When your student is making a recurring mistake, it is an opportunity to pause, and then ask together, “Okay, what parts of this are we not understanding? Is there a way we might approach this differently?” Instead of beating themselves up every time they get something wrong or make a mistake, your student will learn to see math mistakes as opportunities to evaluate, improve, and learn. This equips them with a skill that is useful for all of life.
When you help model working through mistakes, you are empowering students to become an advocate for themselves, and this is especially the case as they progress into the upper levels of mathematics where the level of abstraction can be especially challenging. This is true even for the student that tends to pick up new mathematical concepts quickly. I am an artist and art teacher. Often at the beginning stages of a project, I’ll say to myself, “okay, I’m just going to slop paint down, go with instinct to start out with, and see what I’ve got.” After I’ve done this, I can then look at it and say, “I need to be more intentional here,” and “Oh, this is where I’m having trouble,” or “I need to change this up.” In this process, what starts as a mistake when viewed in a certain light, quickly turns into an opportunity for improvement when viewed with a growth mindset.
As an instructor, it is important that I model this process of turning math mistakes into opportunities for my art students. When starting a class I show examples of my own work to show that not everything goes as planned, and use this as an opportunity to incorporate what would be otherwise considered a mistake into my learning process.
Since implementing this mindset, I’m finding that not only are my own art skills improving, my students are also improving at a much higher rate than they were before. They’re also coming back to my classes at a much higher rate too, because the class has become a safe place for them to make mistakes part of the process. Not only is it a safe place for mistakes, it is also a place that actually celebrates those mistakes as learning opportunities. My fellow artist and I grow comfortable saying things like, “something doesn’t seem right here,” and “oh, I see, I see where I’m having trouble.”
My process for art skill development can be translated and used in math as well. If your student is not understanding something or having trouble with a new concept, we can help them to see that it’s not a reflection of their intelligence, potential or their skill. Instead, we can help them understand that the struggle to acquire knowledge is an intrinsic part of the learning process.
Because eventually, they’re going to have to learn to deal with mistake-making too, and the frustration of not getting it right away. And so learning to view mistakes as opportunities is a good skill for all learners.
Math Mistakes and Math Anxiety
Earlier I mentioned that my art students come back again and again because I have made my class a place where they feel safe to ask questions and make mistakes. Some students who have had bad experiences with mathematics, can experience math anxiety and even panic when faced with the prospect of making mistakes or revealing they do not yet understand something. It is not uncommon for some students to have immediate panic when they see drill sheets, workbooks filled with word problems, lengthy tests, etc.. I encourage parents and teachers whose students experience math anxiety to consider these possible solutions.
• First, make sure you’re only drilling or testing on material that you’re confident the student knows well. Drilling is a great way to practice known skills but not a particularly effective (or inspiring) way to learn new skills. If you see your student shut down or meltdown at the site of a drill sheet, begin with a few problems and work up. Our worksheet generator allows for as few as 4 problems per sheet. Additionally, avoid timing the drills until the student requests to be timed.
• Limit the time you spend on a concept that your student has not yet mastered. For example, the attention span for an 8-year-old when trying to understand something is typically around 10 minutes. Use their age number plus two as a guide to determine what is average for your student’s age. If you want the math session to be longer you can either switch out to reviewing math the student has already mastered or work with games or activities using known skills. Another option might be 2 short sessions with a 2 hour break in between.
• When introducing a new concept, coach your student toward a more positive mindset by saying something like, “Okay, this is our first day on this, let’s see if we can catch a piece of it today”. Again, limit time spent per session on the new concept to their age plus 2.
• Collaborate with your student to set the pace for each day. If your math plan for the day involves a worksheet, ask “how many problems do you think you would be comfortable solving today?” or “Let’s start out with finishing the odd numbered problems first”. This way you can evaluate any areas which might need additional assistance. Bring them into this process, and help them regain a sense of their own learning.
• Lastly, I encourage you to give your student the permission to skip the questions that they don’t know how to solve. You can then say something like, “Oh good, you skipped that one. We know we don’t know that one.” This gives you an indication of what concepts to spend more time on with your student while sparing them the anxiety of being penalized for knowledge that they have not mastered yet.
The goal is to lessen stress, embrace mistakes, and provide your anxious student with many small victories. Through these kinds of processes, you and your student will begin to realize how to find learning success with limited anxiety. Knowing how to advocate for their own learning process is a skill that will assist them in becoming lifelong learners, and enable them to reach their full individual potential.
Math Mistakes and Test-Based Assessment
In the Math-U-See approach, we’ve included test pages to help students get used to the idea of test-taking and help determine whether your student has achieved mastery. We do not recommend taking the test until the student has demonstrated mastery in the practice and review sheets of a given lesson. If your student needs extra time to achieve mastery, extra online practice is found for elementary students on our worksheet generator and on the Extra Practice Pages for upper level students.
The “wait for mastery approach” to testing teaches your student to develop an understanding of what they need to be prepared for a test. This approach sets your student up for success in testing so when they see the word test at the top of the page, they feel confident in their ability to tackle it.
When there are errors on the test, try to keep them in the same perspective you would with daily work. When working through mistakes you can ask: Were multiple problems missed that use the same concept? If so, this might be an indication that they need to revisit a concept for some additional practice. Did the student work hastily? Were there distractions? These might indicate that your student was tired or not feeling well that day which might have made it hard to focus.
