CHAPTER 1

How does students’ prior knowledge affect their learining?

Principle: Students’ prior knowledge can help or hinder learning.

The first part of this principle is rather intuitive. The second becomes obvious after little thinking. As instructor, I see two main issues realated to this principle: (1) how can I understand what students know when they come into my courses? (2) what can I do to deal with, and help students deal with, inactive/insufficient/inappropriate/inaccurate prior knowledge?

This chapter is exactly about that and it is very reassuring to see that these are general issues not only for people like me, i.e. with no pedagogical background.

• Activating prior knowledge

Despite the 7 principles analysed in this book are domain-independent and experience-independent, the way we choose to face the issues deriving from them (i.e. “the pedagogical implications of the principles”) are, in contrast, very much context-dependent. As for the first principle in particular, I see three main factors influencing how we can deal with students’ prior knowledge, and therefore (try to) activate it: 1) Time and occasions we have to query, observe and become familiar with the learners; 2) Number and type of learners; 3) Classroom set up and technology available;

For example, determing and therefore activating prior knowledge of 20 adults in a 3-day training course in an EBI’s IT room is completely different from determining and activating prior knowledge of 30 teen-agers (average class size in most state schools in Italy) with whom a teacher spends about two hours a week for an entire school year, in a typical high school’s classroom set up (tables, chairs, blackboard, chalks). In most college courses we may have up to 200 students, black/whiteboards and a projector. Once I find something that works in a given context (e.g. real time diagnostic questionnaires), the biggest difficutly consists in adapting it to different contexts.

• Accurate but insufficient prior knowledge

Making a difference between declarative knowledge and procedural knowledge is absolutely crucial. This is very well explained in the book and it helped me understand much of my way of learning in the first place, and therefore of how learning works in general. I did a MD in Theoretical Physics and in almost all exams I took, I was very good at “knowing what” and bad at “knowing how and when” to apply various procedures, methods, theories, etc. I was usually able to explain the theory but often failed in solving exercises. In particular, I found a lot of difficulty in the written exam of General Physics (Mechanics and Thermodynamics), where - in order to solve problems/exercises - students have to be good at coupling what they observe around them with mathematical formulas. In the oral part of the exam, in contrast, where students are requested to state and explain physical laws, I usually didn’t have any problem. The problem was that people can take the the oral part of exams only if they pass the written test. Since at that time I was unaware of the differences between declarative and procedural knowledge, I cronically felt incompetent, with obvious repercussions on my self-confidence. Today, I observe one of my teenager sons, who would never be able to explain what radicals are, making excercises on radicals at the speed of light. When I ask him: “Why do you do this or that?” he answers: “Because it works”. Also, the difference between declarative and procedural knowledge becomes palpable when I teach Python to life scientists with no previous programming experience. What I can say today, is that in the fields where I feel I have good mastery, I can both explain and do things. This is very well explained in chapter 4 (How do students develop mastery?). Can we only claim that learning has occurred when we own both types of knowledge? Not sure. For sure, as instructor, I feel I must have very clear in mind what I want from students for each topic. In some cases, a rough idea of the topic might be sufficient, for other topics I might want them to acquire accurate knowledge or realise that procedural knowledge is particularly relevant. Mastery may be not always essential (despite it is always desiderable). And so on. As a side note, I can say I really master something when I can teach it.

Q: How declarative knowledge and procedural knowledge relate to Kolb’s learning styles? Kolb claimed that effective learning only occurs when a learner is able to execute all four stages (Concrete Experience-Reflective Observation-Abstract Conceptualization-Active Experimentation) of his model. I’m not a fan of learning styles, in particular, I have no idea on how to use them in a classroom, especially in short training courses. I read some controversial literature on learning styles and I don’t know exactly which is my position… I would be curious to know what experts in the field (which I’m not) think about learning styles.

