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Overcoming the Challenges of Math Teams


 I’ve been doing a lot of presentations and working with different groups of teachers, which I love.

I wanted to make sure you knew that we’ve added some new videos and lesson plans to the site such as:

 

1.) Subtracting Decimals Using Base 10 Blocks (two parts) (Grades 4/5)

2.) Subtracting Multi-Digit Numbers using Base 10 Blocks and Subtracting Multi-Digit Numbers using Invented Strategies (Grades 2-4)

3.) Solving One-Step Addition and Subtraction Using Symbols and Unifix Cubes (Grades 3/4)

4.) Solving Percent Problems using Models (Grades 6-8)

5.) Introduction to Decimals Using Base 10 Blocks and Introduction to Decimals Using Grids and Number Lines (Grades 4/5)

6.) Building Place Value Understanding (Up to 4 Digits) (Grades 3-5)

7.) Add By Making 10 (Grades 1/2)

8.) Building Place Value Understanding by Making 10 (Grades K-2)

AND MORE!

 

Check them out! Also, please send me requests for videos. I focus on the topics that I see as trouble areas for most students, such as subtraction. If you have a concept that you’re not sure how to teach conceptually and you don’t see it on our site already, please let me know!

Now that the housekeeping is taken care of, I wanted to write a bit about the Math Teams. Last school year the classes that I worked in all took to the team format really well but this year it’s been more of a challenge. I’ve learned a lot and wanted to share with you some of the things I’ve tried and that have worked well. For those of you that haven’t signed up for our Collaborative Math Teams Course, check it out to see if it’s something you might want to try. I find that math teams do an amazing job at engaging students in the math itself and also in developing the curricular competencies that you will see in our new curriculum. In fact, I’m convinced that using partners and/or teams are the only way to allow our students the opportunity to develop the competencies and I would argue that the competencies are just as important (if not more so) than the content. If students have strong competencies in reasoning, analyzing, understanding, solving, communicating, representing, connecting and reflecting then I believe they are well equipped to learn any new content. These competencies ensure students have conceptual understanding and so are not reliant on memorizing procedures.

“Some students just don’t get along well with others. This a crucial competency for being successful in life. Considering that the skill of being able to work collaboratively is the most important employability skill, this is a big problem.”

Even though the teams work well for the most part, there have been a few groups in each class that are struggling. I’ve identified the three most common challenging behaviours I’ve experienced and then shared with you the solutions I used to resolve them.

Challenging behaviour #1: Not Doing their Role

For example, some students won’t record the groups’ ideas, won’t include everyone, won’t lead the group if they are the organizer etc. Also, some are just not doing the math. They are distracting, talking off topic, copying from others etc.

Solutions:

First, we changed the groups from four students to three students and altered the group roles a bit. The Includer role is now combined with the organizer. See here for the new roles . We also started to give an ‘independent question’ at the end of lessons where they’d already had some time (at least two lessons) to learn the concept. This helped us to see who was ‘getting it’ and who wasn’t and we were able to narrow it down to two or three groups that weren’t functioning well. We then ensured we spent the bulk of our time with those groups and coached them to work together better. This was a slow process but after a few weeks the teams are functioning way better and they know that we will be there to guide them if they cannot work well on their own. Many needed this coaching to interact in a respectful and helpful manner with their peers. We had to coach them on everything from the harmful effects of saying “I told you so!”, to wasting class time. Lastly, we gave them specific feedback on their group processes on certain days (rather than feedback on the math). We had them do group reflections and then share out and then we shared what we noticed. The focus on the importance of the group processes was helpful for shifting the unwanted behaviour.

Challenging Behaviour #2: Not getting along

Some students just don’t get along well with others. This a crucial competency for being successful in life. Considering that the skill of being able to work collaboratively is the most important employability skill, this is a big problem. It is our job to provide opportunities for students to develop this skill and the only way I can see to do this is to continue having them work in teams. I’m not going to lie to you, there times when I thought the best thing to do is to just switch them out of their teams, but then they never get the opportunity to sort out their problems with their peers. I worried that some students just wouldn’t be able to work well with anyone but many of these students have actually made huge leaps in their ability to cooperate. There are still a few students who are struggling, but I’m seeing improvement and believe that with continued support and explicit teaching and guidance, they too can learn how to work with others. I’ve realized that this is a really new skill for many students. They simply don’t know how to work with others and we need to teach it explicitly.