By asking these questions and having a conversation about the errors, you can again reinforce that mistakes are an opportunity for growth. Together you’ll learn and make decisions regarding next steps for continued success in both daily work and test prep. Please keep in mind, our Customer Success Team is here for you to support you and your student’s plans for building math confidence.
At the beginning of this blog post, I talked about the importance of instructors modeling mistakes and the learning process. The more that you and your student can embrace the perspective that mistakes are opportunities to grow, the more positive the learning process will become for both of you. And like myself and my art students, I’m confident that your student will grow to feel like math is something they can do, and maybe even enjoy!
Related Blog Posts
Every year for the past 30 years I have had the privilege of walking alongside families through the ebb and flow of a school year. During May and June, these conversations often reflect that parents are feeling as though they are merely surviving rather than thriving. However, I guarantee that you are not alone, the path that you’ve taken is unique and you owe yourself and your student some reflection and celebrating in this regard.
Regardless of your plans for next school year, wrapping up this year with clarity, reflection and a sense of accomplishment will be an effective vehicle for ongoing success. My hope is that this blog post will showcase some of the ways you are thriving, and encourage you to rightfully reclaim that feeling as the school year comes to an end.
Evidence That You’re Thriving
1) You Seek Clarity on Current Skill Sets
Before you check out of school for a couple of months or start a summer education schedule, I encourage you to evaluate the skill and knowledge your student has accomplished. This will give you clarity and reveal opportunities for you to capitalize on strengths as well as create a plan for filling any gaps. It will also give insight into how much your student has grown during the school year, showcasing how you have thrived in your educational journey.
Evaluating skill sets will serve you better now than in August. When working with parents in August, “summer brain” can be very prevalent, making it difficult to place and plan effectively. Our materials are designed to be sequential and build on the knowledge that a student has already mastered, which is why starting off with the proper placement and skills set is so important for continued success.
Our FREE placement tools are a great tool to evaluate your student’s current skills and gain clarity on potential areas needing improvement.
If you find your student has gaps with addition and subtraction our Accelerated Individual Mastery program could be a helpful addition to your summer plans.
2) You Embrace and Grow from Disappointments
Months ago you may have written a list of goals for your student to accomplish before the end of the school year. Now looking at that list you may realize that these expectations were not met and are faced with the feeling of disappointment. Before you’re ready to embrace that this disappointment is good news, a well-thrown, but brief, what I like to call a pity-party is often important. As you skip out of the party, don’t just crumple and throw that list into the garbage bin, instead take some time to embrace disappointment and know there is gold there and more evidence of thriving.
Teaching your students how to work through disappointments is an important life skill. Plans change, things don’t always go smoothly and we all process information differently which can lead to working at a different pace then expected. Look at the unfinished list not as a failure, but as opportunities to teach your student how to work through feelings of disappointment.
Keeping a hold of your list and reflecting might help to evaluate which expectations are realistic moving forward. This information will provide a filter that is key to planning decisions regarding summer school, next school year, and beyond.
Our blog post 3 Ways to Encourage a Growth Mindset in Our Kids is an encouraging resource to help you focus on a positive mindset towards things that you or your student may have struggled with in the past year.
3) You Celebrate How You Thrived
I continually find myself requiring a reminder that anything I have thrived in has a long cookie trail of risks, baby steps, and “enlightening” outcomes. I tell my students and myself continually, “No risk, no masterpiece…and a well executed risk can go either way.”
As you wrap your school year, keep up your determination, remember that you are indeed thriving, not just surviving, and celebrate all your and your students have accomplished this year.
You’ve Thrived: What’s Next?
You’ve thrived throughout the school year,now what? Before deciding your next step remember that when you know what your student knows and does not yet know, you are more empowered to set that student up for success and make good decisions regarding next steps.
Regardless of your summer plans, you might find some extra peace of mind by taking time to make your curriculum decisions now.
Thriving with Summer Study
Let’s say you and your student have decided to commit to summer schooling, I usually recommend both working in an area your student enjoys and dedicating some of that time to remediate areas that you have observed were a little fuzzy.
As I support parents that have learned their student is struggling with math, I find the number one gap is single digit fact mastery. If you have noticed your student counting or taking long pauses as they work through concepts, AIM for Addition and Subtraction is a great summer program to help fill those gaps.
If multiplication is where your student needs shoring up, contact our placement specialists as we have diagnostics and solutions for not only multiplication math facts but other gaps as well.
Summer is a perfect time to focus on fact mastery. It is always exciting for me as I work with parents to find clarity regarding learning gaps, which when realized and filled are game changers.
Thriving Taking the Summer Off
Remember that taking the summer off is not a bad thing! I will be honest here, looking back my children would have possibly benefited from some review and formal education during summer. However, the reality was we all were in more need of a break then a summer schooling program. Any learning we did was totally unplanned, organic and in the moment. Sometimes a break is what is needed for a fresh and enthusiastic start at Back to School. Somehow they turned out fine and I have some pretty wonderful memories of summers in which we learned more organically and definitely thrived.
If you are nervous about taking the summer off, here are some fun “formal learning” ideas that can help keep things sharp during your summer break:
Continuing to Thrive Involves Trusting Your Gut
While planning your summer program or next school year, if something does not seem to add up in regards to math and spelling, remember we are here to help. Knowing yourself and your family dynamic will direct you. You know your student, we know our products and have additional tools to help plan for success.