• Inappropriate prior knowledge

I’ve been teaching Python programming to biologists and medical doctors (difficult) and Biochemistry and Cellular and Molecular Biology to physicists and to engineers (easier). I also taught Physics to physicists (relatively easy). So, I had the chance to really “touch” with my hands how strongly inappropriate prior knowledge deriving from different disciplinary contexts can hinder learning. Also, I had the chance to teach to both heterogeneous (in terms of geographical origin) and homogeneous classrooms (mostly Italians) and my feeling is that learning goes faster and deeper in homogeneous classrooms. This might also depend on the language spoken and surely depends on the deep knowledge I have of Italian learners’ cultural background. I’m much better at anticipating which prior knowledge they will tend to apply inappropriately compared with classes where participants come from several different countries, including countries the education system of which is unknown to me. It is really important to me to know as much as I can about each single individual in my courses, by reading their CV and responses to application questionnaires, spendind as much time as I can sitting next to them during practicals and asking them a lot of questions like “how would you do this? How would you define this?”.

• Inaccurate prior knowledge

As the authors state, detecting and fixing misconceptions is the most difficult part. I think it is nearly unfeasible in short courses because it requires a lot of time for gradual changes and a lot of reasoning and reinforcement of the correct model(s). Given that models/structures I teach (e.g. for loops) are so familiar to me, I often find very difficult to even imagine what flawed model a learner may have in mind. In the past, when I perceived that a misconception was at work, I tended to explain again the concept using the model “I” had in mind; basically I repeated the initial explanation trying to be slower and clearer. Despite I ended up feeling that now it had to be clearer, it hardly worked… So, I had to try different approaches. The best would be to learn more about the flawed model in order to find an appropriate way to refute it. Unfortunately, this is time consuming and sometime it may be very difficult to really understand what people have in mind. I’ve observed that making several different examples helps, especially when I can find some broken examples based on the flawed model I’ve perceived. I’ve also seen that peer instruction may produce good results: I ask learners having in mind the correct model to re-explain (and make examples on) it. Sometime I form pairs in which at least one component has the correct model in mind.

Fortunately, I noticed that there is not a large amount of different misconceptions in a given topic (as stated in the “Look for Patterns of Error in Student Work” paragraph later in this book chapter); so, after having taught a course several times, I more or less know what I can expect in terms of recurring misconceptions.

What strategies does the research suggest?

• Methods to gauge the extent and nature of students’ prior knowledge

Talk to colleagues: Talking to colleagues for finding out students’ prior knowledge is in general a useful practice, but it only works in specific contexts. For example, it cannot be done in short training courses, where the only (partial) help comes from pre-course questionnaires. I expect it may work in school, college or master degrees, though - as the authors stress - knowing what was taught might be less helpful than we think, as this only tells us what the students were supposed to learn and not what they actually learned.

Administer a diagnostic assessment I use diagnostic assessments everytime I can. More specifically, every time the subject matter allows them, and there is one computer per learner and Internet connection in the classrom. I use “multi-purpose” diagnostic questionnaires as follows: 1) I divide a lesson topic in a limited number of sub-topics I want the students to learn. I try to connect each sub-topic to a learning outcome.
2) I prepare a diagnostic questionnaire exploring the nature of the students’ prior knowledge on the lesson topic. This is a kind of concept inventory with a multiple choice question for each sub-topic. Some answers are designed to reveal common misconceptions, some others to explore the amount of prior knowledge. The answer “no idea” is always included. 3) I distribute the questionnaire at the beginning of each session using a google form and give the students 5/7 minutes to answer (usually a questionnaire includes 5/7 questions). The questionnaire is anonimous. 4) I collect results in real time and project them one by one in the form of pie charts. 5) What I do at this point strongly depends on the the distribution of answers: if 100% of them are “no idea”, of course I give a mini-lecture on the sub-topic (followed by practicals, if appropriate). If there are only wrong answers, I start a discussion/brain storming asking the reason for each answer and I explain why it is wrong. If there are one or more correct answers, I ask the students who gave them (who usually are ok with being exposed as they gave the correct answer) to explain to their mates why the answer was correct and also to give a bit of context - e.g. in which courses they learned it, etc. - in both cases I give a mini-lecture on the sub-topic adapting it to what was said in the discussion. In the remote case in which all gave the correct answer, I ask one of them to say something on the sub-topic, another one to add something else and so on until I feel that more or less everything has been said. 6) I distribute again all the questionnaires together at the end of the course and compare the answers with those given during the course.