Solution:

We started using parts of some lessons to do activities that are designed to teach some of the required skills of collaboration such as: helping others and communication (both listening actively and explaining). I’ve been using activities such as ‘The Broken Circle’ activity in which students are only successful when they help others first and realize that they can only be successful as a team (working as an individual will result in failure). We also did the ‘Master Designer’ activity in which students had to explain their design in a way that others could recreate it without seeing it, just by using verbal instructions and hand gestures. This one was amazing; students realized how difficult it was to not only communicate their own ideas but also interpret others’ instructions. They realized that we all have totally different interpretations of things and that they need to ask good questions, be curious and open-minded in order to communicate well with each other. Lastly, those that struggle to get along in general, we have identified and are providing coaching for them. We work more often with their group and help them to rephrase their words into more kind, inclusive words and if needed help them to identify what else they struggle with (if they don’t like moving at the pace of group we help them to see the benefits of thinking more deeply and differently about the concept).

Challenging Behaviour #3: They just tell the others the answers instead of guiding or coaching them

Solution: I included more general coaching questions on the new roles sheet (see above link). We also gave them coaching cards that were designed for the specific topic they were working on. This is an example we used for multiplying two-digit numbers. We also had students reflect on what they could do on their own that would help their group members understand the math rather than just telling them procedures. It was fascinating for me to watch how ingrained procedural knowledge is in these students and how unfamiliar conceptual understanding is for them. Incidentally, most of these students (who are very procedural) have very little retention of what they have ‘learned’ in previous grades. They could not multiply larger numbers, nor estimate and those that had remembered the algorithm couldn’t explain why it worked and could not estimate at all (they calculated and then wrote an estimate by rounding their answer). We set goals around this and we were more clear about the difference between knowing HOW to do a calculation and understanding WHY that process works.

 

“I sometimes wonder if this is the best way as it seems so difficult at times but then I think about how much more these students are learning, not just math but really important life skills (like working together and communicating well) and I am reassured that this is the best way I can help my students.”

 

I’ve seen some amazing improvements since doing this work (and it’s really hard work). I, like many of you I’m sure, sometimes wonder if this is the best way as it seems so difficult at times but then I think about how much more these students are learning, not just math but really important life skills (like working together and communicating well) and I am reassured that this is the best way I can help my students. Also, thankfully, I see improvements all the time. There are students who all of a sudden just start to ‘get it’ and become leaders in their groups in either their ability to collaborate or the math or both. Those moments always fuel me and keep me staying the course. I know this works because I see it and the students articulate that they see it and feel it working too. Good luck with your own teams – please comment or email to share your own experiences.

 

Educating Now
was created due to teacher requests to have Nikki as their daily math
coach. The site has lesson by lesson video tutorials for teachers to
help them prep for their next math class and incorporate manipulatives,
differentiated tasks, games and specific language into their class.
Teachers who use the site can improve student engagement and
understanding, in addition to saving prep time, by watching a 10 minute
video tutorial and downloading a detailed lesson plan

 

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Early Predictors – What I Learned from Dr. Daniel Ansari’s Webinar


Early math achievement is a better predictor of success in school in general (math, reading, etc.) than early reading!

I find this fascinating considering that there is WAY more funding and research of literacy than numeracy. For YEARS, I’ve been saying that numeracy is too important to always be playing second fiddle to literacy – hopefully we’ll see some more support, research and funding. The researchers don’t know why this is the case – but it does indicate that early math achievement leads to stronger executive functioning.

Understanding the numerical symbols is very important as is matching the quantity with the numeral. For kindergarten teachers this means students understand that 5 means ‘five’ and means  (or any other visual of 5 things). He also pointed out that there is a big difference between knowing how to count and understanding what it means. This is what I’m always talking about – conceptual understanding! Kids can count to 10 often at young ages but they are simply memorizing the words, like words to a song and may not really understand what they mean. Dr. Ansari and his colleagues have created a task that can be used as a screening task for students entering kindergarten and for those who are struggling in later grades.

Screening Tests/Tasks:

This task involves asking students to give you a certain number of items. For example, they have a bunch of blocks or counters, then you ask them to give you 5 blocks, then 6 blocks, etc. Students who can accurately give you the correct number of blocks have ‘knowership’ up to that number. Children may be able to count fluently but have limited ‘knowership’. This could be a very useful way to start the year – ensuring that those students who don’t yet have ‘knowership’ get the support they need!

