Math isn’t always the easiest subject to teach if you’re homeschooling.
Other than the fact that as a parent and teacher your own skills might be a little rusty, it’s not always the most interesting or approachable subject for kids.
Filled with representations and symbols, kids sometimes struggle to grasp its more abstract ideas and more often than not find it hard to connect math to the real world, despite its importance in everyday life.
Introducing hands-on learning activities to math lessons can be a great way to let kids physically encounter and explore math ideas and connect them to concrete experiences.
Doing so can help make your homeschool math lessons more dynamic, multisensory and…dare we say…even more fun.
What is Hands On Math?
Simply put, a hands-on approach to learning math means giving kids the opportunity to feel and touch what they are learning, such as by using blocks, rods, or even model rockets if you really want to get crazy with it.
The general idea is to help kids come to grips with the more abstract ideas of math by giving them something real to work with, ideally something that they can physically hold, touch and use to explore math concepts and problems.
Ultimately a hands-on approach may help guide them in developing a deeper understanding and appreciation of what they are learning and why, which they may not otherwise grasp through abstract representations (i.e. equations and math symbols) alone.
Can You Really Teach Math In A Hands-on Way?
It seems odd to some, especially to those who learned math in what is called a “chalk and talk” method where teachers lecture from a blackboard, but you can certainly teach kids math in a visual and hands-on way…and for a lot longer than you might expect.
When people think of learning math they usually think of it in its abstract form, with symbols, numbers and equations filling up a blackboard.
In reality, all these symbols are abstracted representations of real life concepts – such as putting things together, taking them apart, measuring certain volumes and more.
Many kids, especially younger ones, can have a hard time getting their heads around these representations and symbols and so more concrete objects may be used.
One popular option to teach math in a hands-on way is through the use of math manipulatives. Manipulatives are objects designed to represent a math concept that kids can explore and touch.
Usually these are physical objects, although recently virtual manipulatives have been created that are more visual than tactile.
In either case, working with them allows kids to physically work out math problems to gain an understanding of it and later link that concrete work to equations and such.
Some popular examples of manipulatives and their uses include: adding and subtracting with blocks and cubes, “filling up” transparencies with colored sheets to represent fractions, using special colored tiles to teach algebra, “balancing” equations on a scale, and more.
That said, manipulatives are only one type of hands-on learning.
Any activity that moves math learning out of the textbook and into something that kids can directly interact with and explore can be considered hands-on math learning. It’s a wide open and creative teaching approach that can range from understanding fractions and ratios by filling containers with plastic balls to figuring out angles on a pool table.
Up to What Age Are Hands-on Math Approaches Appropriate?
Most hands-on math activities and programs tend to focus on elementary school students (pre-K to grade 7 for example), as this is the age range where kids tend to have the most trouble internalizing abstract concepts.
From the ages of 7 to 11, kids begin to develop their logical and mathematical reasoning skills but still tend to think in concrete ways. Even at the upper range may still struggle with grasping abstract ideas and concepts.
It is typically only around the age of 12, or at the end of elementary school, that kids start really developing their abstract thinking capabilities.
Because math involves analyzing abstract ideas, younger kids can greatly benefit from a way of easing them into understanding abstract concepts by first using concrete, hands-on learning and so this is where hands-on learning typically enters into the math curriculum.
That said, although methods may vary, hands-on math learning can benefit kids of any age, and can even be included as part of middle and high school learning.
Although they can’t make up the main bulk of a lesson plan for older students, sometimes adding visual and tactile activities and relating learning to things kids understand and can readily connect to can deepen understanding and make it seem less intimidating.
With older students and more advanced math, hands-on learning moves beyond simple manipulatives such as rods and blocks and into more exploratory, inquiry-based active experimentation with math concepts.
This might involve engaging in physical activities and projects that explore math concepts in fun and exciting ways, learning about vectors in precalculus by catapulting marshmallows around the room, for example.
Evidence For Hands-on Learning In Math
If you think back to how small children learn to count, generally they do so with the help of their fingers or things around them.
Before they start using symbols of 1 and 2, for example, young kids will lean on physical objects (one finger, two fingers) that help them grasp the concept in a way that is more natural to them.