Whether you end up using our products or not, expect collaboration at its finest. We are here to help with your next steps and discuss if our products are a good fit for your strategic plan for your student’s success and confidence.
So in conclusion…pause, reflect, celebrate, and do what you know will work for you and your family as you continue to thrive! You are homeschooling, it is what you do.
Thriving in 2019-2020 Badge
We encourage you to download the badge, share on social media how your family has thrived and celebrate thriving in the 2019-2020 school year, and tag your friends who you think would find this encouragement beneficial.
Click on the image to get the high quality version.
The misconception that students are either strong in math or strong in art but not both is something I hear often. As a Placement Specialist, I often find struggling math students do gravitate to the artsy side. So how do we help these struggling math students succeed?
As I collaborate with a parent/instructor, the initial answer has more to do with changing the approach and mindset. The ultimate avenue for success is to reveal both math and art are used to describe concrete objects, tell a story, or reveal a vision. The integer blocks are an effective tool to enhance the student’s ability to make this connection and thrive in both subjects.
Why Math Manipulatives?
Young artists have a rich supply of images in their long term visual memory. These images are stored and built upon. They pull from these treasures as they create and communicate through their art. Long-term visual references have shape, color, angle, texture, and line. They increase and evolve. Resources are continually assessed while they are creating. Math-U-See Integer Blocks have a consistent shape, texture, and color, providing a concrete visual to represent the numbers. This, along with the Build-Write-Say steps, provides the learner with resources to store in their long term memory. When used along with these strategies, they are able to access these mental images making visual sense of the abstract math facts and concepts.
Once the student shows an understanding of the new concept, it is important that the student teaches you the concept using the blocks before moving on. Motivate the student to advocate for themselves as they decide what they need to successfully prepare to teach.
For example, they might find it helpful to have a magnetic whiteboard and attach ½” magnetic strips to a few of the blocks. This would allow them to teach in a similar manner to what they see in the videos. I often find young artists love to educate others as to their process whether it is art or math.
When we prepare to teach something we more intentionally store that information in long term memory. Requiring that your student is not allowed to move to the next lesson without teaching will be a motivator for using the blocks and provide an opportunity to share and further develop their love of teaching.
As a teaching artist, I find this a valuable method for my own learning. There are times I need extra motivation to learn something I don’t yet know. If I schedule a class using the concept, by the time my students show up, I have developed the skill I might otherwise find difficult.
Word Problems and Math Manipulatives
When reading the following word problem, what do you see in your head?
“Sally had 5 apples. She found 3 more. How many apples does Sally now have?”
You might say that you see 5+3=8. You might see 5 apples lined up and then 3 more and you count the apples. (Post what you see in the comments so we can all learn from each other.)
Here is what the artist in me sees:
It’s a sunny day. Sally is standing in a grassy orchard. She has red curly hair and is holding a woven basket to carry apples.
When I say this to parents whose artist student struggles with word problems they often laugh and say, “Yes, that’s about right.” Or they are shocked and say, “I had no idea that might be happening.”
For the “artsy” student, word problems can get cluttered when they visualize the scene instead of the numbers or concepts needed for the solution. If you are using the Math-U-See Curriculum, the word problems on the practice pages are intentionally designed to work with the manipulatives. Encourage the student to choose one of the word problems for “teaching back”. Using the manipulatives in this way will provide them a way to remove the clutter.
Active artists are processors. When your artist is starting to develop their next skill they practice, ponder, discover and marinate. They rarely “get” and apply their next skillset instantly. Often, the creative processor will not instantly “get” a new math concept either. It is not a matter of intellect, it is a matter of how they process new concepts.
Growing up, I survived basic math but it was indicated I would not be able to move on to upper levels. Later, when I was challenged to complete Math-U-See Algebra 1 as part of my job, a major switch happened. I realized when I applied those same processing skills I embrace in art learning to the math, it was a game-changer. Math not only became enjoyable and successful, but I also was able to see that math and art work in tandem. I truly believe the combination of solid art and math skills will be highly valued in future job markets. Math-U-See Integer Blocks, when used as directed, have the potential to reveal the art connection for your student.
For more information on how math and art connect, read my blog post titled “The Connection Between Math & Art”.
When I get something and there are instructions, I give it a quick look and I decide if I need to read them. If it looks pretty clear to me, I’ll skip them or skim them. When I was teaching the Math-U-See program in my home, some of the instructions were missed or forgotten in the struggle of the day. It can be very helpful to review the instructions in this case.
A lot of times on the video, the presenter will give instruction as he’s teaching that may not necessarily be in the instruction manual. Those are easy to forget because you’re focusing on the concept and you may have forgotten what he said.
If you’re struggling with teaching math, you may relate to the following questions.
Is Your Math Curriculum Right For You?
Is the math curriculum you’re using not right for your teaching style or the learning style of your student?
One factor in the equation is timing; how many days a week are you teaching math? How many minutes a day are you spending on each lesson? It will vary depending on the lesson.
There’s also your student to keep in mind; does he shut down at a certain point in the instruction? Could that indicate that you need to review and adjust the timing? Does your student need to take breaks and reset?
Should You Take More Math Breaks?
A lot of parents struggle with particular lessons, and may have taken a short break. After coming back to that lesson again, it all came together.
