In my previous blog, I discussed the creation of learning boxes and child-centered spaces in order to cultivate an inviting, investigative, and encouraging math environment for children of all ability levels.  Objects are included in these boxes with the intent of inspiring young children’s curiosity, engaging participation in their own learning of skills and concepts, and encouraging discovery and innovation with the acquisition of new skills and concepts.  Including rulers, tape measures, yard sticks and even yarn or string into your catalogue of math tools will boost a child’s investigative desire.

Measurement is one of the earliest mathematical concepts that children learn.  Comparing the sizes of objects, determining which toy is the biggest, comparing which child is the tallest, and identifying that a plane is high up in the sky or a car is far away are all examples of how young learners begin to understand this concept. Building upon this understanding creates the foundation of logic, reasoning, comprehension and critical thinking skills necessary to set a child on a positive math journey. Exposure to these early experiences helps children begin to formulate interpretations of mathematical qualities in real-world problems.

Countless scholars and researchers have studied the significance of early math exposure, and the correlation between this and projected proficiency and success. Click here to listen to a top scholar discuss why early math matters!  It is during the early years, that children acquire, practice, rehearse and build upon the skills that will eventually carry them through life.

One way I have found to engage young learners in the attainment of these skills is by allowing them to compare and measure. They often measure one another with yardsticks or tape measures, sometimes standing and other times lying on the ground. They have also traced one another with chalk on the driveway, and then measuring themselves that way.  Often times they walk around our yard and measure flowers, plants and objects. This is a fun, entertaining and engaging activity, and they don’t even realize how much they are learning!

Recently, we realized that a sunflower seed we had planted was beginning to sprout and grow taller and taller.  Each day my kids would observe the stalk getting bigger and bigger.  First, it was taller than the grass, then the flowers, then each one of them!  They loved seeing the change and comparing the height, and I enjoyed watching their amazement.

Finally, one day they asked if it was taller than I was, and it floored them to realize that it was!  We decided to get out the yardstick and measure its final height, just as the sunflower’s face was beginning to bloom.  We discussed how to measure an object and which end to start with.  Then we had to do some adding, since the sunflower was taller than the yardstick (another discovery).  We had a great time checking in on our gigantic plant each day, until we discovered that her head had gotten too heavy and had fallen to the ground.  We did not stay upset too long, because soon they got the idea to get out the rulers and tape measures yet again to measure the width of that as well, which introduced a whole new math lesson on diameter and circumference!

Observing, measuring, comparing and analyzing the things around us helps young children make sense of their world.  This can be an enjoyable way for young children to practice important math skills while guiding their own mastering of significant concepts.  These experiences will then inspire, motivate and encourage them throughout their own life journey.  I hope you enjoy fostering and cultivating your own special math adventures!

One of the most exciting aspects of working with young children is witnessing their sense of joy and wonder in everyday objects.  I often forget that their understanding of many concepts, and their exposure to many tools, is a brand new experience for them.  As an adult, sometimes it is easy to forget this, but children remind us to see the excitement in new things, even if it is just finding new meaning and function in a familiar object.

We all know that young learners find excitement in anything novel and different.  If you ask ten children to collect five objects and create a use for them, chances are you will get many different objects and designs because all children have innovative and pioneering ideas and, rightfully so, they think their ideas are the best! Limitations, boundaries and restrictions are not yet familiar concepts to young children.  Often they are able to express their beliefs, designs and viewpoints about many aspects of their world in a more uninhibited way than adults do; their minds are free to wander, dream and plan to their heart’s content. This is the beauty of witnessing a young child explore mathematical concepts.

For young children, introduction to these new concepts is cultivated through various spontaneous activities and games.  For instance, setting out places for a tea party, counting out spaces during a game of Chutes and Ladders, finding the biggest rock, counting fingers and toes, and going down a slide all incorporate the concepts of number sense, spatial sense, measurement, estimation, and problem-solving and critical thinking skills.  Kids are constantly practicing math skills from birth!

