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07. Effective Teaching: Example in History, Math, and Science

        Different subjects have different organization of knowledge and approaches to inquiry.  Pedagogical content knowledge includes knowing the conceptual barriers within a particular discipline.  This suggests that a good teacher needs more than just general teaching skills - but also knowledge particular to the subject.  
        HISTORY - Most history classes are taught through dates and afacts, missing exciting opportunities.  A study showed that although some students even outperformed historians with dates and facts (after studying a particular subject), formulating reasoned interpretations was far better done by historians.  Another point to note is that teachers' ideas affect how they teach.  
        Expert history teachers help students understand relevance of history and problems of historical interpretation.  One example of an expert is Bob Bain, who shows that history has an abundance of facts and depending on your perspective is a story.  He starts the year by giving students a time capsule activity where they record important historical facts.  Through the year this is a returning point for students to justify (and change justification) for why they chose these.  Another expert teacher spends a week, despite the broad content needed for coverage, teaching "what is history?"  She then uses this conceptual framework to guide the rest of the year.  
        These examples show that gifted teachers have a deep understanding of the structure and epistemiologies of their disciplines, combined with knowledge of the kinds of teaching activities that help students understand the discipline.  
        MATH - Current debate in mathematics is to focus on computation versus conceptual understanding.  A teachers practice is strongly influenced by their opinion on this particular question.  
        Lampert, a math teacher, saw her role as a mediator, giving students opportunities to argue about the reasonableness of certain opinions.  Students had to constrantly explain their point of view, rather than rely on the textbook for validity.  They played the role of sense-makers.  Ball, another teacher, allowed students to conjecture, experiment, build arguments, and frame and solve problems.  She used various models for different concepts, such as understanding that negative doesnt equal zero.  She gave students the responsibility of deciding what is correct.  These two examples also show that teachers need specific knowledge of their students' understanding.  
        Besides content and pedagogical knowledge, teachers also need specific information about how their individual students think about the topic.  For example, one teacher (Annie Keith) gives students problems and forces them to answer them with reasonable answers.  The students than present a variety of solutions and learn from one another.  The teacher uses cognitively guided instruction by choosing either students with weak solutions (to show misconceptions) or strong ones (to demonstrate good strategies). 
        Modeling is used ubiquitiously in the real world, but it is often neglected in the schools.  A model-based approach includes inventing a model, exploring its qualities, then applying it to answer a question.  
        SCIENCE - An experiment showed that student taught physics principles that included doing a hierarchical analysis were able to solve problems more like experts.  Moreover, when taught skills used by experts that are generally not mentioned, such as the ability to describe a problem before attempting a solution, student performed better.  These "strategy" based methods were very effective - the choach helping students apply instead of just giving problems.  
        "Bridging" is used to connect correct concepts of the physical world (called anchors) with misconceptions.  A method based on this involves having students make predictions, performing an experiment, then discussing why their predictions were wrong or right.  both these help students permanently correct misconceptions.  
        Translating theory into practice entails teachers to act like coaches, unraveling students' ideas, replacing erroneous ones with better ideas, and giving them the structure to think like a scientist.  
        Large classes, such as undergraduate science lectures, can use technology such as interactive remotes to provide formative assessment and springboard off students responses, getting students to defend their reasoning.  
        Establising communities of scientific learning can be done through an interactive process of theory building, criticism, and refinement based on self-asked questions, hypotheses, and data-analysis.  Using talk, activity, and interaction around meaningful problems, these things can be created.


The routine focuses first on identifying something interesting about an object or idea:

"I notice that..."

And then following that observation with the question:

"Why is it that way?"
"Why did it happen that way?"

I notice that in each of the example - math, history, and science - a central idea is that teachers give the students tools, or a framework, and students must come up with the questions and solutions.  

It is that way because we want students to become good, expert thinkers.  We know that expert thinkers ultimately are responsible to do the thinking on their own.  They are independent and active.  Still, they have organizational frameworks that help guide their own thinking.  If we want students to become experts (or as close as possible to them), we need to give them the opportunity to develop their thoughts.  Ultimately, there should be no qualitiative difference between the way novices and experts approach problems, but rather quantitative - experts just have more experience.