Another predictor based on evidence is the ability to know which number and quantity are greater (symbolic being a greater predictor of success in future arithmetic tests). There is a FREE screening tool for grades K-3 for just this created by Dr. Ansari here.

How Can We Help our Kids Improve?

The great news here is that the best ways to improve students’ understanding of symbols and their respective quantities are to play games! Games that have a linear measurement component like Snakes and Ladders is great. In order for this to be effective, there must be numerals like you see in the image (for younger students just using a number path from 1-10 is great) and the child is moving a game-piece forwards (or backwards). It is the pairing of a linear model, with the numerals that worked the best in the studies.

Myths:

We only use 10% of our brain – this is not true. At All. Different parts of our brain are used differently all the time. When they do brain image scan it doesn’t show what areas of the brain are used (or else it would all lit up) but rather what parts are used MORE than others, thus the smaller highlighted sections.

Males are better at math than females. Again, not true at all. All of the evidence suggests there is no difference what-so-ever and so he wonders not only how this myth started but also why it’s still around.

There is no evidence to support learning styles. Some skills/concepts are better learned one way or another by most people. There may be some general preferences, like those who like to read rather than hear material but this does not equate to have a learning style.

Mistake don’t grow your brain. Yep, I’ve been touting this one for years as I heard it from Jo Boaler, who is a trusted source for me. Dr. Ansari says that this statement made by Jo is a misrepresentation of the data. This is from the abstract of the research paper that they are both referring to:

‘Findings revealed that a growth mindset was associated with enhancement of the error positivity component (Pe), which reflects awareness of and allocation of attention to mistakes. More growth-minded individuals also showed superior accuracy after mistakes compared with individuals endorsing a more fixed mindset. It is critical to note that Pe amplitude mediated the relationship between mindset and posterior accuracy. These results suggest that neural mechanisms indexing online awareness of and attention to mistakes are intimately involved in growth-minded individuals’ ability to rebound from mistakes.’

I summarize this as there is more brain activity when a growth mindset person makes a mistake than when a fixed mindset person makes a mistake. The attention to and perception of mistakes (as an important part of learning) is greater in people with growth mindsets.

Math Anxiety

There is evidence that students who feel panicky while doing math perform more poorly than those that don’t and that the areas of the brains that are more ‘lit up’ are the fear centers. Essentially, someone with math anxiety feels the same way when they have to math as I would if I was sitting next to a spider (my heart rate would spike, my palms would sweat, etc.). The research also shows that when this anxiety is happening the processing resources are depleted and thus why people can’t perform that math. Can you recall a time when you went blank on a test, only to panic and then never remember what you knew you knew? Me too. I think this is something we need to share with our students so that we can teach them how to calm their minds and bodies and not end up in that ‘fight or flight’ mode that will make learning or test writing nearly impossible.

He also showed the studies that I’ve read before about the correlation between female teacher anxiety and their female students as well as the correlation between parents and their children. One thing I found really interesting was the correlation between parents with high math anxiety who helped their children with math homework – it’s not a good thing! This tells me we need to continue sharing these findings with the parents of the students we teach and promote growth mindset messages at home and at school.

Coming Up Next:

This year seems to be especially busy with pro-d sessions that I’m attending as I’m also attending the Aboriginal Math Symposium this week, which I’ve attended for the past 2 years and have always found really valuable. In early June I’m attending the Canadian Mathematics Education Study Group in Squamish, which I’m also really excited about as I’ll be joining a group working on decolonizing mathematics. Finally, I’m excited to let you know that I’ve been accepted into a Post Graduate Certificate Program in Ethnomathematics at the University of Hawaii! I’ll be heading to Hawaii in July but most of the program will be online and I’ll be working within my community to engage in place-based math problem solving with local environmental, ecological or economic problems as our starting point. I will be sure to share with you all summaries of what I’m learning and how you might be able to implement the ideas in your own classrooms.

Parents – How to Help Your Children to Learn & Enjoy Math Part 3


I saved the best for last!

 

Who doesn’t love playing games?! This last post for parents on how to support your children in building number sense is all about games. So far, we’ve explored how math is all around us and how we can think mathematically while reading, baking, out in nature or anywhere (shapes are all around us!). We also looked at some websites and how to engage in math discussions for the whole family. Last post I wrote a bit about strategies and why they are so important. This post will extend this a bit to incorporate more games. Fluency is key and kids need plenty of practice to become fluent.