A lot of times we think we teach a child something and that they should just get it right then and there. Your brain collects all the data of what happens during the day, and when you sleep it sorts it out. Some stuff goes in the long-term memory and some things go into short-term memory. Sometimes we need to sleep on it to really have the light bulb go on.
I talked to a mom of a 15-year-old who was still struggling with multiplication facts. The thing is we do have solutions for that. So sometimes, if there are missing tools, it’s a good time to just pause. Take a break and do some evaluating.
Pause and say, “Okay, what’s missing here? Why are we struggling? Is there something we can do?”
Are You a Confident Math Teacher?
A lot of times the parent is worried that they aren’t skilled enough to teach math. I want to encourage you that you are the best math teacher for your student because you know your children the best.
Even though Steve Demme is teaching students in the Math-U-See lessons, the intended audience of the videos are the teachers. Steve wants to empower parents to teach math; it’s there to support you even if you’re not feeling confident. And as I mentioned, sometimes the video and the written lessons present information in slightly different ways, so it’s good to use both of them if you’re feeling less than confident with a concept.
Do You Think That Your Student is Behind?
The most frequent conversation I have is with parents who are worried that their students are behind. Once we go through and establish a plan and strategy, the students often start thriving right away; that’s just music to my ears.
When we settle on a plan, we can then plan steps and how much time it will take, so that the students will be solid by graduation. We’re more interested in the student being solid in their math because we’re looking ahead to high school and beyond. We want your student to be set up for success in those situations.
When we map it out, the students are most likely going to be proficient through at least geometry or algebra 2, and that’s a great spot to be. As a parent, I put two kids through college. I remember that they both had to take some high school math in college, and those classes are full of other kids in the same boat. If you could be solid through algebra 2, your student wouldn’t need to be in one of those classes.
If you’re concerned about your student being behind, talk to us. We can help you put together a strategy, identify tools, and help put your mind at ease.
Is My Student Behind? Actually Behind?
When you observe your student exhibiting one or more of the following in their math lessons, it is hard to not become concerned about whether your student is behind or not:
• Student is not ready for the math curricula which indicate their corresponding grade level.
• They are working at a lower level than another child the same age.
• Math does not come quickly or easily.
• The student does not seem to retain previously learned information.
• Math lessons are frustrating and emotional.
The first step to supporting your child is to try to be realistic while taking steps to remove the “my student is behind” mindset. There is no such thing as “behind.” Wherever they are regarding math skill at this moment or for whatever reason, where they are is where they are.
Not Behind? Where Are They?
This is where it starts to get exciting!
Now you can focus on learning what your student knows and does not know. Without this information an effective plan will be more of a guessing game. Often finding out what your student does not yet know will reveal foundational learning gaps. When these gaps are filled sequentially, your student will be set up to move from math tension to math confidence. Filling in these pieces will have a domino effect on more complex math concepts which were previously a source of frustration.
Catching a Vision
As the parent, you foster the vision you want for your student’s math career.
Is it best for your student to align their pace and process with standardized testing correlated with your student’s grade/age? Is comparing skills ofother students you know a successful measurement for success or ability? Or would your student be better served by focusing on where they are and what they need to become confident and prepared for the next step? If we are honest, it’s likely that we want little bit of all of the above.
Being “behind” indicates that someone is ahead in comparison. Consider this, in contrast: What if you spend a school year starting where the student is, putting together a plan to fill in gaps, and seeing confidence build as they begin to thrive at their individual success pace?
At this point you might be concerned that your student does not have time to back up too far.
Let’s take a look at a possible “what if” scenario that I have seen play out many times.
What if, as a result of pausing and filling in important primary math gaps, a 6th grader masters Epsilon (the Math-U-See level on fractions) or confidently completes half of that level.
At some point in 7th Grade they would be in Zeta (decimals and percents)
8th Grade – Pre-Algebra
9th Grade – Algebra1
10th Grade – Geometry
11th Grade – Algebra 2
So by 12th Grade, they are quite possibly ready for PreCalculus.
One of the benefits of homeschooling is that it’s okay if a math book is not completed at the end of the school year. If one of the levels takes a year and a half to achieve mastery understanding, that’s fine. As you can see, the student in this scenario above has the potential of not only completing but being confident in Algebra 2 upon graduation. This student would then be poised for success in attending college, approaching military math tests with confidence, applying for job which require math knowledge, taking trade school entrance exams, or successfully starting their own business.
Once an evaluation of what is not yet known is completed, a strategy for beginning an individualized plan can begin. As part of your planning, a realistic “what if” vision, as indicated above, can provide a renewed vision of potential and hope.
For the Parent Who Doesn’t Feel Confident in Math
When working with families, as a placement specialist, I find most of my consults are not only worried about their student but worry the student is somehow handicapped because the parent does not feel confident or feels they have fallen short.
If you are “that parent,” I want you to know (now, listen up!)…YOU ARE THE BEST MATH TEACHER FOR YOUR STUDENT. If this weren’t true, you wouldn’t have read this far into this blog post.
You are the best person to:
• Authentically model to them enthusiasm for learning as you gain math confidence along with them.
• Demonstrate that allowing time for math to marinate, wrestle, and process results in success.
• Give them the opportunity to genuinely teach you when they understand a math concept you do not yet know.
