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How Manipulatives Can Help Children Understand Complex Ideas

How Manipulatives Can Help Children Understand Complex Ideas

If there’s one thing that all parents want for their children, it’s for them to be successful in life. One of the key ways to achieve success is to give your children a strong foundation in education. And when it comes to mathematics, nothing can help children understand complex ideas like manipulatives can. This blog post will discuss how manipulatives can help children understand complex math ideas and why they are so valuable in the classroom. We’ll also provide tips on using manipulatives at home to help your child with math homework. So keep reading to learn more!

What Are Manipulatives?

Manipulatives are objects that can be moved or manipulated to help children learn. They come in various shapes and sizes and can be used to help explain everything from basic addition and subtraction to more complex concepts. Manipulatives can be used with students of all ages, from preschoolers just learning to count to high school students studying advanced algebra.

For example, using manipulatives like blocks can help children visualize what it means to add numbers together. This can make it easier for them to understand the concept and perform calculations correctly. While manipulatives are most used for younger children when they are learning division, fractions, and other mathematical concepts, older students can also benefit greatly from them. Some advanced math concepts that can be done with math manipulatives include:

 

  • Area, volume, and surface area (snap cubes, power polygons)
  • Exponents (two-sided counters)
Exponents
  • Operations with decimals (base 10 blocks)
base 10 blocks
  • Operations with fractions (fractions strips, relational rods)
fractions strips, relational rods
  • Square roots (graph paper and square arrays)
graph paper and square arrays
  • Ratios (snap cubes, pattern blocks)
snap cubes, pattern blocks
  • Algebraic properties (algebra tiles)
snap cubes, pattern blocks
  • Operations with polynomials (algebra tiles)
snap cubes, pattern blocks
  • Operations with negative and positive numbers (two-sided counters)
two-sided counters

A Positive Attitude

If you are thinking of using manipulatives with your child to help with their math education, your involvement and positive attitude are vital to success as a parent. Even if you are suffering from math anxiety, staying engaged and willing to learn along with your child using manipulatives is important. You will be delighted to see that your child’s understanding increases as your engagement and learning increase. 

At Dropkick Math, we believe a child’s success can largely depend on the involvement of the parent/guardian. All of our programs offer the option for parents to become involved and learn alongside their children. 

Visually Simple

Math manipulatives are traditionally visually simple as research has shown how detail such as that found on play money can easily distract children. Education professionals have carefully designed manipulatives to help bridge the gap between concrete and abstract concepts. 

Why Math Manipulatives Work

So why might a child learn math concepts using the aid of manipulatives better than if they try to solve it in a symbolic form? Researchers think it may be because children think more concretely than adults. They typically rely on physically interacting with the world to make sense of it, and their ability to think abstractly is extremely limited. Some education specialists believe it is because children are in an operational stage from age 7 to 12, where they need to use concrete objects to support logical reasoning. A child can think using pure abstractions in the formal operations stage from age 12 and up.  

Another theory as to why manipulatives work suggests it is because they help to move the body. It is suggested that cognition is not just a product of the mind, but the body also participates. For example, children may have a perception of what the word “kick” means, but the meaning of the work becomes solidified when they experience the feeling of kicking something. 

By this account, it isn’t so much the manipulatives themselves that help children understand math concepts, but the movement behind them. If this theory is true, many people ask if computer-aided manipulatives can be as helpful as the real thing. There are exceptions, but computer-based manipulatives have been found to help just as much as physical ones. 

While more research is needed to understand how manipulatives work and which theories are entirely accurate, one fact remains the same; manipulatives will always lead to better understanding. 

Why Math Manipulatives Are Beneficial 

Math manipulatives are beneficial for students for a few reasons. First, they provide a hands-on way for students to interact with the material and better understand number sense. For tactile learners, this can help children gain a better understanding of math concepts. 

Second, math manipulatives can be reused multiple times, which helps students learn new concepts as they build on what they have already learned. Math is a subject that builds upon itself, and manipulatives offer an excellent opportunity for children to learn how new concepts add to existing ones they have already mastered. 

Finally, math manipulatives can be fun and engaging, making learning math more enjoyable for students. In any math illustration, children will understand that manipulatives are playful tools that will help them understand ideas differently. Educators have confirmed that sorting, measuring, distinguishing patterns, and ordering numerals have been very effective with a conceptual understanding of math. 