Last post I cautioned against using worksheets and flashcards as the ‘go to’ way to improve fluency. They simply don’t work for most (they may work for memorizing but NOT for developing strong number sense and although memorizing isn’t a bad thing, students need to do more than merely memorize; they need to understand the operations and numbers!). So what can you do instead? Play! Here are some games and activities that can be done at home, with minimal equipment.

Spend 10-15 minutes a day on these and your child will make huge gains in their number sense and fluency. I am going to start with more primary games and then move forward to more difficult concepts. That doesn’t mean that kids in grades 6 or 7 won’t need the first few games – many don’t know their “friends of 10”, in which case, this is where we need to start. Learning math is like building a house; there needs to be a strong foundation before we start building walls and ceilings or else it will all crumble down eventually (hitting the ‘math wall’ in grade 10 or 11[1]).

 

When I used to tutor, this is what I spent a good chunk of my time doing: playing games, but with the hidden agenda of building number sense and fluency. If you think about it, it is goofy to ask kids to add double digit or triple digit numbers by stacking them (thus reducing them to digits, not numbers) if they don’t even understand what these numbers mean.

I don’t expect many people to have math manipulatives at home (although HIGHLY recommend it), but luckily there are some free virtual manipulatives that you can use. If you are interested in buying manipulatives for the home, these are the ones that I recommend in order of importance: base 10 blocks, Cuisenaire Rods, Fraction Circles (these can be made at home using paper plates!). However, you don’t need to buy anything – you can print off some 10 frames and use buttons, dried beans, blocks, or any other objects you have handy. These can also be used for multiplication. No need for fancy store-bought manipulatives (especially if you use the virtual manipulatives).

Fluency Games (homemade – you only need dice, cards and other household items):

This handout explains how to play: Make 10 Go Fish, What’s Missing, Make 7 (or 9, 10, 13, etc.) and Memory.

Shut the box – this game comes as a board game but you can make your own as described in this youtube video. It’s a wonderful game for understanding how numbers can be broken apart and involves some great strategy and probability!

Dice/Card Games for Adding, Subtracting, Multiplication, Division: If you have playing cards you can remove the face cards and use these or you can use two dice. I (and kids) love different sided dice, like 10-sided, 12-sided or even 30-sided dice.

 

High- Low: I call this game ‘high-low’ and you can play with any operation (starting with younger kids, you could use two regular dice and practice adding –using manipulatives or 10 frames). Here’s how you play:

Each player rolls the dice (or flips the cards) and adds (or subtracts, multiplies, divides) the numbers. Then roll a regular die and if it is an ODD number then the person with the LOW scored wins a point and if the die is EVEN then the person with the HIGH score wins a point. The first person to 10 points wins. In the event of a tie, both re-roll and that winner gets TWO points for that round. For really young kids, just play that the high score wins to make it simpler.

As you’re playing, ask them how they are solving and this is a good chance to try out the strategies and talk about different ways.

Kids have such fun doing this and they are really just practicing their facts!

More card games for math than you could ever imagine (free!): http://www.pepnonprofit.org/uploads/2/7/7/2/2772238/acing_math.pdf

A few more card games developed by a teacher: https://docs.google.com/file/d/0B_wlnPzXZBUZRk0yNXFBd3dqTDg/edit

Fraction War: Use a deck of cards. There are two versions of this game depending on the age and skill level of the child. The beginner version is all face cards are 10 and the more advanced version is to make the Jack =11, Queen =12, and King = 13.

Divide the pack of cards in half and give each player half of the deck.

Both players flip TWO cards and make a proper fraction (less than 1). Compare the fractions by first benchmarking (estimating) to 0, ½ , 1 (if one player has a fraction close to 1 and the other has a fraction less than half, you already know which is larger). If they are both close to 1, then use knowledge of piece size and number to determine which is larger. This game can be played without using a common denominator (although this is helpful when they are very close together) most of the time. Common numerators are also handy and sometimes easier. We know that when the denominator is larger, the piece is smaller (because you have to break the whole into more pieces). This game is amazing for building fraction number sense and kids love it! If there is a tie (equivalent fraction) then both players flip over two more cards and this winner gets all 8 cards. The person with the most cards at the end wins the game.