Regardless of your math confidence, Math-U-See is intentionally designed to empower, not replace, you as the instructor. Assistance is available should you find that you and your students are not able to figure out a lesson.
Not only are can we collaborate with your goal to no longer feel your student is behind, we are here for you in your learning process!
Begin your plan for success, discovering what your student knows and does not yet know, by using our online assessment or by contacting a Demme Learning Consultant today.
Math and Art Skill Expectations
Math development often has the expectation that at a specific age a student “should” be at a specific level. It is tempting to conclude mathematical potential either by comparing skills with materials marked by grades or by comparing their skills against another student’s abilities. Visual arts development is often judged by the student’s interest level or how his or her work compares to someone who is viewed as talented. Another conclusion is made by how their work lines up with realism. Unfortunately, students are often judged as to whether they are adept at math and or art or not at a young age. The success or failure mindset sticks with them. In my work as an adult beginning art instructor, it is common to have a first time student make a comment such as, “So-and-so is the artist in our family.” They gave up years ago when someone else in the family filled the shoes of the artist in the family. Let us be cautious about labeling a student as not being mathematical, artistic or unable in any subject. Instead, I encourage you to discover ways to build skills in sequential order and at the student’s individual pace. The goal is to assist the student to develop basic skills and learn how to learn. Potential comes in all shapes and sizes.
This is where it gets very interesting. In my 30 years of mentoring and learning from parents as a Demme Learning consultant and an art instructor, I have observed that most students, unless there is an extremely serious learning delay, have potential to be proficient in both math and art. Artsy student can develop confidence in math and “mathy” students can develop art confidence. Not only that, intentional development of art and math will result in a stronger ability to combine both naturally as the student moves into upper level math, professional art and ultimately into the job market. In both mediums the creative strategic thinking, problem-solving, and self-expression developed will set your student up for success for whatever their plans and goals may be. Both subjects correlate directly with science and language expressions as well. To me art is the glue that connects all of the above.
Art and Math Parallels
In my personal art, I am continually considering angle, proportion, perspective, balance, grids, quadrants, slope-intercept and probably more math concepts that I do not even realize. Other artists I have asked about the connections between math and art indicate they use measurement, weight, and even trigonometry.
All you have to do is take a look at the tools both artists and math professionals use and you will actually see the strong parallels.
A special note here: In art especially, using tools is not cheating or a sign of being “less than.” Even the great masters used tools; in fact, they developed many of them. While there are likely a few artists who have developed their skills being a purist, most of us have at least a few favorite tools.
Story and Vision
The most profound way I see this connection between math and art is that both involve telling a story, expressing a vision, working though a strategic process, or yes, sometimes evoking an emotion. The lightbulb in my math/art connection came on when I studied Algebra 1. When preparing to certify to support Math-U-See Algebra 1, the most exciting “aha” moment was the realization that the same learning process I enjoy in my art development provided success in Algebra 1 as well. The skills and concepts I had developed in art began to correlate with the math I was learning. Because Math-U-See focuses on the importance of “seeing” math concepts, I was able to visualize and ultimately find new success in math. Now those formulas that I could not even begin to understand or memorize when I failed Algebra 1 in school were relevant. The same processing I use to develop my art supports my ability to find success in math.
In both math and art a story is being communicated, a vision being processed that you may have seen or wish to create. Students, even if they’re not particularly artsy, benefit from working through art skills, as it promotes strategy processing skills which will ultimately enhance the ability to apply and excel in other subjects. I assure you basic art skills can be developed by all learners. Beginning at any age systematic development of art will encourage creative thinking. In the job market your child will be competing in, being able to be creative and having the skills to communicate creativity in math, visual art and language will be a valuable asset.
Let’s Get Practical
Ok, this is a blog post right? Not a book, so let me prioritize and narrow this down to five things as an art instructor that I would suggest as a starting point.
1) Tension Control / Awareness / Trial and Error
The ability to control tension when creating is something that is both vital and difficult to reteach. By the time the student ends up in my class reworking muscle memory, this is often the number one hill to climb. When the habit is to apply too much pressure to the pencil, it makes it difficult to erase. Consequently, the art student feels they have no choice but to get it right the first time. Learning to draw lightly until you get it right evokes a mindset that promotes trial runs and changes as part of the process, not failure or a sign that you are not capable. When watching even most professional artist sketch, you will notice them making small, light marks to begin their composition. They start out getting a feel for what they are envisioning. They now can see their options and know where to put their hard line or use it as a light line to guide them if they are painting. Because they drew lightly, they can erase all the other lines and have a clean area with which to continue. Here we can learn the incredible value of trial and error. An additional bonus will be as the student begins to work through multi-step math concepts. The skill and mindset that they can find the error and erase without making a big mess on the paper or having to start over can be key to building confidence and lowering the frustration level. Additionally, you, the viewer, will produce something much more enjoyable to look at, lowering your frustration level as well. Teach your budding artists and mathematicians to love erasers and view “failures” as opportunity to grow.
2) Thinking Outside of the Lines
Going outside the lines can be quite risky. In the end, just getting those worksheets completed with a specific percent correct will not be what best serves your student.