As a stay-at-home-mom, many of the “lessons” that I find my children enmeshed in tend to begin organically.  In my experience, children are much more interested in learning something new when they initiate or present it.  To me, it always feels like they are extending an invitation to the adult to help guide the grasping of a new concept or skill that they innately feel they are ready to learn.  As educators, our learners are advancing at their own level, and our job is to encourage and support each one of them as they succeed at one step, then move onto the next.  I find the process captivating. However, many times these learning opportunities happen at inopportune times (i.e., in the car, away from home, outside) when materials that I would typically use to help supplement my teaching are not necessarily available.  Thankfully, math is all around us; and utilizing what you have or what you can find is much better (and usually more fun) than using nothing at all, or waiting and possibly missing the opportunity.  When they are ready, they are ready – jump right in!

In my last post, I discussed the process of organizing child-centered “learning boxes”  and learning spaces where children are able to explore materials on their own and practice math concepts anytime they choose.  Of course, this is helpful when they are at home or in the classroom, but learning does not just cease once they are away from these two areas. This is where being resourceful and innovative in our own right comes in handy.  Having a small set of available materials in various places (in the car, in the garage, in a bag or purse, etc.) materials are available for times when ideas spontaneously strike.

One example of this occurred recently when we were outside and my daughter excitedly decided she wanted to practice her math skills to gear up for the start of school. Naturally, her brother (preschool-age) wanted to join in as well.  Of course, I wanted to nurture this fertile idea, so I knew my responsibilities would involve keeping both engaged, allowing both ample learning opportunities, and allowing all of us to have fun. The first thing they did was to get out the chalk and a big bucket of rocks we had previously collected.  I then asked my daughter to look in her math box for other materials to assist with her vision. She came out with large foam dice.  After some discussion about our process, we came up with the idea that they could each roll a die and count out that many rocks.

After a few rolls, this proved to be a perfect task for my younger son, but my daughter bored of it quickly.  I could sense she was ready for more a challenging task.  Again, I encouraged her to practice self-reliance and creativity and referred her to her math box.  She came out with a white board and dry erase marker found in her math bin.  She had decided she wanted to practice writing out math problems, which is a new concept for her.  While her brother continued having a blast rolling his die all over the driveway,  counting that many rocks out and then putting them all back in the bucket and starting over (practicing number sense, one-to-one correspondence and problem-solving skills), we worked together on addition and subtraction problems.

She would roll her die and write that number down, then she would roll it again and add or subtract these two numbers together to get solve the problem.   Since she is just learning how to write out a mathematical equation, I helped her better understand this method by drawing two boxes side-by-side.  She rolled the die and place that many rocks in the first box.  Then, she rolled the die again and place that many rocks in the second box.  She then went to her white board, wrote out the problem using the appropriate signs and counted all of the rocks to find the answer

They did this side-by-side for quite awhile.  After a bit, this idea then morphed into both of them working together, the older child teaching the younger how to problem-solve higher-level math concepts.  My part in the learning process became unnecessary, and I was there just as a guide when help was needed, which is exactly what child-directed learning should exhibit.

There are many different ways that math can be engaging and exciting by utilizing everyday objects in a new way.  Often the most spontaneous lessons and activities turn out to be the most fun and rewarding.  Allowing children the freedom to explore math concepts in this way makes learning fun for all!

Differentiated learning spaces are simply areas where children of any ability level can visit and practice skills.  The intention of these spaces is to encourage acquisition of concepts, foster independence, encourage growth and development and promote self-confidence.  The beauty of the space is that it is customizable to learners’ needs because you, the educator/parent/caregiver, design it with the best interests of your students in mind. In my experience, this differentiated environment is all-inclusive and allows children to learn from one another and teach one another, demonstrating boundless real-world experience. Whether you are working with one child or thirty, I have found that creating this type of differentiated learning environment not only offers learners of varied ability endless learning opportunities, but also encourages independence, organization and self-reliance. For example, you may have learners who prefer to work on the floor, or sitting at a table.  Perhaps some of your learners can concentrate better on a task in a quiet environment, while others can easily adapt to noise and other distractions. When in a learning environment of varying ability (and, let’s face it, as educators, caregivers and parents we usually are) it is our responsibility to encourage independence, self-reliance and achievement with each learner.  This is what a differentiated learning environment looks like.