When To Stop Using Manipulatives

Math manipulatives intend not to make children forever dependent on them but to use them as they work through complex problems. For example, high school students should not be pulling out a string of beads as they prepare for a math test. Although extremely helpful when first learning math concepts, math manipulatives can be time-consuming and inconvenient. However, when trying to understand a new idea, children should practice with the manipulatives until they can demonstrate the concept without the manipulatives.

They do have their purpose as students grow through high school and university when a new concept is introduced. Older students often find manipulatives helpful when articulating their thought processes when trying to explain a complex concept. When a new concept is introduced, the process of developing understanding strengthens by connecting concrete manipulatives to visual and symbolic representations. When the student is able to connect the different representations to symbolic form, they should be able to stop using the manipulatives. 

Many students find math difficult and frustrating, but using manipulatives can help to make it more accessible and enjoyable. So, if your child struggles with mathematics, try getting some manipulatives to use at home!

Online Math Help

Dropkick Math is a unique tutoring company offering online math help to students who may have experienced an education gap caused by the pandemic. We encourage students to use math manipulatives as a way to understand complex math ideas. Learn more about our programs and if they are the right fit for your child. 

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Learn Math

Understanding Math Tools and Jargon

Understanding Math Tools and Jargon

As discussed in previous blog posts, parents often feel frustrated when speaking with their children about math. Math calculations appear different from when they were in school, and how their child talks about math seems like a new language. This can often create barriers between parents and children in being able to discuss schoolwork. 

Working With Your Child

Being a part of your child’s learning is vital for their success. It is essential that parents work with their children and get involved in their education. However, it can be frustrating if the parent struggles with the topic. This is why at Dropkick Math, we expose the parent to new learning strategies their child may be experiencing in their classroom. Once the parent starts to learn and understand these new ways of engaging with mathematics, they will feel more confident to become more involved in their child’s education. 

Your attitude about learning can directly influence your child’s educational success. Over three decades of research has found that student success is positively impacted by parent involvement regardless of socioeconomic status, background, or parent’s level of education. Dropkick Math provides resources and advice on how to get started learning alongside your child. When you learn alongside your child, you set an example while strengthening your relationship. Your child will see your confidence building in mathematics which will help build them up as well. 

Learning the Language

The first step in being active in your child’s math education is learning about the tools and language of math. By having a foundational understanding of how teachers speak and the tools they use, you can better communicate with your child and their teachers. The following are some of the most common words and sayings that your child or their teacher may use when explaining tools used in mathematics. 

Math Tools

You may envision screwdrivers or a hammer when you first hear the word tools. In the math world, tools refer to devices that help solve a problem. These tools help carry out a particular function and are often referred to as manipulatives. However, in math, tools don’t always have to be physical, some are just representational.

Manipulatives allow children to feel, touch and visualize what they can’t yet create on their own. They can enable children to receive immediate feedback about whether their idea makes sense. Using tools, a child can move hands-on objects to investigate and explore a math concept that may be challenging.

Unifix Cubes

Unifix cubes are manipulatives that are used starting in preschool and can help children understand the foundation of mathematics. Starting from a very young age, children aged 0 – 4 can use these cubes for playtime. Children around age 5 can use the cubes to start practicing counting and represent quantitative measures. As children grow older, unifix cubes can be used to help children draw the connection to multiplication by visually seeing groups organized. These cubes can also be used in older grades to explore patterning and algebraic relationships.

Counters

Counters are a fun, popular manipulative that have many uses throughout your child’s education. Counters come in two forms, either dual-coloured or single-coloured. They are used very similar to unifix cubes; however, they cannot link with each other like cubes can, limiting their use in some ways. Counters are a great way for your child to visualize fractions in different ways, and they can be placed easily to show part-to-whole relationships. As children grow older, counters can help them with the study of percentages, pattering, and algebraic relationships.

Pattern Blocks

Pattern blocks are a type of manipulative that enables children to visually see how shapes can be composed, decomposed, or broken apart. Pattern blocks can be used in many different ways throughout all grades. Common uses for pattern blocks at the early elementary level include identifying and naming shapes, defining attributes, discovering how shapes are composed, and making up other shapes. As children get older, pattern blocks can be used to develop an understanding of fractions, identify angles of shapes through geometry, and recognize visual patterns.

