Visualization as a Cognitive Tool Pt. I

Visualization as a learning strategy is most commonly seen in the language arts department. Teachers may prompt students to visualize what is happening in the text to boost comprehension and recall before, during, and after reading. This is a proven, worthwhile technique, especially for struggling readers and those with attention difficulties. However, there are numerous other ways in which educators can use visualization and visual tools to enhance learning opportunities that span far beyond the “try to picture or visualize what is happening” cue.

 

Visual Awareness

Some students, especially those with attentive or behavioral issues, often find that they are most successful when educational tasks encourage the use of spatial areas of the brain, as opposed to linguistic areas. To initiate visualization processes, teachers and parents can practice many different strategies, across any content area.

 

Math

Because mathematics can often involve complex, abstract, nebulous concepts and values, even grasping a math question can be daunting, especially for people who struggle to tap into their “math brains,” like myself. For instance, questions involving exponents, decimals, and measurements, can be very intimidating. Students may not know where to begin when working with what they believe to be ambiguous concepts or terminology.

 

  • Accompany measurements, whether weight, height, temperature, density, etc., with familiar, tangible comparisons. For example, if the question involves calculating the area of a surface, provide visual context by telling students that the surface would be about the size of a tennis court, classroom tile, standard doorway, etc. On assessments, consider providing images to represent that object, as opposed to just the calculations or measurements. If asking students about three-dimensional objects, prompt them to picture an everyday object that represents the size and shape.
  • Provide learners with opportunities to conceptualize number functions in different ways. For example, understanding exponents, like 2 to the 8th power, might leave young learners scratching their heads. If teachers provide visual context or long-written forms, students can better prepare to grapple with the task. Even a simple visual process, such as writing out the simplified exponent, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, and then grouping them while multiplying, can assist with the otherwise unfamiliar concept.
  • Post visuals around the classroom of commonly used terminology. Especially for younger learners, simple symbols used to exhibit addition or subtraction processes can serve as a subtle reminder to students during instruction and practice.
  • Consider taping simple visual resources to each desk during the start of a new math unit. If beginning to discuss fractions, use a photos of segmented chocolate chip cookies for reference. With a visual, some students may find that decimals and fractions are more approachable when they can see what that fraction looks like in a physical sense; ⅛ of a cookie is much less appealing than ¾ of the same cookie.
  • Teachers can prompt visual thinking as well by asking clarifying questions or having students come up with their own comparisons. If measuring objects, ask students to brainstorm what they think would be a similar sized object. What would be slightly smaller or bigger? Which might weigh more? Ask students to visualize patterns and proceed with the next series of figures.

Math Help at Home

Elementary level mathematics has changed significantly since parents were in school learning their basic addition, subtraction, and multiplication facts. In fact, the math 2.0 curriculum, which coincides with the Common Core State Standards, uses completely different terms for what we would call adding and subtracting. With all of the changes in elementary grade math terminology, application, and processes, parents may become confused as to how to help at home. The goal for this blog is to provide a basic cheat-sheet of helpful hints for when your child is being asked to complete basic math processes using new, unfamiliar methods.

 

 

  • Composing/decomposing

 

In elementary school, I added and subtracted. This meant I lined up the numbers, carried them over if necessary, and probably used my fingers to keep everything on track. Students are no longer using these methods. Now, we see handouts and practices that ask students to “compose” (add) or “decompose” (subtract). Essentially, composing and decomposing involves the student’s ability to break numbers apart and put them back together.