Set-up does not have to be daunting, and you can take comfort in the mantra that nothing is impossible; everything is obtainable with organization and patience.  Furthermore, these spaces do not have to be uniform, and you can take liberties designing the space(s) that best suits you and your learner(s).  The main concept is to create an area (or areas) that engage and invite all learners to explore, together or individually, and will change and grow along with their dynamic development.

Here are some tips:

• Whenever possible, put materials at child’s height – this invites learning and independence.
• Invite children to find a space that will help them learn. Allow them the opportunity to have control over their own learning.  This will give them the confidence and self-reliance they will rely on later in life.
• Label everything: even if the child is not a “reader” yet, exposing him/her to letters and words will only help develop those literacy skills in conjunction with math skills, which enriches their learning experience. Additionally, this will help you stay organized!
• Create “learning” boxes (or ‘fun learning boxes’). Fill a shoebox, cardboard box, Dollar Store container, or basket (whatever you have on hand and works for you) with everyday materials you have in your home (tape measure, ruler, crayons, markers and pencils, dice, blocks, LEGOs, measuring cups, etc.); anything they can use to count and become more familiar with math concepts.  Nothing too complicated or elaborate (for the learner or teacher), just anything students can play with and explore, either with you or on their own.

• Allow children to explore these learning boxes at their own readiness. You may initially invite them to play with you, whereas you introducing the box and you both explore the materials.  You can also explain the traditional use for each tool, and together you can make a list of fun activities to try.
• I find that the adventure of discovering new things gets young children very excited about learning. A few other ideas to try when setting up these math boxes are to invite children add materials they find to the box. Being adventurers and explorers together, you and your children can explore your home and neighborhood to find other math tools to add to the box.
• Include a variety of materials for learners of all ages and ability level. Some helpful and inexpensive tools are:
  • Mini tape measure and/or measuring tape
  • Egg cartons or ice cube trays for 1:1 counting
  • Large foam dice
  • Rocks, LEGOs, small animals or gems for counting
  • Number flashcards for number recognition (you can easily get these from the Dollar Store or make them yourself with notecards)
  • Ruler
  • Paper and pencil; white board, small dry erase marker and erasure
  • Calculator
  • Abacus
  • Inexpensive math counters and math games.

*(Tip: use your local second-hand store or Facebook groups!)

• Allow children to learn and explore on their own, encouraging independence and creativity, while also offering “lessons” and “guided play” as well.
• Keep materials and supplies at their level – this allows them to explore, and invites them to play with the materials whenever and however they wish.
• Allow time for children to discover new materials. They may not know what a tape measure is, but they will enjoy the process of investigating what it can do.  Not to mention, watching them interact with new tools and materials will allow you to assess their understanding and give you an idea of what you can present to them.
• Have a number line located somewhere children can see and access when they need assistance with number recognition and counting.
• Frequently ask children to refer to the learning box in order to become familiar with and utilize the tools inside. For example, if they ask you how tall something is suggest they explore their math box to find a tool that can help with this.  If they need help remembering, “Which number comes next?” direct them to use the available number line you have displayed.  This encourages necessary life skills, such as, independence, self-reliance and resourcefulness. If you teach them now they will have the knowledge for a lifetime.

Learning boxes are a fun way for students to develop early math skills and practice early math concepts.  Additionally, for children with learning difficulties, this type of differentiated setting promotes self-regulation and confidence because its design endorses aptitude and capability, rather than helplessness. This type of learning environment cultivates the development of important self-confidence and critical-thinking skills, which allow children to grow into self-regulating, inventive, capable and creative individuals.

