How Do Our Beliefs in Math Affect Our Students?

I was honored to work with amazing teachers this week. We took a survey from NCTM (National Council Teachers of Mathematics) on our beliefs regarding student learning and our instructional practices in mathematics. This, in itself, led to amazing discussions about what we truly believe math IS and how we interpret that into instructional decisions within our classrooms.

But then we took it further. We got into groups and discussed not so much whether we agreed or disagreed, but whether it was a productive or unproductive belief in respect to student access and learning.  Here are two to consider:

There were fantastic discussions about these particular ones, especially for educators of EL and SPED. We also considered how parents might respond to these. Powerful conversations around access, flexibility in thinking, understanding conceptual and procedural mathematical ideas, and yes, fluency.

Here was the point. Our beliefs, whether productive or unproductive, affect our attitudes towards mathematics and the children we are blessed to teach. Those attitudes affect the actions we take. Who gets to answer which questions? Who gets the “tough” tasks and who has to keep doing drill and kill worksheets? Who gets to explore puzzles and who has to retake tests or do homework (because their home life doesn’t lend itself to being able to do it at home)? And those actions MATTER. They affect the results you will get from your students.

Belief chart

So as you gear up for this school year, consider taking the beliefs survey yourself. Even better, have your team take it and REALLY dive in to what beliefs are productive an unproductive. The more we reflect, the more we can grow and be effective at what we truly want; to teach students to love, learn and understand mathematics. Have a great year!

For the beliefs survey: 2017_06_19_Holstrom_Grady_2BeliefsSurvey


How Do Our Beliefs in Math Affect Our Students?

Playing with Math: The Function Machine

I love this game, because you can tailor it to the level of your child. Any child, preK through adult, can play and find it challenging and fun!

The Function Machine

Grade Levels: Any, depending on how complex you make the function.

Materials: paper and pencil (whiteboards or Magna Doodles are great, too!  We just used the Magna Doodle in the car on a 3-hour drive and it worked great!!)

  1. Draw a function machine. It need not be fancy, but if you google image function machines you will get tons of ideas. function machie twoMine (as I am on the lazy side) typically look like a rectangle with an opening at the top (for the input) and an opening at the bottom (for the output). They are just very boring and sad. The one to the right is super cute and soooo not me.
  2. Choose a rule (function) to use. So my rule for my PreK could be “one more” or “+1”.
  3. Your child gives an input number. You give the output number. Example: My son loves the number 5 (after all, he IS 5).  So he would put in the number 5 and I would tell him the output is 6. [It is better if you make cool sounds as if the function machine is DOING something. This is supposed to be FUN, remember???]
  4. Your child keeps guessing numbers, as you fill in the outputs each time, until they realize the pattern and can express it either in words or as a ‘math rule’ (expression). If they guess the rule wrong, keep playing until they get the correct rule.
  5. This is really fun when you have more than one kiddo playing. However, they may only guess when it is their turn. That way, everyone has a chance to play and learn.

Let’s Try One! 

  1. You enter 5 into the function machine. beep boop beep boop! Out comes 7.
  2. You enter 2 into the function maching. beep boop beep boop! Out comes 4. (Got a guess for what the function rule is????)
  3. You enter 10 into the function machine. beep boop beep boop! Out come 12.
  4. You say the rule is “plus two each time”. Yup! The rule is the machine adds two to each input (or y=x+2 for your middle schoolers).

Suggestions for Different Grade Levels:

Grades K-2: add 1, add 2, add 5, add 10, add 100, subtract 1, subtract 2, subtract 10, subtract 20, etc

Grades 3-5: same as above (Fluency in arithmetic is important!) and multiply by 2, multiply by 5, multiply by 10, take half, divide by 10

Grades 6-up: combine operations multiply by 2 and add 1 (2x+1), triple a number minus 1 (3x-1),  a number times itself (square it), take half of a number and add 1 (1/2x+ 1), etc. You can also include negative rules as well (like multiply by -3).

You can also create a function table and just fill in as input/outputs as well, if they are above having a cute function machine. I have inserted one below as an example. function table

These are so great for trips and such, because all it takes is a napkin and a pen (and your rule). Finding relationships is imperative for algebra. This is a great way for kids to play with the ideas they need for later mathematics!


