Category: Math Education

When I was an elementary school student, math was not my strong suit. However, I found it easy to learn multiplication facts; all because my math teacher had a strategy that helped me to learn them fast. When I became a special education teacher, of course, I had to teach math, but I had gotten much better at it throughout the years.

A couple of my students suffered from dyscalculia, which made learning multiplication facts hard for them. So, what did I do? You guessed it, I thought back to my days as a student and pieced together the strategy that my math teacher used. And to my amazement, it worked like a charm. My students learned their multiplication facts super fast, and when I quizzed them a month later, the skill remained.

Fast forward to today, and while I was looking form some info on math teaching tips, I found a video explaining that very instructional strategy. I was so inspired, I decided to share it with you all. I have provided the video below, just in case you want to use it with your students.

For grade school and high school, there are set educational standards for certain subjects. These are the guidelines that each teacher must follow for their core classes, such as English and math. However, sometimes teachers will try to bend the rules and teach these courses their own way. Math is a subject that may face issues when it comes to the Common Core Standards.

The Purpose of Common Core Standards

The Common Core Standards are in place to ensure that all children get an equal education regardless of where they are attending school. These standards are created to be consistent and easy to understand so that kids will test well during assessments. With the Common Core Standards, students should be set up with all the tools and knowledge they need by the time they graduate high school.

What are the Common Core Standards for Math?

The specifics for each grade varies, but there are a few specific guidelines that must be met for every grade. Those common core standards are as follows:

• Make sense of problems and persevere in following them.
• Reason both abstractly and quantitatively.
• Create feasible arguments and critique the reasoning of others.
• Model with mathematics.
• Use the appropriate tools strategically.
• Encourage precision.
• Look for and make use of structure.
• Look for and express regularity in reasoning.

Math teachers must follow these rules regardless of which grade they are teaching. These standards will enhance the learning of students and make sure all schools teach math equally.

Do Math Teachers Follow These Core Standards?

For the most part, math teachers follow the Common Core Standards well. Kids are taught at a pace that is easy to understand, which includes basic adding and subtracting in first grade, multiplication, and division in third grade, and finally, more advanced topics in high school, such as algebra, geometry, and statistics.

While many teachers follow both the general and grade-specific standards, there will always be some that don’t agree with it and don’t completely follow it. This is because many teachers believe that all kids learn things differently and at different paces, so there cannot be just one way to teach them. The common core standards can often put pressure on teachers to teach a specific way, regardless of whether or not they feel it is the best way to teach, which is why the Common Core is not always taught as it was intended.

The 2018 Education Next poll revealed that more people have approved of their schools presently than they have in the past. Those who participated in the poll were instructed to rate their public schools with a grade from A to F. Each group, which includes parents, teachers, and the general public had given significantly more As and Bs than Ds and Fs. This is generally an improvement from past polls, revealing that more and more individuals are becoming satisfied with the common core system.

Therefore, some teachers may try to put their own spin on the common core standards, but for the most part, math educators just try to stick to the formats that they’re supposed to.

Our brains are like computers in the sense that some things that we put in them stay there for years. Multiplication facts are like that—information that you will use for the rest of your life. This is why mastering the multiplication facts early is a critical building block for many other math applications in life.

As teachers, we can become a little lazy in practicing the multiplication tables, so using fun, hands-on games can be a lifesaver for math instruction. Our students need math skills to apply to most any career choice, not to mention higher level math in high school and college.

Use these jobs as a way to show your students that multiplication is necessary to real life.

• Photography: A photographer needs to understand angles, perspective, distance and resizing to be excellent at taking pictures.
• Travel Consultant: As a travel advisor, you must work out arrival and departure times, money exchange calculations, and distance calculations.
• Architect: Most of what an architect uses on a daily basis for designing things and calculating dimensions is addition, subtraction, multiplication, and division.
• Chef: Chefs all over the world must multiply to produce mouth-watering pastries and delicious meals.
• Automotive technician: Anyone who does car repairs knows that the ability to use math, and specifically multiplication, is essential to replacing an engine, measuring for a new gearbox, or calculating how much transmission fluid is needed.