Now that’s all well and good for babies and young children, parents may say, but what about older kids, those in school who need to solve equations and pass tests in math, does the evidence stand up?
There is strong evidence that hands-on learning, whether through physical activities, traditional manipulatives or even virtual manipulatives can have a strong positive effect on math learning as compared to more traditional “Talk and chalk” methods of teaching math from the blackboard.
A metastudy from 2013, for example, found significant advantages in information retention, problem solving and math skill transfer when lessons included hands-on activities compared to just relying on teaching with traditional, abstract math symbols.
In fact, even just using virtual manipulatives, yielded strong effects on student achievement in math, improving ability, understanding and attitude towards the subject.
Why Should We Consider Hands On Math Learning In Our Homeschool?
When considering whether to include hands-on math learning into your homeschool math lessons, there are some distinct benefits and potential pitfalls to consider.
Math isn’t always the most intrinsically interesting subject for many kids. Oftentimes when going over different math concepts you can almost sense your child’s eyes glaze over as their attention wanders.
Adding colorful blocks, lego pieces and other unusual physical objects into a lesson can make learning feel more like a game or fun activity and help redirect a child’s attention to the lesson plan.
Encourages Active Learning
If you’re homeschooling math it can sometimes feel overly passive and almost like you’re lecturing your child to death with math facts – a far cry from how many parents pictured their homeschooling experience.
By including hands-on activities, students have to physically do things in order to get through the lesson, thereby making them much more involved and active in their learning.
Creating an active learning experience has several well-known effects, such as increased enthusiasm for learning, increased knowledge and retention, deeper understanding and critical thinking and more.
Show math as it works in the real world
By bringing in hands-on learning activities sometimes you can show your kids how math can work in the real world, connecting it not only to something concrete but to show math’s importance outside the classroom in a way kids can understand.
Having kids handle and use real money, for example, can be a great way to show how basic math is used and its importance in day to day life.
Strengthen learning pathways with multisensory learning
Although the concept of learning styles is sometimes a bit overstated, bringing in different ways of learning (tactile in the case of hands-on learning) can engage different pathways of the brain and can deepen connections and strengthen memory.
Inability to connect the real to the abstract
Manipulatives or hands-on activities may not be readily understood by kids as representing an abstract concept..
Sometimes hands-on learning can require some creative thought from students and a lot of explaining on the part of homeschooling parents in order to get the point across.
Failure to do so can cause general confusion, frustration and a lack of learning.
Simply put, the more interesting the hands-on activity or manipulative the more kids will want to play with them or get distracted by them.
Teachers and homeschooling parents will therefore need to keep a closer eye on things and watch out for off-task behavior than they might with traditional textbook based learning activities.
Kids can use hands-on learning as a crutch
At some point, students have to move on to becoming comfortable with abstract manipulation of math in order to transfer their learning of math concepts and make them generalizable and therefore useful.
So if you use hands-on learning activities, you typically have to build some kind of process for moving from concrete examples to abstract math expressions into your lessons, which isn’t always so easy to do.
How To Introduce Hands On Math Activities
From lesson supplements and manipulatives kits to full homeschooling curricula designed to make learning as hands-on as possible, there are tons of resources out there to help homeschooling parents at any stage of the K-12 learning process.
To avoid the potential downside of hands-on math learning, however, parents need to make sure that any resources and activities they use:
1. Fits into their lesson plan and minimize disruption.
Hands-on activities should flow organically as part of the lesson.
You don’t want an abrupt break in the lesson or to surprise your kids too much, since that will require periods of adjustment before and after to get back to more formal learning and slow lessons down considerably.
2. Have meaning and be purposeful.
It’s easy to turn hands-on activities into chaotic play, therefore any activity or object that is brought into a lesson plan should be:
- Understandable and easily connected to the math concept
- Have clear objectives and outcomes for the student
- Encourage analysis, creativity and critical thinking, rather than just engagement or play.
3. Can be easily translated to abstract expressions and equations.
As discussed previously, eventually students will have to move on to connect what they’re doing with the symbols and representations that make up math and be able to transfer their conceptual understanding into computational skills, as in being able to solve problems and pass exams.