Playing with Math: The Function Machine

Cool Tools for Kids in Math

Happy Mother’s Day AND Teacher Appreciation! Here are my gifts to you: FREE APPS and Sites to help your children (and students) learn math!!! Read on!

These past three days I got to geek it up at the NCTM annual conference in San Francisco. I have gone to several annual conferences, but this was the first time I worked in an exhibitor booth rather than attending as a participant. I was excited to be on the other side of the conference scene, but sad that I wasn’t sitting on the carpet (like so many) scouring the magazine o’ options for the perfect sessions.

As a teacher, I would ditch the exposition hall (except to get the free Legos and swag for my boys!) and attend every session I could. I would take copious notes, trying hard not to miss anything that was said in case THAT was my take away for the trip. Those fabulous notebooks that I poured my 72 hours of the conference into gather dust in a box in the garage. Don’t get me wrong; I would typically use 3-5 ideas/worksheets/tasks/quotes per conference. But was that worth the hours I sat in the back of a crowded room? Was there more to the conference than the sessions?

YES! This year I attended a single 60 min session and got several great ideas for a district I work with. The rest of my time was spent in the exhibition hall talking to reps (and long-time friends!), discussing mathematics, and truly learning from one another in a more intimate setting. I learned so much in these conversations, AND spent time at many vendor booths playing with the technology that I believe can truly make a difference in how students view mathematics. Though I am still grappling with the lack of notes in my handy-dandy notebook, I feel I am leaving with far more applicable ideas and tools than ever before!

The links below are (free!) sites you and your child can explore to really learn mathematics. They allow students to truly see what is going on and why the math “is what it is”. I hope this summer you are able to spend some time on these sites and give your students an opportunity to open up mathematics in amazing ways.  

Note to teachers: These are open source and free to use on your devices at school. You are welcome!

NumFu: fu

Currently their Mastering Addition Facts app is free. Get it now before they change this! Students work on their math facts in a developmental way, understanding as they gain mastery. (They do have a multiplication app as well, but it is not free.)



This is a site that allows you to graph functions, plot tables of data, evaluate equations, explore transformations, and much more! Desmos



Geogebra makes a link between geometry and algebra using visual representations students can manipulate and finally see what is going on mathematically.Geogebra 2


math Learning centerMath Learning Center:

These apps are amazing! So many to choose from to help students conceptually understand mathematics. There are number lines, geoboards, money pieces with a number rack, rekenreks, ten frames, pattern blocks and more! Just allowing your child to play with these apps will enhance their understanding of number! Here are just a few from the site:math learning center 2

 Finally, this is a book that came highly recommended. Though not free, it can be a support for parents in navigating Common Core mathematics. (It does come with videos as well!)CCSS Math

Cool Tools for Kids in Math

My Nightmare Learning Algorithms (And Why I Am Thrilled We Now Encourage Multiple Strategies!)

CCSS math debunkIf you are on Facebook, you have seen this (or one similar to it), usually followed by stating that a certain set of standards are evil and we should be teaching the kids drill and kill through the “right way”. So let’s clear the air (Or let me fill it with hot air and you can comment below. Bring it on!).

To start,  “our way” is not the way of all. The step and structure with which we add, subtract, multiply and divide are not used by all countries. In fact, these methods are just some of the many ways students can simplify problems using these four operations. The ones we traditionally use are examples of “algorithms”. If used correctly, each will work for different number types and you can get “the right answer” pretty quickly if you have had lots of practice with them.

CCSS math debunk 3BUT THEY ARE NOT THE ONLY ONES! And I would fight the good fight that there are MUCH easier ways to get to the value using other strategies. I will even throw myself under the bus and tell you that I do not use the traditional multiplication algorithm. I make too many mistakes when I use it. I know it, but there is another method that works just as fast for me, and I get the correct value using it. And long division? Ugh. Why not just start with something I know, chunk it out, and get to easier numbers??? May look a bit odd, but still it is faster than sitting there trying to find out how many times one value goes into another (More on this division idea in an upcoming post for all you 4-6th grade parents!).

