Math Manipulatives: Tools to Help All Students Become Effective Problem Solvers

Summary

Students with learning disabilities (LDs) often find math challenging due to difficulties with number facts, calculations, and visual-spatial relationships. At Sagonaska Demonstration School, teachers use manipulatives like algebra tiles and digital tools to help these students grasp math concepts. Manipulatives provide a hands-on, concrete way for students to understand math, reducing reliance on memorization and improving problem-solving skills. Digital portfolios and apps like Book Creator also aid in documenting and showcasing students' progress. These approaches help students build confidence and think of themselves as problem solvers, benefitting all learners, not just those with LDs.

Takeaways

• 📚 Many students, especially those with learning disabilities (LDs), find math challenging due to difficulties with number facts, calculations, visual-spatial relationships, and problem-solving.
• 💡 Students with LDs can benefit from understanding math concepts rather than just memorizing procedures, which can help them approach problems in various ways.
• 🛠️ Teachers at Sagonaska Demonstration School use manipulatives such as algebra tiles, snap cubes, and colored rods to enhance students' mathematical reasoning and problem-solving skills.
• 🔍 Manipulatives provide a concrete understanding of math concepts, making abstract symbols more meaningful and accessible to students with LDs.
• 🤔 Manipulatives reduce the cognitive load on working memory, allowing students to focus on the task at hand without being overwhelmed by the need to recall procedures.
• 👀 Students with LDs often have strong visual reasoning, and manipulatives help them build a deeper understanding of math by seeing concepts physically in front of them.
• 🖥️ In addition to manipulatives, the use of tablets in math class, such as iPads, allows students to convey their understanding of math concepts through videos and voiceovers.
• 🧩 The use of manipulatives encourages students to explore different approaches and take risks in finding solutions, fostering a growth mindset.
• 💪 Manipulatives help students see themselves as problem solvers, boosting their confidence in their mathematical abilities.
• 🔄 The flexibility of manipulatives allows for easy correction of mistakes without the frustration associated with erasing written work.
• 📈 At Sagonaska, students have a digital portfolio to document their learning, providing a record of improvement for students, teachers, and parents.
• 🌐 The use of digital tools and manipulatives in math class benefits all students by promoting a deeper understanding of concepts beyond memorization and tricks.

Q & A

Why do many students struggle with math?

Many students struggle with math because the subjects of algebra, geometry, and fractions can make them anxious. For students with learning disabilities, math can be even more challenging due to difficulties with learning number facts, doing calculations, understanding visual-spatial relationships, or solving math problems.

What challenges do students with learning disabilities face in math?

Students with learning disabilities may struggle with learning number facts, performing calculations, understanding visual-spatial relationships, and solving math problems. These difficulties can make math appear as abstract symbols and make it hard for them to recall procedures, leading to anxiety and blanking out during problem-solving.

How can manipulatives help students with learning disabilities in math?

Manipulatives, such as algebra tiles, snap cubes, and colored rods, help students with learning disabilities by providing a concrete way to understand mathematical concepts. They enable students to visualize and physically manipulate math problems, reducing reliance on abstract symbols and enhancing conceptual understanding.

What benefits do manipulatives offer in math education?

Manipulatives offer several benefits, including allowing students to demonstrate their thinking without relying heavily on working memory, fostering conceptual understanding, enabling hands-on learning, and helping students with strong visual reasoning build a deeper understanding of math.

How do manipulatives change students' perception of math?

Manipulatives help students see math as a series of concepts rather than a set of abstract symbols or tricks. This change in perception helps them become problem solvers, gain confidence in their abilities, and approach problems with various strategies.

What role do tablets and digital tools play in math education at Sagonaska Demonstration School?

Tablets and digital tools, such as Book Creator and Algebra Touch, help students convey their understanding of math concepts through videos, voiceovers, and digital portfolios. These tools provide alternative ways for students, especially those with learning disabilities, to show their work and understanding effectively.

Why is it important for students to use multiple senses in learning math?