In regards to art development there will be more obvious ways to think outside the box and color outside the line…keep it simple. One of my favorite ways is through photography. Next time you and your student are sitting somewhere waiting, hand your student the phone and say, “Okay let’s snap a few shots.” Do not just take pictures of people or buildings. Find some texture, interesting colors, and surprising scenes. Play “Who Can Take the Most Unusual Photo in Four Shots.” Later you can teach them about cropping. How do you make it look better? How do things look better if you crop it this way, or that way? Be ready to print two or three of them monthly to mat and frame for your gallery wall at home. Maybe rotate them and put the previous one in an album. We miss so much in life by not really seeing our surroundings. Learning to “see” what is really there is definitely a math/art connection.
3) Limit Time for Intense Instruction
When I teach children’s classes I typically figure in 10-15 minutes of formal instruction mixed in with a remaining experience of free play. It is often better to leave the project unfinished, move to free play and come back for multiple additional brief sessions either during the session at another time. I have learned from experience that students start out doing great and all of a sudden trash it because they need a break from that level of concentration. A mature artist knows breaks are vital for a quality result. My best works often involve a break at 80% finished or sooner. I then leave the work out so that it is somewhere where my peripheral vision will keep working on it during my day. Our brain is so amazing that it will continue to create when we do not realize it. Often out of nowhere I will know exactly how to finish it with the “edge” I want it to have. I encourage you to be aware of this and build the habit of knowing and honoring when it is time to “step away from the art work”. It is the same with math. Try 10-15 minutes of math when learning something new, then walk away for a spell and re-approach with fresh eyes.
4) Free Play and Exploration
I get it…not everyone enjoys messy art as much as I do. I am one of those glitter grandmas. If the kids come over, we usually end up with glitter, paint, and glue somewhere. However, I cannot stress enough the value of your student experiencing both inside and outside the box creative discovery. This is where they learn to understand when and where both are appropriate. A balance of messy art at the level you can handle, brief sessions of formal skill instruction, and frequent habits of drawing, photographing, or taking note of what you see in your daily surroundings is important. The same goes for math. The student who insists on getting the answer “their way” will be well served by learning to balance that wonderful ability by simultaneously being required to solve at least some of the problems as instructed. Another thing to keep in mind is that while some need complete order to function, others of us need things at least a little messy.
5) Think Intentionally
Likely, you plan with intent as to the best fit for your student’s math. What makes Math-U-See a well-rounded program is that we teach to master concrete understanding, not only at the student’s individual pace, but we also provide potential development of all learning preferences. While your student may have a favorite way to learn, do not underestimate the value of strengthening the other preferences. If you are using Math-U-See currently and find your student “block resistant,” be sure to require that they use the blocks until they can teach the lesson back to you while using them. Even if they can get answers correct without doing this, you will be connecting to the valuable creative thinking and promote deeper mathematical creativity. If you need support as to how this might work in your individual classroom…call for a consult for some ideas as how to do this without either of you becoming frustrated.
Art needs intentionality as well. There are tons of purchase choices out there. If you as a parent are not confident as to what to do or where to start, post in the comments and tell us more. Also tell us about how art and creativity already happen or do not happen in your family. I learn so much from the parents and students I have the privilege to walk along side. Hearing from you will help me know what to include in my next blog post. The key here is let’s keep it simple…but in some way intentional.
In 2016 I wrote a blog post similar to this: How to Teach a Child Math Facts. However, because I have the privilege of consulting with parents weekly–even daily– and addressing fact mastery strategies, I have learned more. I want to share this additional information I have acquired during time spent in the trenches with you, the parent.
Fact mastery is a hot topic with parents of students of all ages. If nothing else, after reading this post I hope you remember two things: 1) Regardless of your student’s age, you are not alone, and 2) We do have solutions.
Is Fact Mastery Really Necessary?
Often I am asked whether fact mastery is really necessary. To be honest, I have no doubt there are adult mathematicians out there who do not know all of their math facts and may even need to count on their fingers. However, when consulting day to day, I have talked to many parents who admit that they still count on their fingers. They are often even more committed to finding a better way for their students because they tell me “I have always struggled in math because of it.”
I like the way Mary from our customer service team says it:
Fact mastery will give the student confidence. When they are solving complex problems they do not have to stop to think what is 5 + 6 or 7 x 9. When they must stop and think about these facts, it makes them think “If I can’t do something simple, how can I do something like Algebra?
So yes, while your student might become confident in math and be set up for success in upper level concepts without having facts mastered, chances are that it will affect their ability to efficiently process more complex concepts. It is possible that you would be sending an otherwise successful future math student to try to master higher level concepts with a math deficiency.
Let’s Inventory What You’ve Likely Tried
For some students flash cards will work. If you are making progress using flashcards I recommend that you read this blog post written by Gretchen to even find more success.
2) Speed Drills
Speed drills can be an effective tool for some. However, if you find your student panics or seems to forget everything you thought they knew once you start drilling, the drilling activity may need to either cease or be modified.
It is rare that speed drills teach. However, they can be a tool that helps a student become faster with their fact recall. It is recommended that you drill only math facts the student already knows. As an adult, I can’t think of any new information I have learned by just going faster. The Math-U-See website offers a worksheet generator to help with this. You will find addition/subtraction drills under Alpha, multiplication drills under Gamma, and division drills under Delta.
3) Math Games
Games are another commonly used tool that can result in supplementing success. Amanda has some great ideas in her blog post.
