degree. Does this parallel make sense?
I think it's telling you discovered a love of information and the internet through something like Encarta in middle school. As I'm currently working on a very complicated project with MS students, I find myself often trying to lead with their love of knowing things.
ReplyDeleteThe project is based on designing the physical layout of a refugee camp for people seeking asylum on the US / Mexico border. They need to consider a wide variety of criteria, such as food, water, shelter, education, transportation, etc. While not every category was a hit for students, many of them led their exploration by identifying what they wanted to know more about. I find indeed it's easier to start by having these students gather facts, and then build up toward a broader "understanding" about the relations between these areas, as it can sometimes become too much to handle if they try tackling everything at once. This, too resembles the movement you describe between narrow and deep thinking (gathering lots of facts on one thing) and broad general thinking (seeing the enormous scope of the project)
Graham,
DeleteIt's wonderful to see that you're giving your students so many criteria from which they can begin their exploration. I agree with you that, for problems with a wide scope like the refugee camp physical layout design, starting with facts is good. Otherwise, the sheer volume of relations can get overwhelming.
I think we adults too do this in our daily lives when we encounter a new problem/situation that seems impossible to tackle at first. We try and break it down into more manageable pieces and work through it accordingly. Your last sentence made me think about how these two types of understanding/thinking exist in a kind of dynamic equilibrium and we move back and forth between them depending on the context. :-)
Hi bhaiya !
ReplyDeleteThe question which rose at the time in 7th is been rise now in my mind. That why does marks matter? As I moved to college I have wasted my one year in deciding whether marks truely matters or is the skill or the personality matter. One thing I would like you to clarify is that at the time you was preparing for entrance exams there had been ups and downs so to over come that who helped you. You had resources for yourself to be prepared but when a Person is not having any resources to prepare what would you suggest him to do?? That person is on one but me. 1 year have gone U do not have any clear vision what would you suggest??
Hi Adnan,
DeleteFirstly, I want to appreciate how open and honest your comment is. You have written exactly what is going on in your mind and that is wonderful to read! :-)
Systems in India are such that marks matter. There are a lot of young people in India looking to get into colleges and jobs and a good academic record is helpful in achieving these goals.
Instead of thinking about whether marks or skills/personality matters, how about thinking that both are important for different reasons? Can a person not aim to score well while also developing his/her skills and personalities? I think that is possible, right?
Yes, there were ups and downs in my life in 11th/12th too. Family and friends were definitely helpful. In your case, you have said that you don't have the resources to prepare. Have you tried reaching out to your former teachers in Pune? How about your current teachers who I am sure have helped students such as yourself in the past? What about your friends - how are they getting their resources?
See if asking these questions gives you some useful answers. :-)
Hi Shreyas,
ReplyDeleteThoughtful post! I have always believed that the deepest form of understanding is "conceptual understanding" where students have a comprehensive grasp of concepts, from which they would be able to solve any type of problems associated with the concepts. These concepts are what I would call "timeless" knowledge - which they would need to learn, in order to deal with "timely" contexts - new problems that come about with changes in time and technological advancements. A challenge that I face is how do I assess students' "conceptual understanding" such that I am able to pick up the particular aspect of the concept that they are not familiar with?
Loved the "timeless knowledge" being required to handle "timely contexts" - really elegantly put! :-)
DeleteA lot of the work that my company (Educational Initiatives) does is centred around assessing conceptual understanding through the design of thoughtful diagnostic items. Since our work is at a large scale with thousands of children, we end up using multiple choice questions with four options - one correct and three wrong - but the three wrong options (called distractors) are carefully thought out such that we can say, with some confidence, that children choosing a particular wrong option lacks a particular skill or have a particular misconception. I admit that this technique has its flaws (children have a 25% chance of guessing correctly, we have no evidence of the child's working and are assuming that a choice implies a particular thought process etc.) but it is more informative than not having any assessment items!
Another possibility is to use technology-enhanced assessment items where a child's answer to a question can be followed by 2-3 more "clarifying" questions that serve to better understand the thought process behind the answer. The system can record data at each step along with parameters like time taken and this data can be analysed to draw more effective conclusions on which aspect of a concept a child is struggling with.
If your requirement is at a smaller scale and you have teachers/schools invested in the process, then I firmly believe that nothing beats giving a child a well-designed, open-ended question that involves the application of two or more concepts from a topic and then going over the work, one step at a time, to see where the breakdown happened. We should communicate the purpose of the test clearly to the child, emphasise that it is low stakes and they don't have anything to worry about and outline how their responses can benefit both them and us. This can increase the possibility of them sincerely attempting the question which, in turn, leads to more insights for educators.
What are some things that you have seen tried out with regards to conceptual understanding?
I feel, this is one of your best expressed blogs (may be because it documents reflections from your 'own' journey)
ReplyDeleteWhen I was in college, I had the liberty to choose a few courses every semester. It served two purposes- i) when I chose elective courses outside my discipline (civil engineering in my case), I catered to the breadth (general) and ii) when I chose courses from sub-disciplines of civil engineering in the later semesters, I catered to depth (specific).
Notwithstanding the benefits of this system, I feel I wasn't enabled enough to make the decisions. I never had to make any such decision in my school days, except after class 10th, when all of a sudden, I had to make one of the biggest academic decisions of my life to choose between arts, science and commerce- which again I feel, I was definitely not equipped enough.
(If we can ignore the practical challenges (though I would like to know you views on that),)
Do you feel, allowing students to pick electives in school can help in dealing with the problem of 'breadth vs depth' or 'aptitude/ interest vs marks' better? Can it also provide a smoother transition between different academic phases? This also reminds me of Rousseau- 'Between the ages of 12 to 15 years, let a child discover' (though I feel the lower age limit should be lower than 12)
Your point about not feeling "enabled enough to make the decisions" is one that I would like to draw on in answering your first question. I think allowing students to pick electives in school (maybe, from 8th standard onward?) could be an avenue to addressing the problem. However, there are some points that must be kept in mind. First, children/parents should be guided towards how to pick and choose an elective. Just putting a whole lot of options in front of them isn't going to cut it. This guidance will enable them to slowly start making decisions for themselves.
DeleteSecond, children/parents should be encouraged to take up electives that address both depth and breadth (like how you consciously chose your electives in college); otherwise, growth could be one-dimensional. Third, electives shouldn't be viewed, either by schools or parents/children, as toppings or add-ons to more "important subjects"; electives are essential to gaining a wider spectrum of knowledge and should be given respect accordingly.
I believe that giving kids choice and introducing them to making decisions for themselves (be it through electives or other means) is vital to providing a "smoother transition between different academic phases". When I was with my 5th graders in 2014, one of the class values was CHOICE and I believed in treating my students as young adults capable of making decisions. They voted on things like class activities. I tried to emphasise that every action that they took was a choice that they were making. Empowering children from a young age might better equip them to handle independence and make sensible life choices down the road...