Using multiple senses in learning math is important because it helps students with learning disabilities, who often have working memory deficits, to grasp concepts better. Engaging in hands-on activities, seeing, touching, and speaking about math concepts allows them to manipulate information effectively and demonstrate their understanding.

How do manipulatives help students become flexible thinkers?

Manipulatives help students become flexible thinkers by allowing them to explore different approaches to solving problems. As they manipulate the materials, they can easily adjust their strategies without the frustration of erasing or starting over, fostering a mindset of experimentation and adaptability.

What impact do manipulatives have on students' confidence in math?

Manipulatives positively impact students' confidence in math by enabling them to see themselves as problem solvers. As they successfully use manipulatives to understand and solve problems, they build confidence in their abilities and become more engaged in math learning.

How do workshops at Sagonaska Demonstration School help educators use manipulatives?

Workshops at Sagonaska Demonstration School help educators by demonstrating how to use manipulatives effectively in math class. Educators work in small groups to solve math problems with manipulatives, gaining hands-on experience and understanding how these tools can support students with learning disabilities.

Outlines

00:00

📚 Enhancing Math Understanding with Manipulatives

The first paragraph discusses the challenges students, especially those with learning disabilities (LDs), face in mathematics. It emphasizes the abstract nature of math for these students and how understanding math concepts can alleviate anxiety. The paragraph highlights the use of manipulatives such as algebra tiles, snap cubes, and colored rods at Sagonaska Demonstration School to improve mathematical reasoning and problem-solving skills. The benefits of manipulatives include providing a concrete understanding of abstract symbols, reducing the cognitive load on working memory, and allowing for hands-on exploration. The paragraph also mentions the use of tablets to convey understanding and the importance of multisensory learning experiences to support students with LDs.

05:01

🌟 Broadening Math Education with Digital Tools

The second paragraph expands on the use of manipulatives and digital tools in math education, noting their benefits for all students, not just those with LDs. It points out that relying on memorization and math tricks can lead to fragile understanding and test anxiety. The paragraph describes a workshop at Sagonaska where educators learned to use manipulatives and tablet applications like Book Creator, See Saw, and Algebra Touch to enhance learning. The workshop aimed to deepen educators' understanding of how these tools can support student learning. The paragraph concludes by reinforcing the effectiveness of manipulatives for students with LDs and invites interested parties to visit LDatSchool.ca for more information.

Keywords

💡Learning Disabilities (LDs)

Learning Disabilities refer to a variety of disorders that affect the ability to learn, particularly in areas like reading, writing, and math. In the video, students with LDs face specific challenges with understanding math concepts, performing calculations, and solving problems. The school's approach focuses on accommodating these needs through specialized teaching methods.

💡Manipulatives

Manipulatives are concrete materials like algebra tiles, snap cubes, and colored rods used to teach math concepts. They help students with LDs by providing a hands-on, visual way to understand abstract symbols and relationships in math. The video emphasizes their role in improving mathematical reasoning and problem-solving skills by allowing students to physically manipulate and explore math concepts.

💡Mathematical Reasoning

Mathematical reasoning involves the ability to analyze, interpret, and solve math problems logically. For students with LDs, manipulatives help enhance their reasoning by providing a tangible way to understand and work through problems. This is crucial for developing a deeper understanding of math beyond rote memorization of procedures.

💡Visual-Spatial Relationships

Visual-spatial relationships refer to understanding how objects or symbols relate to each other in space. Students with LDs often struggle with these relationships in math, which can make solving problems difficult. Manipulatives aid in visualizing these relationships, making abstract concepts more concrete and easier to grasp.

💡Working Memory

Working memory is the ability to hold and manipulate information in the mind over short periods. Students with LDs frequently have deficits in working memory, making it hard to follow multi-step math procedures. Manipulatives reduce the cognitive load on working memory by allowing students to physically represent and manipulate math problems.

💡Digital Tools

Digital tools like tablets and educational apps are used alongside manipulatives to help students with LDs demonstrate their understanding of math concepts. The video shows how tablets can make it easier for students to show their work and understanding through videos and voiceovers, enhancing their learning experience.