Breaking the Habit
When a student has been finding the answer by finger counting for several years, the key is to assist them in breaking the habit. For them the only place to look for the answer is on their fingers. When instructed to stop counting and memorize they are being asked to develop a new tool to help them see the answer. The Math-U-See curriculum focuses on giving them effective and alternative strategies which intentionally pave the path to memorization so they can store the needed information in their long-term visual memory.
The key to no longer needing to count to add is subitizing. Subitizing is the ability to see a small group of objects and know the amount without counting each singular object. A common example of this is dice. By regularly playing games involving dice we are able to roll a 4 or a 5 and, without counting, quickly know the numbers that are represented. Another example of subitizing would be Legos. If your student often builds with Legos you will notice while they do not count the knobs, they are able to quickly fill in spaces with the correct block or two without counting.
Math Manipulatives: The Secret Sauce
With the Math-U-See program, the blocks are more than just an option: they are an integral part of the mathematical learning process. Through intentional use they become a tool not only for understanding but to be able to see facts and remember concepts. The blocks and the strategies combined provide the important bridge to committing math facts and other formulas into long-term visual memory.
Intentional Order of Mastery
The order in which math facts are presented is another key to escalating fact success. Once the zeros, ones and twos are memorized along with the Commutative property, the student is ready to find success with eights and nines, because of the way the Math-U-See program connects them to the mastered ones and twos. Once the eights and nines are mastered, there are only a few addition facts that remain. Taking the time to solidify the addition facts along with what makes ten and the introduction of algebraic thinking with solving for the unknown, the student will find a higher level of success when they spend the second half of Alpha mastering subtraction.
Here at Demme Learning we get excited when supporting parents, especially those with older students who have been striving for success and need the tool of fact mastery to achieve that success.
So let’s take first things first. It is important to pause and evaluate exactly which of the addition and subtraction facts your student knows without counting or long pauses. With that clarity it is easier to put together a plan which will replace the need to count with a strategy intentionally designed to strengthen your student’s fact mastery in the most time and cost effective way.
Due to knowledge of the materials and years of learning from the parents we talk to, we have designed support strategies which we are privileged to share with you to assist you in building a plan to fit you and your student’s specific learning needs.
We all know the importance of math fact memorization as a part of the framework that underlies success in all math concepts. One of the most common “go to” math manipulatives students use to learn their math facts are their fingers.
Some students are able to transition from finger counting to rote memorization. However, many become more reliant on finger counting and do not transition. I have no doubt there are mathematicians out there who, as adults, have figured out how to be successful without mastering facts.
Most of the parents I speak to regarding their struggling math student report that the student is still counting to solve single-digit math facts. Many parents who themselves struggled in math know the limitations of finger counting.
Long-Term Effects of Counting on Fingers
Often the finger counter can “get by” for a few years. However, the wheels often fall off when they encounter long division. With all the steps involved in long division, even when the student understands the concept, the process becomes cumbersome due to working memory over load. The bottom line is that there is only so much room in the brain’s working memory to process the growing complexity of more advanced math concepts. Finger counting requires the use of working memory. There just is not enough room, or as my colleague told me recently, “Finger counting drains the battery.” That “shut down” you may have observed in your student is not intentional or a lack of intellect; it is how the brain is designed.
The Role of Subitizing
For the student who has learned to add, subtract, multiply. or divide by counting fingers, there is no other place for them to look for the answer. The answer is not in their mind (unless they envision the counting there.) It is important to replace the physical action of counting with a better, more effective tool. The most effective tool will be some form of subitizing.
My favorite way to describe subitizing is, “To suddenly see without counting.”
Think about what you experience when you roll dice and you see a four and a five. Through repetitive exposure of the same pattern combination, you eventually do not need to count the individual dots and know immediately the combination is nine. Another example is building with LEGO® blocks. As a child repeatedly plays with these blocks, they no longer need to count the nubs on the top to distinguish between the pieces. If they run out of a specific size block they quickly learn that they can substitute smaller blocks to replace the larger missing block. This is what subitizing or using visual memory “looks like.” Research shows that rectangular and dot arrangements are the easiest to retain in long-term visual memory.
Students of all ages are unfairly judging themselves as “just not good in math” because of the missing tool of fact automaticity. It is important to think of fact memorization recall as a vital tool for math success. For many students, their reliance on finger counting is preventing this tool from developing.
Story of Success
In closing, I tried to think of a specific story to share with you to personalize this topic and provide an example of hope.
The “story” has been shared with me hundreds of times over the past 25+ years collaborating with Math-U-See parents. It is more important to me to speak to the heart of you, the parent who has tried everything to encourage your student to no longer count on their fingers to solve math facts. I hear your concern every day in my phone conversations that you have tried everything. You may be just discovering the effect it is having on your student’s ability to find success as math concepts become more complex. Your student could be anywhere from 6-16 years old. Some of you are homeschooling for the first time; others have always homeschooled. You have not failed your child.
Many curricula teach counting as a pathway to learn math facts, and for some it does work. Most students, whether they have it modeled to them or not, will discover the option of finger counting if counting is presented as a process. You did not know it would become an ingrained habit instead of a temporary method. If you personally still use counting to solve math facts yourself and consequently do not feel confident in math, think of it is a bonus, not a limitation. To model to them your willingness to seek solutions to set them up for academic success and learn alongside them will one of the most important lesson you ever teach them.
There is a reason I have the word WE in the title. So often, this is where many parents assume they will not be able to support or continue as their student’s math teacher.