Integer Game: use a deck of cards with the RED = NEGATIVE and the BLACK = POSITIVE. Each player gets half a deck of cards and one player is ‘negative’ while the other is ‘positive’. Both players flip one card and add (subtract, multiply) their cards. If the result is positive, then ‘positive’ gets the cards and if the result is negative, then the ‘negative’ person gets the cards. You can either remove the face cards or use Jack =11, Queen =12, and King = 13.

Online Games:

Greg Tang (http://gregtangmath.com/games)I love this site! There are so many games. I especially love the break-apart game but all are useful.

KenKen (http://www.kenkenpuzzle.com/#) – these are great puzzles to develop fluency and for fact practice. As I’ve mentioned many times before, these are best done with some discussion around strategies.

I need to note here that although there are SO MANY math games online, most are not great, which is why I haven’t recommended many. Most are focused on speed which, research shows, are detrimental to many kids and many games are usually just for memorizing. If you can disable the timing and have the opportunity to talk to your child about what facts they are struggling with and what strategies they are using, this is the best way to use these sites, if at all. There are some good sites being developed but they are not free. I’ve not tested them yet, but I’ve heard Motion Math is particularly good.

Apps:

There is a free app that I like, it is locally developed and called ‘MathTappers’. It has visuals so is better than rote memorizing and has basic facts practice and fractions!

 

Polyup is another free app that is great for number sense but suitable for older students (grades 6 and up).

 

Dragon Box is also fantastic but not free (it teaches algebra visually).

Board Games

Not all of these games are specifically designed for developing fluency but some do anyways (bonus!), while others are great for logic, problem-solving, patterning, etc. Remember, math is a LOT more than just computing. My grandpa taught me how to play cribbage when I was 8 years old and it was always something we did together when we visited. I have very fond memories of this time together! These games help to explore some of these other mathematical aspects (this is just a few- there are so many more!):

Snakes and Ladders (younger)

Sum of Which (https://www.sumofwhich.com/)

Prime Climb

Set

Racko

Blockus

Cribbage

Yahtzee

Tangos

Mastermind

Dominoes

Mancala

Chess/Checkers

If you have other games that you’ve been using please comment with your suggestions!

Have Fun!


[1] Hitting the ‘math wall’ is when a student who has not developed conceptual understanding and has only memorized math facts finally starts to really struggle and often fails to achieve success in their grade 10 or 11 math courses. It usually ends with the student forever swearing off math and any careers that require math. You may have had this exact same experience!

Parents – How to Help Your Children to Learn & Enjoy Math Part 2


Most adults use estimation and calculators to do their daily math, rarely do they get out a piece of paper and pencil, yet so many of us view this as what math really is: worksheets or textbooks.

There is often a big gap between ‘life math’ and ‘school math’. As we work on narrowing that gap at the school level, we are incorporating more estimation, sense-making, problem-solving and explaining and justifying why the math works. The great news is that you don’t need to buy anything to engage in these types of mathematical activities with your kids AND you can do many of these activities anywhere! Remember, math is all around us. 🙂

 

We want all students to be fluent in their basic facts, and many people think that means just memorizing by using flashcards, worksheets, etc. Fluency actually means: efficient, accurate and flexible. Flexibility is where we need to do more than memorize and extend further, to deeper understanding. Flexibility means that a person would choose a strategy that is best suited to the numbers. Here’s an example: If I wanted to mentally calculate 78-52, I would just subtract the tens and then the ones as the numbers lend themselves to this strategy (70-50 = 20 and 8-2 = 6 so my answer is 26). However, if the numbers were 101-97, I would ‘add up’ or find the distance between the numbers (image them on a number line) to get 4.

There are quite a few great strategies for subtraction that DO NOT involve regrouping and that are much more oriented to developing number sense. Many adults don’t know these well because they only learned the traditional way and so subtracting mentally is quite challenging as they often need to ‘borrow’ etc. This is way too taxing on the small working memory, especially for children, whose working memories are not yet fully developed. So, how do we become flexible thinkers? First, we allow students to problem solve and find strategies that work for them and then we provide lots of opportunities to practice the various strategies until they are efficient and accurate. This can be done in the car, while cleaning their room, sitting around the dinner table, out on a family walk, etc.

 

You can ask questions like, “What do you think 81-26 is?” and when they answer ask, “how did you get that?”, “Can you prove that your answer is correct?”, “How else could you have solved it?”, “Here’s how I solved it?”, “Can you understand my method?”