💡Conceptual Understanding

Conceptual understanding in math means comprehending the underlying principles and ideas rather than just memorizing procedures. The video highlights how manipulatives help students with LDs build this understanding by allowing them to explore and interact with math concepts physically, leading to a more robust grasp of the material.

💡Problem Solving

Problem solving in math involves finding solutions to complex questions using logical reasoning and critical thinking. The video illustrates how manipulatives enable students with LDs to experiment with different approaches and strategies, fostering a more flexible and confident approach to solving math problems.

💡Confidence

Confidence in math is the belief in one's ability to understand and solve math problems. The video shows that using manipulatives can boost students' confidence by making math more accessible and less intimidating. As students successfully interact with manipulatives, they begin to see themselves as capable problem solvers.

💡Number Sense

Number sense is the intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations. Students with LDs often have weak number sense, making it hard to recognize patterns and perform calculations. The use of manipulatives helps strengthen number sense by providing a concrete way to explore and understand numerical relationships.

Highlights

Many students struggle with math, especially those with learning disabilities (LDs), facing challenges in learning number facts, doing calculations, and understanding visual-spatial relationships.

Students with LDs often perceive math as a bunch of abstract symbols and may go blank when trying to recall procedures.

Conceptual understanding of math allows students to approach problems in various ways, increasing the likelihood of finding solutions.

Teachers at Sagonaska Demonstration School use manipulatives like algebra tiles, snap cubes, and colored rods to help students improve their mathematical reasoning and problem-solving skills.

Manipulatives provide students with a concrete understanding of math concepts, making math less mysterious.

Using manipulatives allows students to demonstrate their thinking without relying heavily on working memory.

Manipulatives offer hands-on experience, helping students with LDs, who often have strong visual reasoning, to better understand math concepts.

Combining manipulatives with technology, such as tablets, helps students convey their understanding of math concepts more effectively.

Students at Sagonaska use digital tools like Book Creator and See Saw to document and demonstrate their learning in math.

Manipulatives encourage students to explore different approaches and take risks in problem-solving, building their confidence.

Hands-on exploration with manipulatives prevents reliance on memorization and promotes flexible thinking in math.

Sagonaska hosted a workshop to teach educators how to incorporate manipulatives in math class to support students with LDs.

Educators used manipulatives in small groups to solve math problems and represent their thinking visually.

Manipulatives help educators understand how these tools can support students' learning and mathematical reasoning.

For more information about manipulatives, visit the website at LDatSchool.ca.

Transcripts

Many students struggle with math.

The thought of juggling algebra,

geometry and fractions is enough to make them anxious.

But for students with learning disabilities

– LDs – math may be more challenging.

Students with LDs may have trouble learning number facts,

doing calculations,

understanding visual-spatial relationships

or solving math problems.

These difficulties mean that on paper,

math often looks like a bunch of abstract symbols.

When they try to solve a problem,

they’re trying to pull out of their memory

which procedure do I use and they can’t so then they go blank.

If they have understanding instead and realize

that math is based on concepts,

then they can try to attack the problem

in a variety of different ways

and they are much more likely

to come up with a solution

or at least get themselves started down a certain path.

If the numbers hadn’t worked out where they were identical on the top,

what tool could you use to solve this?

Teachers at Sagonaska Demonstration

School are using manipulatives

– concrete materials like algebra tiles,

snap cubes and coloured rods

– to help students at all grade levels

improve their mathematical reasoning and problem solving.

15 to get these ones

then it won’t take 25 to do these ones.

Looking at symbols doesn’t really have any meaning for them.

So if they look at a series of numbers,

that doesn’t have any kind of meaning for them.

So manipulatives really give the kids

conceptual understanding so math isn’t this big, magic mystery.

Moving away from paper and pencil learning,

manipulatives allow students to demonstrate their thinking.

They don’t have to hold as much information

in their working memory

which allows them to focus on the task at hand.

We see such an amazing benefit to using math manipulatives

because it provides the students

with that concrete awareness

and that hands-on experience of actually touching

and feeling manipulatives,

instead of just seeing them symbolically.