I’m now thinking how this model can be reproduced in courses where students have no computers and/or Internet connection is not available (e.g. in school and most college courses). Suggestions are of course wellcome.

Have students assess their own prior knowledge Using the approach described above, students have the chance to also assess their own prior knowledge (for example, when they answer “no idea” several times). In short training courses, I also use pre-course questionnaires (in the application form), but it is absolutely true what it is said in the book: generally people tend to overestimate their knowledge and skills.

Use brainstorming to reveal prior knowledge Except for the discussion of the diagnostic questionnaire’s answers, I don’t use frequently brainstorming to reveal prior knowledge; perhaps because during brainstorming I tend to focus on other aspects of learning and I’m not very good at systematically identifying prior knowledge. I know I have to work on this.

Assign a concept map activity I constructed my first concept map as described in the book during the SW/DC instructor training in Lausanne (January 2016) and the second as exercise for the check out. Since then, I use concept maps to prepare teaching sessions, though I find very difficult to make good ones. I only assigned concept map activities to students in a few Python courses for beginners as group activity to make participants reflect on the structure of the language. They had to individually list Python keywords (e.g. “module”, “method”, “import”, “function”, “loop”, etc.) and work in group to classify and group them. Then we built together a sort of concept map representing the structure of the language. I find this exercise extremely useful though it requires a lot of time. Therefore, it can’t be made in every course.

Look for patterns of errors in student work As previously mentioned, I was able to recognise patterns of errors from one course to another (on the same subject). Rarely in the same course. I would love to have the chance, at least once in life, to see how it is to work with a classroom response system. But, at the moment, it requires technology we don’t have. Perhaps, as in the case of the diagnostic questionnaires distributed via Google forms, it would be good to find an alternative that does not require any techonology.

• Methods to activate accurate prior knowledge The methods described in this section are quite normally used in classrooms, singularly or in combination. The most important lesson I received here is that methods to activate prior knowledge can generate inaccurate and inappropriate as well as accurate and relevant knowledge. Therefore, we have to be constantly aware of what is happening in the classroom and be very very good listeners.

• Methods to address unsufficient prior knowledge

Identify the prior knowledge you expect students to have This paragraph is full of food for thought. In particular, about what instructors can do to keep themselves “mindful”. Examples: “Identify in your own mind the knowledge students will need to have to perform effectively in your course”; or “ask yourself ‘What do students need to know to be able to do this?’”; or “be sure to differentiate declarative from procedural knowledge”.

Remediate Insufficient prerequisite knowledge I also found very useful the pragmatic advice provided in this paragraph. In particular, the fact that teachers’ responses to students’ insufficient prior knowledge need to be tuned on the scale of the problem and resources and options available to them and to their students.

• Methods to help students recognise inappropriate prior knowledge

I’ve seen that building a discipiline-specific vocabulary, i.e. a set of words belonging to the jargon typical of the discipline at hand, writing them on cards, classifying them (as “operators”, “modules”, “Built-ins”, “methods”, “reserved words”, etc.) and sticking them on the walls of the classroom every time they are introduced during the course, is of great help. In a very quick way, several times during a course, learners are asked to pick one term, stand up and tell the definition out loud. Sticking to the Python example, when I explain for loops (“for i in seq:”) the two words “for” and “in” will be written on two cards and stuck to the wall. The former term will go under the “Python reserved words” category and the second under “Operators”. This ensures students learn quite fast the new vocabulary and the peculiar meaning and usage of certain words and quickly stop associating them with their common meaning in English, or with the meaning they have in other disciplines.

• Methods to correct inaccurate knowledge

Asking students to make predictions based on flawed metal models and test them, and inviting them to reason on the basis of what they believe to be true (but is not) seems pretty unrealistic given the high number of students in a course and the little time a teacher usually spends in a classroom. Perhaps, these tasks can be assigned as homework in courses where students are supposed to do some (not in short training courses, for example). Providing multiple oportunities for students to use accurate knowledge seems more realistic and can be useful for all the students, not only those with flawed mental models.