So think back to your elementary days. How many days were spent drilling the algorithms you now know (or pretend to know since you use a calculator instead)? How many hours? For me, it was a nightmare. I didn’t get them. I didn’t know when to move a little 1 (And why was it so tiny if it meant a bigger number???) in addition, why we crossed out stuff on top and not only moved it over, but made a double digit number in subtraction (What happened to my little 1 friend in addition? Where did she go???), when to put an “X” and why the heck were we even using an X in multiplication when it isn’t even a number, and so on. I was confused, and I covered it up by checking with a calculator and fixing each line to pretend I knew what I was doing. It was horrible, and I felt stupid, slow and sad.

CCSS math debunk 2I had my a-ha moment in seventh grade. (So it took EIGHT YEARS to finally figure it out.) My math teacher took me out of science, my favorite class mind you, to have a double dose of math. (Great. Now I get to hate it twice as long.) However, he started showing me other ways to do the math. What other countries and cultures were using to figure out the exact same problems, but with visuals and graphic organizers and all kinds of craziness. It was wonderful. It was a breath of fresh air. It was my lifeline to true mathematics.

You see, math isn’t just about calculating. I think of mathematics as finding patterns and relationships in and among quantitative items, and using those patterns and relationships to create rules, strategies and “algorithms”, prove or disprove others (And my own!) rules and algorithms, and figure out how the world works on a quantitative scale. It is beautiful. It is elegant. It makes life make sense.

Keep in mind, the standards DO say for students to eventually use our traditional algorithms as ONE STRATEGY for finding the values. But it is at the end of their journey of understanding. It is the final step of a long walk through discovery; using manipulatives, moving to visual representations, conjecturing student-strategies (whether they work all the time or not), and finally moving into the algorithm you all claim to know and love.

puzzle piecesThink of a puzzle. My husband starts with the border. I start with the middle and the pieces that have the same color or object. Yet we will both finish the puzzle, even though we went at putting it together differently.  Some of the representations will be easy for your child, others a bit more difficult until they understand how they are relating to the operation. Yet, they will get to the end and finish the puzzle, even if his struggles are different than another’s. That is why working together is so important. We can help each other make sense and persevere to the end!

So, at the beginning of another school year, take a deep breath. Give different models and strategies a chance. Ask for help in understanding how the strategies or models work and their significance to understanding an operation (Send ME questions and problems!!!!). Encourage your child to try something new, and be supportive. As the child who needed something different, I thank you. 🙂

My Nightmare Learning Algorithms (And Why I Am Thrilled We Now Encourage Multiple Strategies!)

Helping Your Child With Math HW: Some Don’ts and A Lot of Do’s

The struggle is real. Your child is frustrated, you are frustrated, and the homework you both have been working on STILL is not complete. Your child screams, “You aren’t doing it RIGHT…That’s NOT how my teacher showed me…I HATE math!”

Here are the 2 mistakes we as parents make. Since it is the beginning of the school year, let’s really make an effort to abide by these Golden Rules. These are followed by helpful hints to make it a successful year in mathematics.

Golden Rule #1 (Even if you dislike math A LOT) Never Ever say negative remarks regarding your abilities in math or about math in general. I cannot tell you how many Student Study Team meetings began with a parent saying, “Well I was never good at math”…That is your golden ticket for your child to say the same thing, and think it is okay to just give up. It is not okay. Would you admit that you couldn’t read? No. So just don’t say it. Don’t say the homework is “stupid” or disrespect your child’s teacher in front of her. The results will not improve her performance or her efforts in her math class. If you have a problem with the mathematics coming home or with your child’s teacher, discuss it with the teacher.

 Golden Rule #2 Do not do your child’s homework for her. I often tutor my family and friends. My favorite comment is, “I don’t get (insert child’s name) math homework. Can you come explain it to me?” Though I would love you (the parent) to understand the mathematics as well, you should not be the one doing the work. Your child needs to do the work, needs to struggle and figure out where he is lost, and needs to feel what it’s like to finally “get it”. That is the goal of the homework, not just completing the problems.

