One of the most common complaints I hear from friends with young children is that they have no idea how to help their children with math homework. I’ve heard many parents say that while they can solve the problem, they do not understand the process that is being taught to their child at school.

                                        Photo source: www.danscartoons.com

Let me start by saying that it’s not a parent or caregiver’s job to be a master at all subjects their child is learning in school. It is more than ok to just check to make sure that your child has completed the homework even if you don’t know if our child has all correct answers. The teacher will most likely have students self-check homework, collect the homework at school, or go over problems as a class. However, I imagine most of you reading are thinking more about scenarios like this one:

Child: “I have no idea how to do my math homework”

Parent: “Ok, let me look at it… oh this is addition – you just line up the digits and then add them, carry the one if you need to”

Child: “No! That’s not how we do it!”

The best way to handle this type of situation is to have your child show you similar problems from class that they do know how to solve and ask them to explain the steps to you. Oftentimes, having kids (and adults) explain the thought process used to solve a similar problem is all that is needed to realize they actually do have the tools to solve the problem they are struggling with. If that doesn’t work, there is no harm in showing a method that is not exactly how they learned it in class as long as you can explain why your method works. The entire basis of inquiry-based mathematics is conceptual understanding. Oftentimes, teachers now will ask students to solve a problem using more than one method in order to help deepen understanding. Let’s start by assuming you have no idea how to do the problem (the new way or the old way). Don’t worry; there are plenty of resources out there to help you. It’s best to start with the child’s teacher. The teacher will often have suggested websites, YouTube videos, or even handouts for parents. If that’s not an option, here are some resources that I find helpful:

IXL Math: https://www.ixl.com/math/

You can search this site for similar questions to whatever it is your child is struggling with. It is broken down by age group and then by category. Once you find a similar problem, you or your child can attempt to solve the problem. If you get the answer wrong, IXL gives a short tutorial on how to do the problem.

Khan Academy: https://www.khanacademy.org/

Khan Academy has video tutorials created by experts in mathematics and math educators for almost all types of math concepts and questions (so far, I haven’t been able to think of a topic in math that isn’t covered on Khan Academy).

U.S. Department of Education: http://www2.ed.gov/parents/academic/help/math/index.html

Many people don’t realize that the U.S. Department of Education actually has resources for students, parents, caregivers, and educators. While this hasn’t been updated since 2005, the activities and ideas are still relevant. If you’re looking for ideas for activities that you can do with your children to help support mathematical thinking, this site actually has quite a few excellent suggestions.

State Board of Education Website: http://www.corestandards.org/standards-in-your-state/

You can use the link above to click on your state. It will take you to your state’s board of education website, and many of the state websites have resources and ideas for parents.

Modeling and encouraging perseverance is one of the very best things you can do for your child. The process it takes to get to an answer is equally as important as the answer itself. Having your children explain their thinking, encouraging them to talk to the teacher, talking through the steps with them, and using online resources to learn together are all excellent ways to work through a problem. Building these foundations will help your child from early math through high school math and beyond.

More often than not, when I tell people I am a high school math teacher, the response I get sounds something like “Wow, that sounds awful. I hated math in school” or “Oh. I am so bad at math!”

At the very beginning of each school year, I give my students an assignment called “My Mathematical Biography.” This assignment includes questions about students’ past experiences with math, expectations for the coming school year, feelings about math in general, and more. Some students put a great deal of effort into this assignment while some answer each question in only one or two sentences. Regardless of the effort a student puts into the biography assignment, I have found the relationship between a student’s success in my class and the answer to the first biography question to be very interesting. The question reads as follows: Overall, how do you feel about math? Have you always felt that way, or were there specific experiences or moments that have given you that feeling? If the latter, what were they, and why were they important?

Negative feelings about math are often traceable to a previous teacher or class, but a positive relationship with math often is credited to parents or siblings.

The two most harmful attitudes to portray to children as a caregiver are either: you hate math and just aren’t a math person so that means they probably won’t be either or math has always come easily for you and it’s not hard so your kid shouldn’t be struggling with it. Both of these portrayals ignore the fact that each child has his/her own potential for success in math. My experience as a teacher has shown me that attitude and perseverance have just as much impact on success in math as predictive test scores. So how can you, as a caregiver, make sure that your child develops a positive attitude towards math?