Our Recommendations for a Hands-on Math Curriculum
While some parents are comfortable supplementing their existing curriculum with hands-on activity plans, others can benefit from a variety of well-respected math curricula that understand the importance of a hands-on, concrete approach to teaching math and integrate it into their lessons.
Below we’ve included some of the ones we think are worth a serious look.
A rigorous and deep understanding of math concepts where hands-on learning is a core tenet
|Set Price: From $98||Grades: Pre-K to Grade 8|
|Spiral/Mastery: Mastery Approach||Conceptual/Procedural: Conceptual Math|
|Manipulatives: ✔||Rigor: About a grade level ahead`|
|Common core option: ✔|
Non-common core option: ✔
|Ease of Teaching: ⭐⭐⭐1/2|
A rigorous curriculum with a focus on fostering deeper conceptual math understanding and critical thinking skills in its students, Singapore Math is also well known featuring manipulatives and hands-on learning activities as a core part of its learning process.
Its CPA ( Concrete, Pictorial, Abstract) approach specifically introduces new concepts through the use of manipulatives and other hands-on activities before moving onto visual representations and symbols.
As a result, Singapore Math takes a very deep, hands-on learning approach all the way through its curriculum, to the end of elementary school math,
But don’t let its use of manipulatives and its hands-on learning style fool you, Singapore Math still maintains a well-deserved reputation for its rigorous curriculum. Although it is only a K-8 curriculum, Singapore Math explores math topics earlier and in more depth than many other math curricula and often advances students a grade level or more ahead of their peers in math.
If you’re looking for a rigorous K-8 curriculum that uses a multisensory, hands-on math to foster the strong mathematical understanding and critical thinking/logic skills that can give kids a leg up in math, Singapore Math might be the right choice for you.
Check out our in-depth review of Singapore Math.
Math U See
An approachable and clear math curriculum that extends hands-on learning into upper grades
|Set Price: From about $130 & up||Grades: K-12|
|Spiral/Mastery: Mastery Approach||Conceptual/Procedural: Conceptual|
|Manipulatives: ✔ (to middle school!)||Rigor: Average|
|Common core option: ✔|
Non-common core option: ✘
|Ease of Teaching: ⭐⭐⭐⭐⭐|
If you’re looking for a K-12 math curriculum that explains math in a straightforward and approachable way and also uses hands-on learning, Math U See might be worth considering.
In addition to using videos and workbooks, Math U See places a heavy emphasis on hands-on exploration, extending the use of manipulatives far beyond most other programs and well into Algebra 1.
In addition to simply providing hands-on activities, Math U See’s videos (taught by veteran math teacher and company founder Steve Demme) provide step by step instruction on how to use manipulatives and other objects to explain concepts to kids in an efficient and clear way.
Also, while Math U See gives homeschoolers a core lesson framework, it also provides a lot of freedom in terms of actual lesson plans, giving parents more of an opportunity parents introduce their own hands-on supplements if they so choose.
Although it’s not the most rigorous or advanced program out there, with clear explanations of concepts, a strong dose of hands-on learning and plenty of thorough practice and review, Math U See stands out for its ability to develop math competency in all students, even those who usually struggle with it.
Check out our in-depth review of Math U See.
A more classic approach to math that doesn’t ignore the importance of hands-on learning
|Set Price: From about $100 & up||Grades: K-12|
|Spiral/Mastery: Spiral Approach||Conceptual/Procedural: Procedural|
|Manipulatives: ✔||Rigor: Average|
|Common core option: ✔|
Non-common core option: ✔
|Ease of Teaching: ⭐⭐⭐⭐⭐|
With its back to basics approach to learning math focusing on memorizing math facts and learning to use math algorithms, Saxon Math is a complete K-12 math curriculum that has been quite popular with homeschool families who are more interested in developing solid, number crunching math skills than they are at exploring math conceptually.
As such, it’s not exactly the curriculum you might think of when you think of hands-on math learning, yet, contrary to popular belief Saxon Math does actually teach math concepts (even if not to the same degree as other programs) and it does include hands-on math learning as part of its curriculum.