Ways to Help Your Child With Mathematics

  1. Set a schedule. Your child should do his homework at a regular time each day. My son’s schedule is crazy: Cross Country in the am two days, in the pm two days, and Youth Group one night. Yet the schedule is the same every day. Whatever time he gets home, he eats something (whether it’s a snack or dinner) then gets down to homework. He knows this is the routine, so there is no griping.
  2. Set a standard place to complete HW. It is a pain, but I like him to do his homework at the dinner table. He can spread out, and I am usually fixing (or cleaning up) dinner nearby to ask questions when needed. We have a side tray table with materials he may need (paper, calculator, pencil, colored pencils, etc) set up for him so there is no reason to leave the space.
  3. Encourage. Encourage. Encourage. The students whom I hear the most from aren’t the ones who got it the fastest. They are the ones who put in the effort, with me cheering them on through their frustrations and never giving up on them or their learning mathematics. It means the world to your child to know you are rooting for them to be successful (Even if they won’t admit it!).
  4. Give directives/Ask questions FIRST. Here is a list of prompts and probing questions to move you along.
    • Tell me what you are doing (or working on).
    • What did you do in class that was like this problem? Do you have an example in your notes we can look at? Let’s re-read your notes and see if that helps you remember.
    • Could we call someone from your class? (This is great with social media. They can facetime, Skype, Google Hangout, etc. Get your kids to make study groups from friends in their classes!)
    • Let’s look in your math book and see if the examples from the section you are working on will help us.
    • Does your math book have video tutorials? (Most do! Get the login and password from your teacher BEFORE a crisis!) Let’s watch it and see if it helps us understand more.
    • What did you try first?
    • How did you get that answer? Explain it to me.
    • What is the pattern?
    • What doesn’t make sense? Where did you get stuck?
    • Does your teacher offer tutoring tomorrow morning? Let’s get you there!
  5. Email me the math! Love to blog about math problems in REAL time!
  6. If none of this is helping, and your child has worked on her math homework for over 30 minutes will little (or no) understanding, STOP. I would email her math teacher and ask for advice. Explain the attempts made and where your child is stuck. Most teachers will be understanding and give her more time. If the teacher does not, request a meeting with just the two of you to discuss the difficulties your child is having and intervention options the teacher (or school) offers.

Good luck and have a great year support your child’s success in mathematics!

Helping Your Child With Math HW: Some Don’ts and A Lot of Do’s

Top 5 Things NEVER to Do/Say AGAIN When Helping Your Child With Math!!!

What we want is to see the child in pursuit of knowledge, and not knowledge in pursuit of the child.   

George Bernard Shaw

Happy Teacher Appreciation Week!!! I had a blog all good to go with stories from my own edcuational journey, my son’s, and others. Yet it didn’t seem to fit my purpose, which is to support parents in helping their children with math. So I decided to let y’all in on some secrets. Here are the top 5 things teachers wished you would never do (or say) when helping with math. Likewise, here are the top 3 things teachers wished you would always do when supporting your child in math.

