Learning Middle- and High-School Science
Ways to more effectively learn quantitative science
Introduction
We can divide up the study of K-12 science into two main phases. During the first phase, which happens mainly in pre- and elementary school years, the focus is on the qualitative aspects of science. Students learn scientific concepts, the names of phenomena, and how phenomena relate to one another: farm animals and their behavior, the types of clouds, the hydrologic cycle, what are the different kinds of energy, the food web, the names of different kinds of trees, etc. During the second phase, which happens mainly in high school years, the science focuses more on the quantitative aspects of science. Students learn how to solve problems: how to use conversion factors for handling units, how to balance chemical reactions, how to calculate the change in velocities after an elastic collision, how to calculate the percentage of descendants that inherit a particular genetic trait, etc. During middle school, students are transitioning from focusing more on qualitative aspects to more on quantitative aspects.
Of course, we’re generalizing. High school students learn plenty of new scientific concepts and vocabulary and elementary school students will do some calculations in their science classes. That being said, there is a real shift in what doing and learning science means as a child grows older. Accordingly, when students move into middle- and then high-school, they need to learn new techniques for learning science. Memorization and categorization are used for learning qualitative science. But, because quantitative science uses scientific models (e.g., conservation of mass, conservation of energy) to solve problems, memorization and categorization have limited utility for learning quantitative science. In this article, we describe a process for learning quantitative science.
The three main steps to learning quantitative science
Learning quantitative science—that is, learning to solve science problems—involves three main steps:
The “what” step: To learn how to solve problems we have to first figure out what the words mean in a problem. In this step, we learn the names and descriptions of concepts; this is the same as learning qualitative science.
The “how” step: In this step, we read and dissect model problems. These problems illustrate how the concepts studied in Step 1 are used to solve specific kinds of science problems.
The “practice” step: In this step, we do problems similar to the ones we analyzed in Step 2. Typically, we start with simpler problems that are similar to the model problem and work up to more complex problems.
These main steps for learning quantitative science are typically done in that order, but other pedagogies might use a different order or include other steps. For instance, in The Art of Problem Solving mathematics curriculum, one of the best curricula for high-performing primary and secondary mathematics students, an “initial practice” Step 0 is added. In that pedagogy, students are trained to handle uncertainty when solving problems by being asked to try to solve problems at the start of a new unit. They haven’t seen these problems before; the students try these problems before any concepts or example problems have been discussed. For some students, this Step 0 can be frustrating, but when implemented carefully, this Step 0 can help normalize struggle while solving problems. This is similar to the benefit of letting a student spend some time in the “learning pit” that we discussed in a past article on the role of failure in learning:
An example of the three main steps
Let’s pretend we are taking a high school chemistry course and are in a unit on how to write electron configurations for atoms. Here are the three main steps as applied to this topic.
In Step 1, we read the textbook, listen to lectures, and watch videos describing:1
What are electrons.
What is the quantum atomic model.
What is a quantum number.
What is an orbital and how many electrons can go into an orbital.
What is the energy for an electron in a given orbital at a given quantum number.
How and in what order do you fill orbitals of the same kind but with different orientations (e.g., x, y, and z-oriented p orbitals).
What is the syntax for writing an electron configuration.
In Step 2, we look at a model problem on writing the electron configuration for an element. For instance, we might read about how to write an electron configuration for the element Boron, which has five electrons. When filling the orbitals, two electrons will go in the 1s orbital, two in the 2s orbital, and one in one of the three 2p orbitals. The electron configuration for Boron is thus 1s²2s²2p¹.
In Step 3, we practice writing electron configurations for other elements. We start with elements whose configurations will be similar to Boron (e.g., Carbon and Nitrogen). Later, we write configurations for even heavier elements. Some of those elements will have electrons in d orbitals, whose energies may not follow the s and p pattern of increasing energy that we came to expect with lighter elements. In our practice, we ideally want both quantity and quality of repetition. In the former, we want to do enough practice problems that we build up an intuition of how to solve problems like these. In the latter, we want to consider a wide-enough range of different kinds of problems so we can really see how the concepts work.
