In AP Physics (and many other science studies) the journey to find an answer to a problem is the most important component of the learning process – not the answer itself. Our need to make sure students think deeply about the subjects they study is one key reason The College Board AP Program is undergoing revisions of several courses and exams in history, science and world languages.

The science course changes are driven by data from a 2002 National Research Council report and aim to implement improvements in content and pedagogical approaches that represent best practices in teaching and learning.

The curriculum frameworks for the new science courses are organized around subject specific ‘Big Ideas’ with a strong focus on scientific reasoning and inquiry. The courses will emphasize depth over breadth and will include cutting edge areas of research within each discipline. The College Board recently released the new Biology curriculum framework.

For students to be successful in these courses, teachers will need to use instructional strategies that require higher-order thinking skills and help students develop a deeper conceptual understanding of the topics.

This is the first post in a blog series that will explore how the AP Science Practices can be integrated in the 21st century science classroom using a variety of strategies and digital tools. While the primary focus will be in physics, the series will have relevance for other courses such as biology, chemistry and environmental science and could be used at the middle and high school levels.

##### Scientific Problems and Representations

The first science practice states:

*The student can use representations and models to communicate scientific phenomena and solve scientific problems.*

Problem-solving is a major part of a physics course. When confronted with challenging problems it is common to hear students say: “If I had the formula, I could solve this.” After all, finding the right equation is a key element in most textbooks’ problem-solving strategies and is often reinforced in the classroom through lectures, quizzes and tests.

In most cases, by using appropriate equations, a student is able to find the correct answer, but I will argue that *finding the correct answer to a problem does not necessarily reflect a deep understanding* of physics concepts. There are several studies in Physics Education Research that substantiate this claim. See, for example, the works cited in “An investigation of introductory physics students’ approaches to problem solving.”

##### Effective Approaches to Problem-Solving

The ability to relate physics concepts to the situations presented by problems and questions is fundamental for success. A powerful strategy in developing a deep conceptual understanding is the use of Multiple Representations of Knowledge.

The diagram below is an example commonly seen in kinematics problems. This example demonstrates how physics equations are only one representation of knowledge.

Here as an analysis of each of the representations above and its usefulness in helping the students deepen their conceptual understanding:

**–** The real situation is the context of the problem; i.e., a car moving down a hill. It is common to represent real scenarios with a * pictorial* representation such as a sketch. It helps the students that have a preference for visual learning.

**– **A * verbal* representation could describe the motion of the car in the context of the problem, in this example students could say that the car speeds up as it travels down the hill, or the student can describe the energy transformation that occurs. It helps the students articulate what is happening in the given scenario to specific physics principles.

**– **The equation that describes the velocity in an inclined plane is the * mathematical* representation. This equation is usually derived from a free-body diagram by analyzing the forces acting on the car while it is accelerating.

**– **The situation can be represented in a * numerical* way by providing data of position and velocity with respect to time. Data acquisition is often done in physics labs where students have to opportunity to gather the information in a hands-on experiment.

**– **The data obtained can be represented * graphically* in a velocity versus time graph. Graphical representations are commonly constructed from data collected in a lab experiment. Through graphs students can obtain information from the slopes, intercepts and areas under the curve. In this example the slope of the line represents the average acceleration and the area under the line yields displacement.

**– **A motion * diagram* can be used to illustrate the velocity vectors. This is another example that helps the students visualize the situation (a car speeding up) =i.e. increasing arrows as velocity vectors.

Students can demonstrate a deeper level of understanding of physics concepts *by their ability to translate* (move back and forth) between different representations of knowledge.

**Multiple Representation Resources**

Rutgers University Physics and Astronomy Education Research (PAER) group has written a document with the rationale about using multiple representations in physics, how to implement them in the classroom and how to score them.

Multiple Representations in Physics

You can also download power points with multiple representation exercises:

1. Mechanics: kinematics, dynamics, energy, momentum and statics

2. Electricity and Magnetism: electrostatics, DC circuits and magnetism

**Digital Tools for Multiple Representations **

**– ***Verbal Representations*

These tools can be used individually or in collaboration among students

Google Docs

**– ***Pictorial Representations*

Image editors

Sketchcast (Record a sketch with or without voice)

Google Sketchup for 3D Modeling

**– ***Mathematical Representations*

Google Docs includes an Equation Editor

**–** Graphical Representations

Google Docs spreadsheets

Another powerful tool that helps with the implementation of Multiple Representations is the use of *virtual simulations*. In my next post, I will be describing effective strategies for using simulations and a variety of resources for simulations in all core areas of science.

Figure adapted from: Redish, Edward F. Teaching Physics: with the Physics Suite. Hoboken, NJ: Wiley, 2002

#### Dolores Gende

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I would have loved science had I been in your class, Dolores. This is rich–and powerful with your diagrams and examples. I’m seeing this post being retweeted all over the place:) Thanks for all the good work you do.

I’m sending this to our science department, Dolores. Thanks for sharing these ideas and resources. Excellent.

While I teach 6th graders, multiple representations is something we spend years working on together. Like the diagram you drew, at our middle school level we look first to represent a situation with a data table. That’s the easiest way for our young kids to understand and from which to detect patterns.

As soon as they seem able to grasp that method, we move onto doing both the table and then a graph. Slowly they are able to match what they know about the table patterns to what they see on the graph (that’s after we break them of making a bar chart of everything…yikes!!!). It also is the best place to talk about what ifs…….I’ve actually taking a Matchbox car and a motion detector and explored the way in which the graphs changes based on the motion of the little car. If they get that, they have to walk the pattern.

Lastly we layer on understanding how all this is represented with an equation. Surprisingly this comes pretty fast (except for they can’t remember which side is for the coefficient and which side is for the variable).

Our favorite wrap-up conversations is when do you use each kind of representation…trying to teach them when does each one have it’s advantages/disadvantages. By the time they leave 6th grade, they pretty good at it. Then our 7th grade layers on another round of all this for about 2 months of that grade level.

I wish someone had taught me how to do all this because I would have had some real depth to understanding it all…. I loved your post because I can see where all this hard work can be put to good use upline from 6th grade. Thanks for sharing.

marsha

Marsha, thank you for sharing your experience with multiple representations.

I agree with you that they really help cement students’ understanding of concepts. Older students tend to simplify scientific phenomena as simply mathematical representations and they often leave the classroom with a shallow level of understanding.

Your approach to teaching science does make a difference!

You can also use GoogleDocs for pictorial representation (Drawings).

Great post!

Thank you Ellena, you are right, Google Docs is also a great option for drawings.

I am now not sure where you are getting your info, however great topic. I needs to spend some time learning more or figuring out more. Thank you for magnificent info I was on the lookout for this info for my mission.

I’ve just come across this, pleased to see that problem solving is becoming such an important part of the learning process. I think that understanding how problems are solved and why they have been solved in the past really brings the sciences (and maths) to life.