Promote good learning practices while doing STEM activities. The approaches described here are methods recommended for approaching all types of tasks, whether homework or supplementary activities.
Thinking-Oriented, Investigative Tasks
Have your student do real thinking rather than memorizing procedures. Give different types of tasks, such as authentic, context-free, and hypothetical (see examples below). Investigative tasks should allow your child to wrestle with material in an exploratory way, taking from minutes to weeks or even longer to arrive at a well-reasoned response. Resolving questions might involve experimenting with physical or computer models, researching information on the Internet or in libraries, and/or asking the opinions of experts in relevant fields. In essence, your student should be responsible for doing important thinking and explanation when working individually and collaboratively. Choose questions and tasks that appear to be sufficiently engaging, which can differ among students. Examples:
- How can we determine how much paint is needed to paint our living room? (authentic)
- Develop a report that shows which of several cell phone plans seems best for the family. (authentic)
- Why do you think popcorn kernels pop when heated? What other things might respond similarly in the real world? (authentic; similar situation might be something like car windows cracking on a very hot day when the windows were fully closed for some time)
- Can you find the sum of three consecutive numbers using a different method than adding them? Can you find any other "number rules" that work consistently for problems like this? (context-free; an answer to first question is to multiply the middle number by three)
- How can you design a computer spreadsheet to add all whole numbers from one number to another for any two numbers whose range is an even-numbered set (such as 1 to 100)? (context-free; a procedure is to add the two given extremes and multiply the sum by the number at the midpoint of the series; for 1 and 100, that is (1+100)50; for a story related to this topic, consult information on Carl Friedrich Gauss)
- Can you determine a rule that can be used to find the angle sum measures for any polygon (a closed figure with all straight sides that do not cross over each other, such as a square or pentagon)? (context-free; a standard procedure is to take the number of sides minus 2 and multiply it by 180)
- What do you think would happen if another star suddenly started burning as brightly as the sun and we now had two suns? (hypothetical)
- If you were an engineer designing a dog house in an earthquake zone, how might you try to design it to withstand an earthquake? (hypothetical)
- If a new drug came out that cured cancer for 99% of people but killed the other 1%, do you think it should be released to the public? (hypothetical; involves science ethics)
Explanation and Discussion
Take sufficient time for discussion after your student has explored questions and tasks. Your student should tell what they think something means or why it happens, what strategy might be used to approach a task and why, whether their solution method seems to be working (and why) while they are implementing it, and whether they think their conclusions for a task are reasonable and why. For example, have your student tell why or why not for decisions such as letter I above. They should be expected to explain and defend their thinking and conclusions and respond to questions posed about them. They should try to tell why they think something works. For example, if you take one number off the largest of three consecutive numbers and add it to the smallest, you have three identical numbers. This is why you can multiply the middle of three consecutive numbers by three to find their total. For the most part, your student should explain ideas, orally and/or in writing, rather than hearing someone else explain them to them. However, it is appropriate for parents who are knowledgeable about particular STEM content to explain and show it to students to some degree while engaging them in thinking about the material.
Struggle and Support
Be sure tasks are pursued in a nonthreatening environment where your student feels intellectually, psychologically, and emotionally safe to take risks. Allow and encourage sufficient time to struggle with material since this is where real learning occurs. This includes homework. Give support, provide a quiet workspace with needed materials, and monitor homework completion. However, be careful not to be overly involved, which can give the impression that you perceive that your student needs help or is not sufficiently independent and could thus cause them to have lower self-confidence about their competence in the subject matter. Encourage experimentation, some degree of calculated risk-taking, and creative efforts. This includes exploring computers with no agenda, in other words, simply "tinkering" with them to see how they work. You and your student should not shy away from mistakes and wrong answers but rather see them as rich opportunities to learn. Expect some disequilibrium and confusion to be part of the process. Help your student learn how to accept that and find ways to move past it. Especially, if they get stuck or frustrated, resist the temptation to "bail them out" by telling your student how to think or proceed. Instead, give support and appropriate hints, or pose questions that do not give away too much but which might help them think about things differently. General questions you can pose for most tasks involve asking your student to explain what problem they are trying to solve, what they have tried so far, why they think those methods didn't work (if relevant), and what they might try next and why. If your student is still stuck or can't remember specific information, try "scaffolding" their thinking. For example, if your student can't remember the answer to 8+5, you might say, "Can you first get from 8 to 10 by breaking off part of the 5? (yes, 2) What is left over from the 5? (3) So, what do you get if you add on that remaining part? (13) Do you think that is the answer to 8+5? Why or why not?" (You might have your student use dried beans or other objects to explore this.) Or if your student can't remember the formula for finding the area of a rectangle, you might first ask them to explain what area is. Next you might have them draw a rectangle on grid paper and ask how to find the number of square units inside. If your student counts them all, ask if they can think of a faster way to find the answer. Be sure to avoid finalizing tasks by presenting the "right" way to do or think about something.
Ask your student to complete tasks in more than one way, if possible. For example, when they solve a math word problem and explains why they think it is correct, ask if they can find a different way to solve it (which might confirm or call into question her original answer in addition to expanding their repertoire of strategies). Have your student brainstorm more than one scientific reason why things might work as they do, such as why a shorter person can typically change directions faster than a taller person when running, why a shower curtain might blow inward when the shower is running, or why cracks are put into in sidewalks. Ask your student to do some work mentally, as in figuring math in their head or imagining various science-related scenarios.
Permit your student to use a calculator to do carefully chosen explorations or to assist with tedious computations. In the former case, an example for a younger child who has not yet studied negative numbers is to ask if it is possible to "take away"/subtract a larger number from a smaller number. Let them give their prediction (always with an explanation) and then have them test it with some examples on a calculator, recording the results. When they see the answer to problems such as 4-5, 3-6, and 2-8, let them try to determine the "rule" for finding answers to these types of problems now that they see they do yield valid answers. You might even see if they can give a real-world example of when this can happen. Another example is determining whether multiplication always "makes bigger" and division smaller. Exploration on a calculator should show that the answer to both of these is no. For problems involving large computations, the guideline is that calculators are appropriate, real-world tools to use when they do not replace the very thing a student is trying to learn. For example, it does not make sense to use a calculator to find the answer to double-digit subtraction problems if the focus of the lesson is to learn how to subtract two-digit numbers. An appropriate use of a calculator is to perform difficult or lengthy computations while solving word problems. In this case, the focus is learning how to solve word problems, where the most important and challenging part is determining what solution method to use.
Students tend to like using hands-on models (sketching drawings may also be helpful). However, variety is important and students should use abstract and mental methods as well. Students also tend to like working collaboratively on tasks (including on the computer) and to do tasks that have a purpose, such as creating a spreadsheet that calculates pay for a dog-walking or babysitting business, using the Internet to research information for a specific project, or preparing a class assignment with presentation or graphing software. Again, some context-free and hypothetical activities should be included with more authentic tasks to provide a more varied experience. Please note that the learning preferences presented here do not imply biological differences in processing information. Rather, they are research-identified tendencies-across studentss as a group-that likely have sociocultural origins.
Be sure tasks given are developmentally appropriate, meaning neither too easy nor too hard. For example, a younger child might be asked to think about ways to add two numbers less than ten that are two numbers apart, such as 6 and 8 or 3 and 5, for which they might determine that they can use doubles to find the answer. (Examples: take 2 off of one number, add the doubles, and then add the 2 back on; double the numbers and subtract 2; double the number between the two.) As a science example, a younger child might be asked to consider why ice is bigger than the amount of water it came from or why pancakes are round.