Study tips for each of the three main steps
The above three main steps describe a framework for learning quantitative science. There are any number of different studying techniques you can use at each step. Different students will learn differently and should use the techniques that work for them. Below we describe a few techniques for each of the three main steps. This list is not exhaustive.
For Step 1 (“what”):
Take notes as you read the textbook. Unpack each sentence that you’re reading. What does it mean? What do the terms mean? If you don’t know the terms, look them up (many introductory textbooks have a glossary in back). Can you rephrase the sentence in your own words? Articulate this out loud to yourself.
When you see graphs, you have to slow down your reading. Ask yourself what the graph tells you will happen if the variable on the x-axis changes. What will happen if the variable on the y-axis changes? How does this behavior relate to the physical, chemical, or biological concepts that this graph describes? Articulate this out loud to yourself.
Make a list of questions and, after you finish reading the section, find the answers to your questions (by looking back through the text, looking at other resources, talking to others, etc.). Write this list on a sheet of paper separate from your notes. Write down the question right as you think of it. Don’t say to yourself, “I’m sure the author will answer my question later on” and choose not to write down the question. If the author does answer the question later on, you can put a check mark by it. But, if you don’t write it down now, you’ll forget it. If you forget it, you’ll never be able to answer it.
Don’t limit yourself to a single resource. Use multiple textbooks, web pages, articles, videos, etc. Ask a classmate or tutor to give you an alternative explanation of the concepts. Do whatever is needed to enable you to figure out what the concepts mean.
Make flashcards of terms, definitions, concepts, and problem types and problem-solving techniques to help with memorization and to help you schedule the concepts for reviewing. For concepts and problem types, you won’t be able to describe it all on the flashcard, but if you write down the concept or method on a notecard, you can use that notecard as a placeholder in a spaced repetition system (see the next bullet point) for whether or not you understand the concept or can solve the listed problem.
Use spaced repetition to make your learning more efficient. Here’s a nice video describing spaced repetition:
For Step 2 (“how”):
Do not just read through a model problem but really analyze the steps of the solution: What concepts are being used? How? What assumptions are being made? What mathematical techniques are being used? (And work out the algebra, line-by-line!) What does each term in each step of the solution mean and how do they relate to one another? Is there another way to solve the problem? If so, what is it? Articulate your analysis out loud to yourself.
Ask yourself what would happen if you changed the “given” values by a little bit. How would the solution change? Why?
As in Step 1, make a list of questions and answer those questions after you’ve gone through the model problem.
For Step 3 (“practice”):
Do many practice problems. The problems should be varied and illuminate different aspects of the concept you’re trying to learn.
Do your practice problems by hand. Avoid asking AI for help. AI is a powerful tool, but your goal at this point is to learn. The work product (i.e., solution to the problem) is not your goal. The goal is to teach your brain how to understand the scientific concepts through solving science problems. So, you have to make your brain work at it 🙂.
Try problems that have different “given” or “input” values. Make up some yourself by asking what would happen if you doubled or tripled one of the given values.
Try out different problem-solving techniques. One useful technique is the strategy of breaking a larger problem into parts. In a past article, we provided tips for helping our children with their math and science homework. Tip 6 in that article describes the strategy of decomposing larger problems into smaller problems:
If you have solutions to your practice problems (or know someone you can ask to check your work), check to see if you got the problems correct. For those you missed, analyze the solution with what you did to see why you got the answer wrong. This last stage is most important to our learning. This is also a great time to practice the seven “whys,” as we described in this past article:
Conclusion
The transition from learning more qualitative science to more quantitative science takes a lot of work. It’s not easy for middle-school students, and unfortunately too many students are discouraged during this process. But, you and your child can successfully navigate this phase in learning science!
What ways have you found helpful for learning or teaching scientific problem solving? Please share them in the comments below!
Author: Johnny Lin.
Some of the science content in this section comes from Chs. 12 and 13 of Mays, John D. Accelerated Studies in Physics and Chemistry. 2nd edition. Camp Hill, PA: Novare, 2021. This curriculum is designed for accelerated 9th grade students.