Base-Ten Blocks

Base-ten blocks are also known as multi-base arithmetic blocks or place value blocks. This tool can help children recognize the value of numbers using three-dimensional blocks that come in wood or plastic. In early grades, children can use the units to represent one place or begin to make sense beyond whole numbers as they represent decimals. The blocks can help your child add or subtract whole numbers, focusing on place value. Older children can use the blocks to multiply and divide whole numbers, focusing on place value.

Representational Models

Physical tools are classified as manipulatives or hands-on models. Children can easily manipulate them with their hands, and they act as a great starting tool for many mathematical concepts. These tools can be a great way to help support student learning as they navigate through math concepts. Representational models are tools too, but rather than being tangible like manipulatives, they are representational, or drawn. 

It is important to understand that each representation is not an exact copy of representational models. Young children can sometimes get wrapped up in drawing perfect pictures, and they lose track of the actual math concept. This is an excellent place for parents to support their child learning by asking them questions such as “Can you draw a picture to represent the situation or story?” “How does your picture represent the story?” and “Where in the picture can I see the quantities from the story?”

A Deeper Understanding

Understanding the fundamentals behind the mathematical foundation is critical for a child’s fluency and math development. Using both manipulatives and representations, your child can build a deeper understanding of the four pillars of math (number sense, operational sense, algebraic reasoning, proportional reasoning). When confronted with a problem they have never seen before, children will be able to extend their thinking to the basic operations of addition, subtraction, multiplication and division by using their tools. 

Understanding the language and tools used in your child’s education can help them grow in their studies and give them the practices necessary for future success. At Dropkick Math, we involved the parent/guardian in our programs. We believe that it is essential for a child’s growth to have the guidance of their parent/guardian and that good schools become even better schools when parents are involved. 

As one of the leading math services in Ontario, our certified teachers support learning key math skills by focusing on relationships and engaging the parent/guardian. Don’t waste more time searching for “math tutor near me.” Get started today with Dropkick Math today by learning more about our programs!

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Report Card

Part 2 – How To Talk To Your Child About Their Report Card

How To Talk To Your Child About Their Report Card

Part 2 – How To Talk To Your Child About Their Report Card

How To Talk To Your Child About Their Report Card

In the second part of our series, “Report Cards: What Do They Really Mean,” we will discuss how to speak to your child about the marks they received on their report card. Students will be receiving their report cards any day now, and parents must understand what the marks mean and speak to their children about them. 

Many parents struggle with how to speak to a child who may have a gap in learning. They often don’t want to make the child feel bad for falling behind, so they tend to shy away from the situation. But this won’t help the child with the problem they may be facing. 

Find Some Quiet Time

If a child brings home a report card that indicates they may be struggling, a parent must address the mark. The best way to approach a child is by finding some quiet time where you can sit down with them one-on-one. You will want to give them your undivided attention, without any distractions, so try and set aside enough time to have a quiet, relaxed discussion. 

Find Some Quiet Time

Focus On Effort

It is important not to focus on the child’s marks on the report card but to focus on their effort and attitude instead. The teachers’ comments can provide a lot of insight into how the child performs and if they are limited in any way. Focusing on effort over achievement isn’t going to reduce their motivation to work hard. If a child is focused on trying their best and feels that their efforts are seen and valued, they are much more likely to be resilient learners. A child who is a resilient learner is more likely to challenge themselves and are more comfortable making mistakes.  

A child needs to understand that everyone is different, and we all struggle and excel in different areas. Try to avoid any comparisons between your child’s report card and a sibling or classmate’s report card. The focus should be on where they achieved well or greatly improved from their last report card. Siblings should be reminded that comparison is pointless because they have been graded on entirely different outcomes. 

Set Plans And Goals

Set Plans And Goals

If a child’s report card indicates an area of challenge, or a gap in learning, speak to them about using it as a way to plan a learning goal. Use their current report card as a baseline and then set an individual learning goal for the next term. 

It may be helpful to compare your child’s last report card to the current one to help them see their progress. Identify any areas that the child is still struggling and discuss why they may still be falling behind in that area. Be sure to praise any improvements made and their areas of growth. 

After making a comparison of the last report card, it can be helpful to set a plan to focus on the areas that may need attention. Along with your child, decide on steps they can take to progress towards their learning goal. These steps could include asking to meet with their teacher to discuss suggestions of ways to meet challenges. They could also set a weekly goal for a little extra study time or revision with your help. 