But now they can manipulate them literally

and move them around and explore.

Many students with LDs have strong visual reasoning,

so being able to see math concepts right

in front of them helps them

build a deeper understanding of the math.

I think that any time that we can access multiple senses

– so they can see it, they can feel it,

they can speak to it, they can touch it

– is really, really important cause

we know that students with learning disabilities can have

or usually do have deficits in their working memory.

And anytime they need to hold onto information

and manipulate it in their brain,

if they can do that using hands-on skills,

then they’re able to show their learning

and that just maximizes their ability

to show their understanding with manipulatives.

Combined with manipulatives,

students at Sagonaska also use tablets

in math class to help convey

their understanding of math concepts.

Mr. Brown showed me how to do dividing

and multiplying with the integers and adding.

I found it harder to do that with pen and paper

and show my work.

I understood it, but I didn’t know how to show it.

And using the iPad, I can do videos and voiceovers

and then he can still look at that and grade me

on what I know cause

I couldn’t show my work properly on pen and paper,

and using the iPad and manipulatives,

it makes it a lot easier for me to show it.

Students are encouraged to try different approaches

with the manipulatives

and take risks to discover the answers for themselves.

The nice thing about manipulatives too

is that as they’re exploring,

they might be slightly going down the wrong path

and they’re able to just rearrange the manipulatives

and that doesn’t feel the same

as if you’re using paper and pencil

and having to scratch something out.

Manipulatives also allow students

to start thinking of themselves as problem solvers

which helps them gain confidence in their abilities.

I’ve seen students who come in not liking math,

feeling like math is just a bunch of tricks.

They need something else.

They need to have some other ways

of showing their thinking because they’re bright students,

but they just haven’t had the opportunity to do that.

And so if everything is given to them symbolically,

if they don’t have good number sense,

they’re not gonna recognize patterns and they’re not gonna be successful.

So they need to have opportunities to show what they know as well.

I’m a very hands-on guy,

so you gotta it’s easier just to touch it

and then actually like move them around.

Like take it apart and put together.

And then actually count and touch and see.

At Sagonaska, all students have a digital portfolio

where they can document their learning and work,

which in turns helps them,

their teachers and their parents see how they’re improving.

Technology has helped me a lot.

Like using Book Creator for work

and handing in assignments

and stuff like that,

it’s so much easier than doing it all on paper.

Mr. Richardson handed out like a format,

and then we just have to fill it all in.

So here’s like a blank one.

And then you have to go in and answer all the questions.

And he can put audio in there so we just listen to it.

Using manipulatives and tablets

or digital tools in math class

doesn’t only benefit students with LDs.

Hands-on exploration means that students

don’t need to rely on math tricks and memorization.

What I find is students have a really fragile

understanding of the math then.

And as soon as something gets changed,

they’re not able to change with it, they’re not flexible thinkers

because of all a sudden the procedure

is broken or they’ve forgotten it.

We all know students who freeze on tests.

And I think a lot of the reason they freeze is

because they’ve memorized everything

and then come test day, they’ve forgotten it

and they can’t regenerate the procedure cause

they didn’t really understand it in the first place.

Sagonaska recently hosted a workshop

where students demonstrated how they’re using manipulatives

and tablet applications like Book Creator,

See Saw and Algebra Touch in math class.

X is equal to 45.

At the workshop, educators

learned how to incorporate manipulatives in math class

to help students with LDs.

You have to add three red in so you have them to take away.

Using manipulatives, educators worked in small

groups to solve math problems

while visually representing their thinking.

So add this all together we have 100 plus.

By putting themselves in their students’ shoes,

educators familiarized themselves with manipulatives

and deepened their own understanding of how manipulatives

could be used to support their students’ learning.

Sometimes teachers are going to be uncomfortable using manipulatives

because you’re never sure where they’re going to go

with students and that’s okay.

We have to make sure that we model that.

For students with LDs,

manipulatives like algebra tiles,

snap cubes and coloured rods

are effective learning tools

that can improve their mathematical reasoning

and problem solving.

For more information about manipulatives,

visit our website at LDatSchool.ca.