Of course, as parents, caregivers and educators we are all constantly changing and implementing the directions we give and the way in which we interact with each of our “students”.  I usually do not give my four-year-old the same task as my six-year-old because they are at different ability levels, both cognitively and physically.  This is not to say that they are not able to do the same activity or task simultaneously, it just takes a bit more planning to make the activity enjoyable and inclusive for all.  Not to mention, skills and abilities are dynamic, so what my kids can do is constantly changing and evolving – so I have to be on my toes!

Now that I have my own children, the importance of meeting learners at their level, creating a space where they feel confident in their abilities, and giving them opportunities to flourish is a part of my every day life.  When a child does not feel that they can succeed at a certain task, they can become easily discouraged, which can have dire consequences on learning.  We have all been there.  Irritation, anger, and shame are all common feelings to experience when we just can’t get the hang of a skill or task. In fact, most of us experience it every now and then.  After all, making mistakes is all part of growing!  However, there should always be an element of fun to learning anything new.  It should never be exasperating, wearisome, and infuriating all of the time.  When a young child constantly feels that he/she cannot achieve success, even in the smallest of tasks and skills, this can greatly affect how they approach learning anything new in the first place.  For children who have learning challenges, this can be a daily struggle.  Over time, this can have a serious impact on their self-esteem.

Fostering confidence, independence and self-reliance is of paramount importance to educators.  Meeting each child at their level allows them to acquire skills and knowledge, which in turn, supports growth and development and gives them assurance that we (their parents/ educators/caregivers) have faith in them.  This is what occurs when adults allow children to explore and discover and learn in their own ways, and this is at the heart of differentiated learning.

In short, differentiation describes the process of utilizing multiple strategies to teach a skill or concept to a heterogeneous group of learners.  As a 2014 Early Math Counts blog pointed out, differentiation does not necessarily mean you are providing every single individual learner with a modified set of instructions.  It simply specifies that educators implement modifications, when necessary and needed, based on the needs of learners.

For example, if I am baking with my children I may give them a similar task, but differentiate the instruction based on ability level. The directive for both could be “measure out one cup”.  Now, I know that they both can accomplish this task; therefore, I must modify my assistance and facilitation with each to create an environment of success.  By giving instructions that are too complicated right away, I run the risk of one or both children beginning our fun activity with a sense of failure, which is never a good way to start.  I find it is best to start small and work your way up.  Build upon skills and utilize the learner’s abilities to best help them acquire the development of new concepts.  This way, children feel confident and more likely to try something new, which is a win-win for all!

Since I already know my youngest can recognize the number 1,  I know he will be proud of himself for locating the correct measuring cup, then filling, and pouring it in himself. However, if he didn’t yet know his numbers (or needed further assistance due to physical challenges, etc.) I could modify this even more by providing a visual cue for him (e.g., writing it down on a piece of paper or white board, or have number flashcards available) and have him match it to the correct number on the cup.  Another modification could be that I set out all the measuring cups and have him find “the biggest one”. It’s all about setting up a successful experience for the learner at his level of ability, encouraging independence and self-reliance early on, and allowing him to experience those important moments where he makes his own connections with new concepts.

For my eldest child, having her simply find the “1 Cup” measuring cup would be far too easy.  Instead, I could ask her to find the 1/2 measuring cup or ¼ measuring cup, and then we could have a discussion introducing concepts of division and multiplication (i.e., two halves make one whole; four fourths make a whole, etc.).  This slight modification encourages independence, self-reliance and success and gives them both the own connections with new concepts.  exposure of new concepts in a fun way.

Teaching is not a “one-size-fits-all” approach, and this is why creating a differentiated learning environment is so important.  Whether there is one child or thirty, utilizing various strategies to support each learner does not have to be cumbersome, can be done in any type of setting, and will help all types of learners gain confidence in their abilities while having fun learning math skills!