• Provide them with opportunities to learn from mistakes. Allow them to try problems that you know they may not be successful with on the first attempt.
• Reinforce the idea that learning comes from trying new things. Try a new recipe with them or have them read a book aloud that they’ve never read before.
• Only talk about your own math experience as a positive learning opportunity regardless of your grades or test scores. Say things like “I learned so much about ____ in ___ grade or ____ math class” or “The first time I ever thought about that was in ____ class.” Avoid saying things like “Oh I hated division problems,” “I was so bad at word problems,” or “That class was so easy for me!”
• Highlight connections between math and the world. A great list of resources and lessons that provide connections between early math through adolescent math and real life applications can be found here: http://www.educationworld.com/a_curr/mathchat/mathchat019.shtml

Fostering a positive attitude towards math and mathematical concepts allows students to reach full potential in each class and become a strong math student from early childhood through adolescence and early adulthood.

As teachers, we constantly remind students about the importance of mathematics if you want to be an engineer, chemist, architect, archaeologist, astronaut, astrologist, biologist, and many more. What people don’t realize is that spatial skills are key in transforming mathematics into three-dimensional objects with limitless uses. Spatial reasoning is essentially the ability to think about, visualize, and mentally organize objects in 3 dimensions.

Here is an example of a standard spatial reasoning test question:

Which of the following cubes represents the unfolded picture on the left?

Question and photo from http://dudye.com/challenge-your-creativity-77-problem-solving-exercises

The correct answer to the above question is the cube shown in choice C. These visualization exercises involve the same thought processes that allow surgeons to visualize the next steps in surgery, architects to convert floor plans into real life buildings, engineers to use formulas and programs to form electrical circuits, and so on.

Most people think spatial reasoning is specific to geometry class, but spatial reasoning is involved in all mathematics and science classes. I teach high school students, but spatial reasoning skills can be built and expanded from a very early age. We all use our spatial intelligence on a daily basis. When you look at a map to figure out relative location, rearrange your living room, try to figure out if your stroller will fit down the aisle in the grocery store, or decide whether or not that last pan will fit in the dishwasher; you are using your spatial intelligence skill set. Even something as simple as involving your children in these types of questions, decisions, and activities can help strengthen spatial reasoning skills.

Playing with toys and games that allow imaginative building can help improve spatial skills. Some things that probably come to mind immediately are toys like Legos and building blocks, but there are many more options for individual play or group play and board games available. A great list of construction toys is available here: http://astore.amazon.com/parenscien-20?_encoding=UTF8&node=35

There are also countless puzzles and games that involve spatial reasoning skills. A list of board games that involve spatial reasoning is here: http://astore.amazon.com/parenscien-20?_encoding=UTF8&node=35

(Blokus is one of my all-time favorite games! I think playing this game has made me much better at visualizing when teaching geometry.)

If the test question above was interesting for you to think about, there are a number of spatial reasoning challenges and tests you can find online. I did a quick Google search for online spatial reasoning tests and I found one similar to the question above at https://www.123test.com/spatial-reasoning-test/

(This is not a test you’d give young children, but I found it to be a fun mental challenge).

One of the best things about working with construction toys or board games that involve spatial reasoning skills is that they truly are games that allow children to come up with their own plans, outlines, or strategies without one correct answer. This is always the goal of inquiry based mathematics, so introducing games and play objects that allow for this type of thinking early on will go a long way in students’ future success in mathematics.

Charlie has been accused of pulling the fire alarm on Friday, 12/5. Help him argue that he is innocent.

The facts:

• The fire alarm was pulled in the student cafeteria at 11:55 am
• Charlie has math period 5 with Ms. Smith
• Charlie was in math class for the ENTIRE period on Friday, 12/5
• 5^th period starts at 11:45 and ends at 12:25

Prove Charlie did NOT pull the fire alarm.

The above is an opener that I give my geometry students when we start our unit on proofs. It may seem obvious that Charlie did not pull the fire alarm, but being able to come up with a string of statements that logically prove he did not pull the alarm is the same thinking process as reasoning through a mathematical proof. This type of thinking can be encouraged at a young age, and the more opportunity kids have to think this way, the more open minded they will be as students later on.