Now that it is clear that multiplying confidently is a skill everyone needs, use these enjoyable games for math reinforcement:

• There are many Multiplication Songs that can be found on the internet. Singing along, this is a great way to reinforce what the students are learning visually.
• com has many free games that are fun and reinforce the multiplication facts.
• SushiMonster is a great math app to practice multiplying and could be added to tablets for reinforcement each day.
• Here is an I Spy free printable game for practice.
• Even when using math multiplication worksheets, have a race to see who finishes with a prize at the end.
• You can use skittles, goldfish, or any other small candy to play Bingo.

Searching for games and creative ways to move beyond simply reciting multiplication facts over and over helps to cement the concepts in their brains. Using all of the learning modalities to reinforce the facts teaches each student in the way he/she learns best.

Lydia Colgan, a math professor at Queens University, says, “Being able to recall basic facts efficiently is a necessary first step in the development of more advanced skills for computational fluency with larger numbers and algebraic expressions.” She goes on to say that children as young as kindergarten can begin learning that multiplication is just repeated addition, only faster, through the use of games.

The more time a student spends just trying to calculate can use up a disproportionate amount of time for a test or other evaluation. It may seem archaic in the age of calculators and computers to teach basic multiplication facts and skills, but helping our students achieve automaticity and fluency produces long-term memory with very little effort.

When most people think of the word pattern, various repetitive wall-paper designs come to mind. What could this have to do with math?

As it turns out, patterns have everything to do with math. Mathematics itself is the study of patterns. These mathematical patterns can include simple repeats, such as the repetitive nature of kitchen linoleum or children’s rhymes. But the term mathematical patterns also refers to number-related patterns. For instance, recognizing that nine is a square number because it contains three groups of three involves mathematical pattern recognition.

Pattern recognition is a fundamental skill

Children participate in pattern recognition from a very early age. Children first begin their journey of pattern awareness by sorting objects. As they grow a bit older, they will begin arranging these sorted objects into repetitive sequences.

As you may have observed, some children naturally gravitate toward pattern recognition and formation while others do not. For instance, you may spot a child arranging colored blocks into a red-green-red-green pattern by picking up both a red and a green block at the same time from the pile next to her. Understanding that the entire pattern as a whole is made up of constituent parts, which themselves can be though of as a whole unit (i.e. a red and a green block together are a whole) is actually a very advanced skill. Children who struggle with pattern recognition and formation may grab a red and a green block separately, or they may be unable to understand that the ABAB pattern of red-green-red-green can be generalized to dog-cat-dog-cat, or that it can be transformed into a more complex pattern such as ABBABB, red-green-green.

Despite what some parents and educators may be led to believe, these skills of pattern recognition are more than just child’s play. These fundamental abilities to recognize and repeat basic patterns at a young age are foundational to the mathematical skills children learn later in life. In fact, research has shown that a strong correlation exists between fundamental pattern recognition skills and ACT scores in the teenage years. Recognizing that a whole pattern is made of constituent parts develops the later mathematical skill of recognizing that numbers are made up of smaller numbers and will add up to the same number regardless of the order in which they are added.

Help children build these fundamental skills

Patterns help children learn sequences and make predictions, skills that are foundational in subjects such as Algebra and Geometry. To help build these foundational skills in children, it is important to promote pattern awareness wherever you go. Patterns can be found in the sidewalk, in the window arrangements on houses, in rhymes and poems, the beat of a song, or even in flowing water. When talking about patterns with children, you can ask them what their pattern is called and ask them to repeat it, or to generalize it. While we may find the teaching of pattern recognition monotonous, children enjoy searching for patterns. Giving them various leaves and sticks, or even various words and numbers, to arrange into patterns will help substantially in developing these fundamental skills.