At the K-3 level, manipulatives are required and are tightly woven into the lessons, while at the Intermediate or grades 3-8 levels manipulatives are optional, but available and are frequently referenced in the lesson plans.
In addition, starting in grade 3 each lesson mixes in in-lesson activities and investigations of math concepts, some of which can be quite hands-on in nature.
If you prefer a back to basics approach, with a focus on learning and applying math facts, memorization and “doing math,” but still want to integrate active, hands-on math activities, Saxon Math may be the math curriculum to look at.
Check out our in-depth review of Saxon Math
An affordable and innovative hands-on math program for Grades 1-3
|Set Price: From about $80 for the program||Grades: 1-3|
|Spiral/Mastery: Both options can be used||Conceptual/Procedural: Conceptual|
|Manipulatives: ✔||Rigor: A little ahead of most curricula|
|Common core option: ✘||Ease of Teaching: ⭐⭐⭐⭐|
Inspired by the work of Lore Rasmussen at the Miquon School in Whitemarsh, Pennsylvania, Miquon Math is an early learning math curriculum that combines hands-on learning with a strong student-led and exploration-based approach to math.
Rather than being taught in a top-down manner, Miquon Math presents students with exercises and encourages them to work their way through the material, using their creativity and logical thinking to intuit and discover the answers themselves.
Parents in Miquon Math take a step back, acting as guides to help provide suggestions and explanations and to formalize their discoveries into more explicit, generalizable learning.
Although it sounds a bit informal, Miquon Math and its methods can help students cover some surprisingly advanced topics, with the program introducing and exploring some fairly advanced topics earlier than many other programs.
Manipulatives and other hands-on physical activities play a prominent role in this program, with the use of Cuisenaire rods and other physical items being tightly woven into the lessons and used to model abstract equations, operations, numbers and shapes in a more understandable way for kids.
Interestingly, rather than being told what to do with their Cuisenaire rods, students are given ample freedom to use their imaginations and logic to decide what they represent in a given exercise. As such, they can represent distance, quantity, shape or something completely different, depending on the current need and the student’s thinking.
If you’re looking for a math program for a young student that will provide them with a strong math start but also allow them to get tactile and use their imaginations, Miquon Math might be the program for you.
Check out our in-depth review of Miquon Math
Math With Confidence
A hands-on math program that’s also gentle and approachable
|Set Price: From about $50||Grades: K-6|
|Spiral/Mastery: Mastery||Conceptual/Procedural: Mixed|
|Manipulatives: ✔||Rigor: Average|
|Common core option: ✘||Ease of Teaching: ⭐⭐⭐⭐⭐|
Math with Confidence is a unit-based math program that makes math more approachable for students through a combination of hands-on manipulative work, activities, books and games and relatively short, clear lessons.
The program places an emphasis on helping students understand and be more comfortable with math through its clear, step by step explanations of math concepts and dedicated spiral review.
The program also stands out for its use of picture and living books that can help students approach math concepts from another angle and create a more enjoyable, literature-rich learning environment.
In terms of hands-on learning, throughout its lessons students engage in a variety of parent-led activities and physical games, such as playing go fish, flipping coins, card games and working with counters.
These not only increase the level of tactile learning in each lesson, but also can be a lot of fun for both parent and student and are a more engaging alternative for those sick of traditional number blocks.
If your student has struggled with math in the past or if you’re looking for an affordable and fun K-6 math curriculum, you should definitely check out Math with Confidence.
Check out our in-depth review of Math With Confidence
Homeschooling math doesn’t have to be a passive and boring experience for your student.
From simple blocks to complete K-12 curricula, hands-on math resources can be important assets for teaching math that we think should be a part of any homeschooling parent’s teaching toolkit.
Properly introduced and woven into a lesson plan, manipulatives and other hands-on activities can transform typical math tedium into dynamic lessons that not only help kids become active participants in their own learning but deepens their understanding of math concepts at the same time.
About the Author
David Belenky is a freelance writer, former science and math tutor and a tech enthusiast. When he’s not writing about educational tech, he likes to chill out with his family and dog at home.