  • For example, if given the simple subtraction problem 46 – 8, our past elementary school days would tell us that, since we cannot take 8 from 6, we need to “borrow” 1 from the 4 so that we’d be left with 16 – 8 in the ones column and a 3 in the tens column.
  • Now, students are prompted to simplify their thinking in order to decompose without the “borrowing” component. Instead, the process would look like this:

46 – 8 = (46 – 6 – 2)

 

    • Because breaking the 8 in to 6 and 2 makes for friendlier mental math, the 8 no longer requires students to borrow, which eliminates the possible confusion that comes from borrowing from the tens column.
    • In this new 2.0 curriculum, elementary students will also be asked to use visuals or numeric symbols charts to assist with simplifying a question. For example, if presented with 9 + 5, the old method would require young math learners to use fingers, adding one at a time from 9 until 5 fingers are up.
    • Now, the problem might recommend a visual such as:

    9

    5

    I I I I I

    I I I I I

    I I I I

    • Since it is much easier for students to mentally compose from ten, they know to break or decompose 9 into 5 + 4; they know that 5 + 5 = 10, so 10 + 4 = 14

     

    Might this all seem like a slew of extra steps when students could simply count up using their fingers like we did? Yes—for sure. However, the push for this type of thinking is to better prepare students for algebraic concepts to come later.

     

     

    • Multiplication/division

     

    Multiplying and dividing in elementary mathematics 2.0 is also going to utilize the compose/decompose processes. The key behind this is again to simplify the numbers for ease during any operation.

    • For example, if a student is given 6 x 8; our old method would be simple memorization or flashcards. However, now students would simplify the equation like this:

     

    6 x 8 = 6 x (5 + 3) = (6 x 5) + (6 x 3)

     

    It is much easier for students to add when tens are involved. So, when 6 x 5 gives us 30, we simply then add the result of (6 x 3), which is 18, to 30. Giving us 30 + 18 = 48

     

    • This is especially helpful for students who struggle with memorization. Instead of hours of flashcard practice, students are able to use simply mathematical concepts to attack the problem with skills, as opposed to arbitrary memorization.

     

    While these new methods and extra calculation steps may seem foreign and frustrating now, stick with them. Once your children master these methods, they will be better prepared to tackle more complex calculations in the future. Who knows, your child may even take great pride in teaching you for once!

Making Math into Games: Activities in the Classroom and at Home

Take it from me, a self-proclaimed math loather: when math concepts just do not click, the fallout can be extremely frustrating for kids. No matter the age, a student in the classroom or a child at home can quickly become discouraged when the math just doesn’t add up. For these children, who struggle with the ins and outs of successive math courses, real-world concepts and engaging activities can make all the difference.

Trick-or-Treat Math

This is the perfect seasonal opportunity for kids to apply real-world concepts of money, numeric relationships and directions to engaging activities that secretly build multiplication, division, analytic and ratio skills. Before trick-or-treating, have kids rate their favorite Halloween candies from 1-10, 10 being their absolute favorite. Then, help kids set up a candy bargaining/trading activity, in which they base their trades off of a certain candy’s rating. For example, if Reese’s Pieces are ranked as a 10, but Twizzlers are a lowly 2, help your children identify how many Twizzlers it would take to equal the ranking of Reese’s Pieces. Help them throughout the trade by prompting them with mathematical questions like, “If cherry lollipops are favored twice as much as orange lollipops, how many orange would I have to forego for 3 of your cherry pops?” Or, “If you have 60 pieces of candy from trick-or-treating, and I allow you to eat 1/10 of your candy over the weekend, how many pieces can you eat on Saturday if you want to eat 4 pieces on Sunday?” (**DISCLAIMER for educators—if you plan to allow for Halloween activities in the classroom, be sure to double check with parents about any allergy/dietary restrictions.)

Scavenger Hunt

A scavenger hunt activity is always good for embedding discrete mathematical practices. Provide students with different word problems and accompany each problem with a “clue envelope.” Each time their group correctly works through a word problem, provide them with a clue to lead them closer to the treasure. This activity allows for plenty of options for differentiation, including high/low grouping, varying levels of word problems, options for graphics or manipulatives, etc. Depending on student needs and abilities, math problems could involve multi-step word problems, multiplication flashcard races, geometric matching, placing items in size order, rounding to nearest tenth/hundredth and matching equivalent fractions. Perhaps the treasure could be a homework-free pass, prize tokens or extra recess time.