The importance of pattern awareness in early childhood cannot be underestimated. Teaching children to recognize and manipulate patterns found in the world around them can provide a lasting foundation for mathematical success. Why not spend a few minutes per day helping your child see the world in new ways? They’ll thank you for it years down the road.

Most mathematicians would say there is beauty in math but beauty is subjective, in the “eye of the beholder.” However, there are compelling reasons why math and art belong together in school. Semir Zeki, a neuroscientist at University College London, conducted a study along with other scientists that found that “mathematical beauty is linked to activity in the same region of the brain as beauty from sensory sources.”

The medial orbitofrontal cortex, which is the sensory area, is very active when the mathematician saw something he/she thought was beautiful. The findings indicated that beauty can be found in math as well as art.

Merging these two subjects makes sense especially for students who struggle with math as it could improve comprehension and performance. There are some distinct advantages to teaching them together.

Benefits of Combining Math and Art

It’s more fun! Math is often associated with boredom and difficulty which could change when combined with art.

Math is a fundamental foundation of art. Think of how much geometry is in architecture, sculpture, and painting.

Scientists “found that van Gogh’s art, in particular in paintings from periods when his mental illness was at a peak, mirrors natural turbulence down to mathematical precision.”

The two can boost creativity and brain-building as they cause new connections and thinking patterns.

Art is a way to be more hands-on with math, often making math more understandable.

Visualizing mathematical concepts and calculations through art can bring accessibility to students.

Technology combines math and art when images are produced in color simulation, prompting the question, “Is it math or art?”

The Golden Ratio has been used for hundreds of years to produce balance in art. “Without mathematics, there is no art,” said Luca Pacioli, a contemporary of Da Vinci.”

Activities That Naturally Combine Art and Math

Complete a self-portrait by copying half of the student’s face onto a piece of paper and discuss proportion and symmetry. Then allow them to sketch the other half of their faces. They are usually amazed at how well they can draw the other half.

Using the app InspirARTion, teach students about radial balance, lines of symmetry, and the color wheel. Then set them loose to create gorgeous designs on their own.

Create Positive and Negative designs using two colors of paper, with one larger than the other. They cut out a design from the smaller one and flip it over to glue to the larger, creating a design.

Teach line, shape, and pattern with an Optical Illusion art activity.

Teach the Fibonacci number sequence using a compass and colorful construction paper on a white background.

Mathematician purist, the brilliant G. H. Hardy, said, “A mathematician, like a painter or a poet, is a maker of patterns.” He proposed that the purpose of math is not solely skills and understanding, but also the beauty of patterns and designs.

If merging math and art can increase a student’s love and comprehension for those subjects, why would we ever object?

Math is one of those academic subjects that many students either struggle in or disengage from. How can you as a teacher create engaging mathematics experiences that make students look forward to math class? I am glad you asked. Keep reading to find out.

Create a Classroom Setting That Encourages Learning

Staging the physical space, getting students to cooperate, creating a communal environment, and maintaining a positive classroom climate and culture have been suggested as four elements to focus on to create a classroom environment conducive to learning. Such an environment encourages students to be willing to try/learn new things and not be afraid to fail because the teacher is caring and supportive. Relationships among students are encouraged and respect is expected.  

Make Math Relevant

All students will eventually ask or think, why do I need to learn math?  When will I ever use math again? Unfortunately, students will lose interest and be less engaged in math if they can’t see the relevance to their everyday lives. There are many ways to make math relevant.  Teachers can consider lessons on using math in real-life financial scenarios that incorporate concepts about budgeting, saving, investing, spending, and how to figure out if, for example, the newest cell phone advertisement is a good deal. For more tips on how to make math relevant, see 7 Ways to Make Math Relevant in your classroom! 