“New Math” has developed a pretty bad reputation over the last few years. Do a quick Google search of “new math” and you’ll find countless YouTube videos bashing it, sarcastic Instagram and Twitter posts demonstrating how confusing it is, and blog posts using “new math” to demonstrate how messed up our education system is. In fact, I received an email from a good friend this past school year titled “This is how they’re teaching math now?” with a forward from his son’s second grade teacher. The teacher had attached links to YouTube videos demonstrating how to do problems the way she was teaching them. Here is one of those links: https://www.youtube.com/watch?v=4UexBOa7u8Y At the end of the email, my friend wrote “This could not be any dumber. I showed him the proper way to figure it out.”

Many of you may be nodding your heads reading this because you’ve felt similar frustrations in trying to help your children with their math homework. You’ve thought to yourself “what was wrong with the way I learned how to do this?” But I want you to consider this: “New Math” is another name for “Reform Math” or “Inquiry-Based Math.” Inquiry-based math helps to develop the foundations of characteristics we all hope our future generation will hold. We want our kids to do things thoughtfully, with an emphasis on intent and process.

If you watch the video I linked above, you’ll see what looks like a complicated process for adding the number 96 and 48. In reality, the process is breaking down the following thought process: If I told you to add 96 and 48 without a pen and paper (so no “carrying” allowed!), you’d think “90 + 40 is 130, then I still need to add the 6 and the 8 so that’s 14 more… together that’s 144.” Inquiry based math helps kids develop methods and thought processes to do what many of us do mentally without the language to explain our thought processes. The image below represents the basis of inquiry-based learning – I like this specific image because it gives a short explanation of each of the inquiry steps.

Photo source: http://cte.smu.edu.sg/assurance-learning/integrated-design/ibl

In early math, students are not yet learning things like adding two digit numbers, but setting up a foundation of inquiry based learning and reasoning skills can be done at any time. In my high school math classes, the most successful students are those who are willing to approach a problem they don’t necessarily know how to do at first glance. The next time you are with your child at home, think about doing some of the following:

• Encourage kids to solve problems in multiple ways. Instead of saying “It is too cold to go to the park, so we can either read a story or play a game,” you may want to try saying, “Hmmm, we were going to go to the park, but it’s too cold. What do you think we should do instead?” Oftentimes, as a teacher, I have to remind myself not to fall into the trap of only giving students a few clearly defined choices. While this is a great strategy for classroom management and behavioral expectations, meaningful thinking occurs more often when kids have the opportunity to come up with multiple solutions or conclusions.
• When you are making a decision, try verbalizing your thought process as a model for your children. For example, while at the grocery store getting groceries for a dinner party, you could say “I had planned to make hamburgers for dinner, but Aunt Kelly is coming over for dinner and I just remembered that she doesn’t like hamburgers. I need to think of something that will make everyone happy. I will make lasagna instead.”
• Encourage your children to make hypotheses and conclusions based on observations. If you burn a piece of toast while you are making breakfast, ask them why the toast burned and what you can do differently next time to make sure the toast is not burnt.
• Give your kids “mysteries” to solve. For instance, ask them if they can come up with any ideas on why the music class might have started late or why the car in front of you is moving so slowly.

All of these activities build a strong math foundation in elementary school and beyond. While it may not seem like these activities involve any math, problem solving and the ability to create a chain of logical reasoning are skills that eventually translate to success in classes like Geometry, Calculus, and beyond.

Sasha Fajerstein currently teaches mathematics at New Trier High School in Winnetka, Illinois. She previously taught at Nichols Middle School in Evanston, Illinois. Sasha received her Bachelors of Science in Mathematics from the University of Illinois at Urbana Champaign. After graduating, she taught English in Costa Rica for a year before returning to the United States to teach math.

 

Sasha is passionate about trying new things in the classroom, and she works hard to integrate technology into her lessons. She recently piloted a new geometry textbook for High School students entirely on the iPad. She has presented at the Illinois Council of Teachers of Mathematics conference and the Metropolitan Mathematics Club of Chicago.