Shaving Cream “Swat”

It may be messy, but shaving cream swat games using mathematical equations can bring a ton of energy to a typically dry math review. Depending on age and ability, groups can swat basic multiplication problems, the next shape in a pattern, addition/subtraction problems, etc. The possibilities are endless so long as the planning and frontloading are in place. Educators will create math challenges on index cards for groups to solve. While solving, the teacher will provide answer options written in shaving cream on paper plates—kind of like a multiple choice selection. Groups will race to “swat” or “splat” whichever answer they agree on using a fly swatter. The caveat, of course, is the clean-up. However, this group activity never fails to drum up enthusiasm when completing a math practice or review.

With a little planning and preparation, these games can reinforce math concepts and build skills in new ways that will get even the most hesitant learners to join in the fun!

Ideas for Summer Learning: Math

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The summer months are full of outdoor activities and opportunities for kids to enjoy the lovely weather. With camps, vacations, and other plans happening throughout the summer months, it is no wonder that academic skills take a backseat. As much as children and teens would like to forget about school over the summer, there is no denying that continuing to engage in academics over the long break is greatly beneficial.

A study performed by Johns Hopkins found that students can lose anywhere from one to three months of learning or previously retained information over the summer. The research also indicated that math skills are compromised at a greater rate than reading skills. With such convincing statistics connected to summer learning deficits, it is extremely beneficial for students to engage in some sort of academics over the break. The thought of academics may initially be met with groans; however, the key is to turn up the fun by implementing games, challenges, or riddles.

          1.     Create math games for road trips. These math-related games not only pass the time, but they also prompt kids to brush up on their basic math skills. Games can be as simple as counting the road signs along the way, to estimating arrival time. License plates also provide plenty of opportunities to practice number recognition, subtraction, and addition.

          2.     If out on a walk around the neighborhood, ask your child to tally the animals that they see, counting dogs, birds and butterflies, for example.

          3.     Hopscotch is another sidewalk activity that incorporates numbers. Use chalk to create a grid on the driveway. Create challenges where your child can only jump on the odd or even numbers. Or, ask your child to add up the total of all of the blocks that they stepped on.

          4.     During a summer thunderstorm, teach your child to count the seconds between lightning and thunder. Then explain how the seconds between can roughly estimate the distance of the lightning strike.

          5.     A pair of dice can be a simple way to create games involving number relationships and probability. You can even create a chores gambling game. Tell your child that the number that he or she rolls will indicate the number of chores that they must complete for the week.

          6.     Mini-golf is another great way to practice counting and addition. Make sure that everyone keeps a scorecard so that each person is accountable for tallying strokes. At the end, have the kids add up the final scores—but remember, the person with the lowest score wins in golf!

          7.     Ask your teen to handle the grocery shopping this week. Give him or her the list and the budget, making sure to mention that he or she may not go over the limit and must get everything on the list. This activity allows teens to practice real-world math skills such as budgeting, estimating, and conversions.

          8.     Create your own geo tracking scavenger hunt. This type of challenge, which practices using coordinates and gauging distance, is another subtle way to hone math skills.

          9.     Puzzles, board games, and Sudoku are a few other fun math options. Gather the family together to work on a jigsaw puzzle when the weather takes a turn. Puzzles are great for fine-motor skills and shape recognition, while Sudoku offers a more advanced level of thinking.

          10.     Cooking or baking is a great method for practicing fractions. Whip up your favorite summer treats with the kids—and let them do the measuring! Baking is also a great way to help children practice following directions.

          11.     Even checking the weather can enhance math skills. Percentages and the likelihood of certain weather events, daily average temperatures, sunrise and sunset times—all of these weather-related statistics can be used to practice math skills. Ask your child to use the weekly forecast to identify the hottest and coolest days of the week. How many days are predicted to have rain? Are there any noticeable patterns or correlations between humidity and air quality?   

With a little planning, your busy summer schedule can easily be modified to include fun math activities for the entire family. No calculators necessary—just curious minds!