Use Technology

The National Council of Teachers of Mathematics has an excellent article on the Strategic Use of Technology in Teaching and Learning Mathematics. The use of technology in a math classroom also helps to make learning math fun because students have almost unlimited access to exciting web tools and applications. Here five (5) technology tools to engage students and help improve their mathematical competency through technology.

Make Math Social

Many students are interested in and participate in social media platforms. Teachers can create problems from social media for students to research and solve. They can then ask the students to present their findings and urge the students to ask questions of each other. For example, a middle school math class might ask students to research the amount of campaign money raised in the first quarter of 2019 by Democratic candidates for president of the United States. Challenge the students (individually or in groups) to present their findings in an appropriate graphical representation. Similarly, you could ask students to research and rank current rap artists or compare the percentage of Twitter followers by the Kardashian family. Students could also work on projects in groups, present their findings to the rest of the class, or even ask other groups to solve a problem using the data presented. Making math social also makes math fun.

Make Learning Math Fun

As mentioned above, making math social is one way to make math fun.  Another way to make learning math fun is to incorporate the use of games and puzzles. Games and puzzles are not only fun for students, but they can also challenge students and help them learn and practice new mathematical concepts. This can be accomplished by answering questions about the game either verbally or in writing. It is also important that after playing a game, students be given an opportunity to reflect on what they learned.  The previous link contains over a dozen questions in three areas to engage students in a fun mathematical learning experience.   What did we miss?

Which is better: having students use pen and paper when working on math problems or allowing them to use calculators to find the answers?

Regardless of the level they teach educators don’t agree on the answer.

Elementary teachers straddle the fence on this issue. Some see calculator use as a way to build numeracy. Others see it as a replacement for strong math skills. Middle school teachers fervently debate the issue for their classrooms. Although high school students may use calculators on their college entrance exams, many math professors refuse to allow the handheld devices in their classes.

Johns Hopkins University Professor of math and education W. Stephen Wilson once wrote, “I have not yet encountered a mathematics concept that required technology to either teach it or assess it. The concepts and skills we teach are so fundamental that technology is not needed to either elucidate them or enhance them. There might be teachers who can figure out a way to enhance learning with the use of technology, but it’s absolutely unnecessary.”

He saw the calculator as nothing more than a crutch.

How students benefit from using calculators

Calculators make quick work of extended problem-solving as long as the numbers for each step are entered correctly and the user understands the order of operations on the device. Problem-solving with a calculator becomes a teachable moment, both in the importance of entering data with accuracy and in understanding the function keys.

Another benefit of calculator use in the math or science classroom is that students develop familiarity with different technologies.

Calculators have the added attraction of being fun to use, but using calculators in the classroom have many drawbacks as well.

Drawbacks to using calculators in the math classroom

The use of calculators in the classroom draws skepticism from teachers, and with good reason.

Some math teachers are hesitant to advocate for calculator use in the classroom. They argue that students become complacent, relying on the technology to think for them, even for the simplest of tasks. Teachers worry that overreliance on calculators will strip students of their numeracy skills.

In a BYOT (Bring Your Own Technology) district, the added expense of a graphing calculator may place math technology out of the reach of some families.

The solution

Students in ELA classes use keyboards to type their essays. Even with the writing apps available to assist writers, students are solely responsible for their word choice and sentence construction. The technology is only a tool.

If we think of calculators as tools to complete a task, math becomes less about the device and more about problem-solving. Calculators do not solve problems. People do.

Students who use calculators in the classroom may find them handy when working with large numbers, scientific notation, or square roots.

The calculator serves a purpose only when the student has developed numeracy skills. Students who understand how numbers work are more likely to spot input errors. Without numeracy skills, however, the math student might not catch mistakes any quicker than an ELA student would locate a usage mistake and correct it.

Calculators can be useful for solving tedious and complex problems. Their employment in the classroom depends on the skill of the students relying on them. Calculators should never be a crutch.

Calculators should be a tool for getting the job done successfully and as efficiently as possible. According to NTCM, they augment reasoning, not replace it.