However, I suggest this is the best opportunity to hang in there. Modeling to your student how to approach material you feel is challenging might be the best instruction you ever present. In fact, if you find there are times your student ends up teaching you, consider that a bonus! When a student is required to have to figure out how to explain a concept to someone who does not quite “get it”, they understand it more deeply.
Regardless of you and your student’s math confidence, pausing before heading into Algebra 1 will have great benefit.
5 Tips for Algebra 1 Success
Success in Algebra 1 requires not only a solid understanding of Pre-Algebra but basic math concepts as well. More than once, while offering Algebra 1 support the student will indicate they thought they were done with fractions and struggled with them previously. This is a perfect time to assess if you or your student need extra support with concepts such as fractions or decimal. You might find our Algebra 1 Readiness Test helpful to pinpoint any gaps.
2) Encourage Showing Work
While mental math is important, you will want to see the process being used. This will also help you identify if there is an area of struggle that needs to be reviewed or if an incorrect answer was merely a careless error. Additionally, if you contact us for a post-evaluation consult, we will be able to more effectively assist you.
Take note of any areas on the assessment where the student either struggled or needed to be reminded of how to complete a problem.
4) Shore Things Up
In any areas you or your student showed lack of immediate recall on the assessment, take the time to lock these concepts in. Take the time to solidify even the most basic concepts. There is no shame in having some missing pieces. The shame would be if you and your student are actually ready for Algebra 1 but struggle due to not having efficient, strong, basic tools for success. Most of the Algebra 1 calls I support are not about Algebra 1, but rather the inability to be able to look at the equations and simplify by applying basic math concepts.
You will find the solutions and corresponding levels/lessons for the previous levels of Math-U-See here. You may find that you only need to use our worksheet generator for practice and review. Print off the relevant sheets and complete just a few problems a day (e.g. no more than 3-4 problems) until they can be solved confidently. If you feel that you or your student need a more in-depth review, contact us for a consultation. We have solutions that are timely and cost effective for these situations.
One of my favorite support experiences was with an 18-year-old customer I will call Alice. When she called for support, it was obvious she needed to go back and review some basic skills. She indicated she was just “not good in math” but needed to complete Algebra 1 as soon as possible because her focus was on graduating. I suggested that it was more important to become solid in Algebra 1 to prepare her for success in the next required levels and beyond. I knew without this, that I would likely not be able to offer her much support. She was willing to slow down and work toward mastery of the material. When she couldn’t wrestle it to the ground herself, she would call for support. Math was a challenge for Alice, but she was able to successfully complete Algebra 1 by the end of the school year.
It was a privilege to see Alice develop into a confident Algebra 1 student. Had she not been willing to slow down, review, and set herself up for success it could have ended much differently.
To me it seems as if Algebra 1 is often the transition into the adult world of math and life. It is an opportunity for many students to pause and learn personally what they need when facing a subject that does not come easy.
Also, remember if the two of you can’t figure a lesson out together we are here to support you.
You’ve got this!
As the school year winds down, parents are faced with the question of what to do to keep math thinking alive during the summer. A creative bridge between your accomplishments of this year to the beginning of the next provides opportunity for a successful transition in those early back-to-school weeks.
4 Tips for Summer Math
1) Be Honest with Yourself
Create a strategy that you will be able to follow through with. Remember that you are on a school break as well.
Keep formal academic practice brief. For example, if your student spent the end of the school year learning multi-digit multiplication, put one problem up on a wipe off board daily to keep the process fresh.
2) Evaluate What You Worked on Last Year
What might still be a little fuzzy? You many find that consistently spending five minutes on practice a few times a week will serve your student well and keep them from needing to totally relearn the same concepts in the fall.
A fast track of math fact mastery is a great summer project. I have discussions daily with parents whose students from 7-16 are struggling to memorize basic math facts. One of my past blog posts, How to Teach a Child Math Facts, focuses on effective strategies that work well with brief consistent sessions.
3) Add Puzzles to the Mix
If I could re-school my children, I would include more puzzle solving in their lives. These could be anything from formal puzzles to life situations that invoke moments of pausing and gathering what we know to solve what we do not know. As they move into higher mathematical thinking, confidence in this kind of reasoning will be of great benefit. Math and puzzles go hand in hand. As you enjoy your vacation, be on the lookout for opportunities to solve situations that naturally arise with a simple problem-solving conversation that starts, “Ok, what DO we know?”
4) Look at Art
As an artist, I have found math concepts connected to art are what have not only improve my art but also given me a love of math. Perspective, ratio, angle, line, balance, graphing are just a few of the obvious. An example would be to visit a farm or gardens, which consist of rows. This could be a single discovery day or make it a multi-day/summer project. While there, pause and observe what you see and know. Gather clues. What size are the plants right in front of you? How about 20 feet away? They look smaller, but are they? Is there a point where all the rows seem to come together and become one or vanish? See if you can find the natural horizon line. Really look at what color(s) are there. One of my favorite arts instructors always said, “Trees are not just green!!” … and it is true! What actual colors are in the sky? Enjoy some time taking photos from different angles.
You will find additional ideas for math art, game and apps in Scottie Altland’s blog post Outdoor Summer Math Games & Apps.
The most important thing is to enjoy your time together this summer. As all grandmothers will tell you, the time passes.