Have A Conversation With Their Teacher

It may also be helpful to have a conversation with your child’s teacher if they appear to be struggling. A parent-teacher conference can help clarify your child’s academic performance and overall experience at school. In a one-on-one conversation, teachers can give more detailed information about your child and offer suggestions on how they can improve in any areas that may be falling behind. This can be an excellent way for a parent to better understand how their child is performing in the classroom.  

At Dropkick Math, we believe that parent engagement is vital for a child’s success. By being actively involved and setting high expectations for your child, you can help guide them towards having high values towards their schoolwork. 

If your child is showing a gap in learning in their math skills, Dropkick Math can help. Through our fun and interactive programs, students can focus on the four pillars of math and get caught up to where they should be in their curriculum. Get started today by learning more about our programs.

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Report Card

Part 1 – How To Read Your Child’s Report Card

Report Card

Part 1 – How To Read Your Child’s Report Card

It is February, and that means that the 1st term report cards are just around the corner. At Dropkick Math, we believe it is crucial for parents to fully understand how to read the report card and decipher what the marks really mean. So, we have completed a two-part series for parents to refer to during report card time. This first article will focus on the marks on the report card and what they mean for your child. 

It is essential that parents understand that this year’s marks on your child’s report card may be hindered by gaps caused due to COVID and virtual learning. The pandemic reshaped Canadian society and disrupted more than a year of schooling, which has slowed progress in math for millions of Canadian students. 

Younger students saw some of the most significant declines, and educators are now left trying to help students catch up to pre-pandemic levels. So, when your child brings home their report card, remember that their grades are just a snapshot in time of where they are now and the direction in which they should be working towards for the end of the year. 

So, what does this mean for your child? 

How do you make sense of what the mark means, and what can you get out of the comment that your child’s teacher has provided?

Let’s break it down for you:

The Mark

If your child meets the curriculum goals set by the ministry in the new math curriculum, they will receive a mark in the B range or something in the 70s. Higher marks represent the notion that your child is consistently achieving the goals set by the ministry. 

But what about if the mark is below?

The grades reflected on your child’s report card are to help them understand how they are performing and where they can make improvements before getting their final mark of the year. So, if students are not doing well, it should be thought of as they haven’t got it “Yet”….as these curriculum goals are to be achieved by the end of the year.

A mark in the C (60s range) or D (50s range) means that your child has learning gaps and is experiencing difficulty meeting the goals set in the math curriculum. Now, these gaps are just that, missed learning that has created some misconceptions in your child’s education. It may be due to a variety of reasons including, an absence in an earlier grade or the result of missed learning due to COVID. Whatever the reason, your child has missed something that has and can continue to lead to problems as their education moves forward. 

The good news is, with the proper identification and effective teaching instruction, these misconceptions and learning gaps can be addressed and filled, helping your child move forward with new math learning. However, if left unchecked, these gaps can continue to grow and often end up creating a variety of math anxieties in your child’s future math education. 

What Do Letter Grades Mean

The Comment

All too often, parents pass over the comment provided with the mark. After all, “It is just a cookie-cutter” comment…right?

Some things can be pretty general in the comment provided by your child’s teacher, but there is also some helpful information if you know what you are looking for. 

Report card comments are often designed from an asset based lens, meaning the first part of the comment should list all the things that your child can do. It is essential to read this section to see if the teacher has provided some information about what your child might be able to do on a limited scale. 

The last part of the comment is also valuable as it identifies the ‘next step’ in your child’s learning or what things your child struggles with and should work on to help their overall math learning for the second term. Reading this comment allows a parent to understand better what their child did, what areas they were limited in, what they could do, and the areas they struggled with during the 1st term.

A report card can provide helpful insight into a student’s learning. If a child is showing a gap in learning, the report card can help a parent understand this gap and inform them where the child may be struggling. Effective teacher-parent-student communication is fundamental to student success. So, it is also a great idea to reach out to your child’s teacher for more in-depth information on how your child is performing if they appear to be struggling.  

If your child is experiencing a gap in learning, Dropkick Math has programs that can help get them back on track. Our tailored programs equip students with problem-solving skills that can help them for years to come. Get started today by learning more about our programs. 

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