Top 5 Things NEVER To Do Again When You Help Your Child With Math

  1. 7cd05c2267bceac7ba2101dc4624d14dNever say, “I wasn’t good at math.” This goes for teachers that do not teach mathematics as well! In fact, on my most recent blog, many responded (on FB) that they were never good at math, nor would they be good at math now. This self-deprecation has to stop NOW!!! This is a cop-out, and it allows your child to think it is okay to be illnumeric (Yeah, totally made up that word.) Would you admit to your child that you couldn’t read or write? Would that be acceptable in your home for your child not to be able to read or write? Heck no! So just stop.
  2. thDVCZDEMMNEVER say the homework is stupid, boring, ridiculous, etc. in front of your child. Jo Boaler, a mathematician out of Stanford University, has done a ton of research on the correlation between student effort and performance in mathematics. Bottom line: the more effort you put in, the better you do. To learn mathematics takes effort, time, and perseverance. You may not like what your child is doing, but relay that message to the teacher, not your child. And please do not write a derogatory note on your child’s homework. This negativity leads your child to believe that he can choose to do some work and skip other work because it is uncomfortable. Would that fly in a job atmosphere? Can I choose to do some of my job-related work and ditch the rest because it is boring? NO, I cannot. Please, support your child at home. Encourage him to try his hardest. “Play” with the problems. And if he goes over the research-based homework time (According to Robert Marzano, 10 minutes per grade level. So for grade 3, 30 min.) take a break, and email his teacher.
  3. 185255772NEVER do the homework for your child! My favorite story about this was with a young lady who was perfectly capable of doing the homework, but got stuck and didn’t know what to do. She asked her father for help. He literally took the pencil from her daughter and wrote it out for her. You could see on the page where she stopped and he began. When I pulled her aside and asked her, she said, “Well, he thought I couldn’t do it so he did it for me.” What did that teach her? When it gets too tough, give up and assume someone else will do it for you? If you want to help, ask questions. But don’t give answers.
  4. stopwatchNEVER EVER attribute brilliance with speed! I am at fault for this. When a toddler can do something quickly, how do we respond? “Wow! You are so SMART.” No, you just already knew how to do it. Children are brought up thinking if they don’t know the answer to a math problem immediately, they are dumb. That is sooo not true!!! Mathematics takes deep focus, diligence, and perseverance. Encourage effort, not speed.
  5. thJ6P17D2JNEVER make excuses for your child to get out of the work. Look, life happens. We teachers get it. Things come up. We love it when you communicate with us, especially when unforeseen circumstances arise. However, your child is still responsible for the work. It may be late, but should still be done. I used to cringe when my middle school student would come in with a big ol’ grin and say, “My mom said I didn’t have to do this and here is the note!” Work it out with the teacher, not your child.

Top 3 Things To Do Right Now To Support Your Child in Math

  1. you can do itEncourage effort. When your child gets frustrated, you can absolutely say that math was tough for you too. BUT MOVE ON. What are the resources she has to support the homework? Was she given examples in notes? Did she already do some of the problems (to look at to refresh her memory)? Are there videos on-line to help? BTW: Many publishers have on-line support via tutorials. Ask your teacher for the link, login and password! Does your teacher offer tutoring? Encourage your child to attend. All of these resources will continue as she moves through education. These are great tools to learn how to access now!
  2. QuestionsAsk questions. My favorite story was of a grandfather who took care of his granddaughter after school. She ended up getting her doctorate (I believe). When asked what contributed to her success, she said it was all the help her grandfather gave her with her homework throughout her time in school. Little did she know, her grandfather was illiterate. He simply helped through questioning. You don’t have to know the math. You need to have good questions to ask.
    • What homework did you have in math today? Show it to me. (Yes, even my child has said his homework is done and…ooops! Still have a few problems left to do…)
    • Tell me what you have tried and where you think you are getting stuck. (Not a question, but a great place to start.)
    • What did you learn in class today that could help you with this? Let’s look it up in the index (if they have a book at home) and see if we can go through the lesson together.
    • Do you have notes from today? Let’s re-read them and see if they can help us.
    • Do you have a problem already done? Let’s go through the steps and see if that refreshes your thoughts.
    • What do you know? Where are you stuck in the problem?
    • Could we go online and look up how to do _______?
    • Who could you call to ask for help? Could you meet with them before school/lunch/etc? (I offered my room for study groups. Kids would come and work together on the homework. Awesome to listen to them help each other!)
    • When does your teacher offer tutoring? Let’s take you to get some support.
  3. Parent teacher ConferenceBe in communication with your teacher. You are your child’s greatest advocate. This is critical in middle and high school, where teachers have up to 200 students a day! Email the teacher when your child is stuck. When he is frustrated. When things get difficult at home. When we had our second child (ten years later), my oldest started slipping in school. I emailed his teachers what was happening, and they were super supportive, giving him the attention and help he needed to get back on track. Teachers do not know what is going on in their students’ outside lives unless you help them know. Help your child by keeping the lines of communication open!

Notice none of my suggestions encouraged you to become a mathematician. Just be a support for your child, encourage effort, and keep in contact with his teacher. These are the greatest gifts you can give a teacher (and your child!). THANKS!!!

To read more from Jo Boaler:

Top 5 Things NEVER to Do/Say AGAIN When Helping Your Child With Math!!!