Praise their effort, creativity and math reasoning rather than getting the answer quickly. Accuracy is important so congratulate that too but really praise the process as much as possible. Did they really struggle and persevere? Did they get it wrong a few times before figuring it out? Celebrate this resiliency! Did they do something creative? Did they connect it to something else to help them solve it? All of these are worthy of praise.

 

See our parent page for a list of strategies that students may use if you are unsure of what kind of strategies might exist (especially for those of us who grew up memorizing our facts, without strategies – note: the list is not in any way exhaustive). Many ask why we can’t just get students to memorize their facts, why bother with the strategies, especially when they seem challenging. There are a number of reasons for this.

I’m not going to get into too much detail here but in order for students to use these facts in the future, they must understand them on a deeper level. Also, if they forget some facts (which absolutely happens) then they are totally stuck without strategies. Students need basic number sense and this is developed through understanding how numbers relate to each other, how they can be broken down and put back together and patterns within our place value system and this is developed by using the strategies, including lots of visuals!

 

10 Frames are great for adding and subtracting. Using blocks or pictures also help so many students to understand multiplication and division. If your child is struggling with the mental strategies then use visuals until they have constructed an understanding of the strategy. One final note: math (like any new learning) is supposed to be challenging. Let’s re-frame the struggle that happens when we are grasping a new concept from something bad or wrong to something good and expected.

Think about something you’ve learned how to do recently…you probably found parts confusing, got a bit frustrated (or a lot), made mistakes, figured out where you were going wrong and eventually felt like you understood the process much better. For some reason, we worry when children go through this process in their math learning. I’d be worried if they didn’t find it challenging or difficult at times (this means we’re not challenging them adequately). Embrace and celebrate challenge (think growth mindset!). Remind kids that when they are really challenged their brain is growing and getting stronger!

 

You can also engage in very open thinking tasks like “Make 20 in as many ways as you can”. There are thousands of right answers and you can push them (depending on their age) to use different operations to stretch their thinking. Again, ask how they know their answer is correct.

There are also some FANTASTIC free websites that provide some really engaging, thought-provoking questions that you can all work on together. Here are some examples and what you might do with them:

1) Estimation 180 http://www.estimation180.com/ There are hundreds of images on this site that ask you to simply estimate. You can fill out the form to compare how others did it or you can just talk about it as a family and then press the answer button to see who was closest. The power comes from discussing how you came up with your estimate. Many children don’t know how to estimate and this skill is a huge component of having number sense. It’s also such a valuable life skill! You will gain so much insight into your child’s mathematical understanding by using this site.

 

 

2) Which one Doesn’t Belong? (http://wodb.ca/) There are 4 choices and you must decide which one doesn’t belong. The cool thing about this one is there is no right answer! You could argue any of them as long as your reasoning is sound. This way we can build success and explore how differently we all view things. Some are geared to high school, so choose ones that you think are appropriate. Simple ones are still appropriate for high school students, especially if your child is feeling frustrated with math – this can open it up for some creativity and personalization.

3) Would you Rather? (http://www.wouldyourathermath.com/) There are choices based on sizes, quantities, price etc. Even younger children can play this game (they don’t need to know about rates or even be correct; it’s about engaging in the math thinking and reasoning).

4) Number Talk Images (http://ntimages.weebly.com/) This is a site filled with images that you can show and ask ‘how many?’ and then ‘how did you figure it out?’. For any children over the age of 7, I ask them not to count by ones, so I’m encouraging them to group the items in some way that makes finding the total more efficient. Again, it’ll be illuminating for you to see how your child thinks mathematically. Feel free to share your strategies but be mindful of valuing what they are doing and recognizing that even if their strategy isn’t as efficient as yours, it makes sense to their brain at this point and so is valuable.

5)  and www.nrich.maths.org. It doesn’t matter if you get to the ‘right answer’ right away as the point is to think mathematically. If you do wish to solve a particular problem and you and your children don’t know how, keep at it and use whatever tools are at your disposal (the internet, calculator, phone a friend). Mathematicians use tools and collaborate. They are creative and try all sorts of things (and fail) before they solve problems.

Engaging in some daily mental math practice and/or in these types of mathematical thinking activities will make a tremendous difference for your child (and maybe even for you too!). I need to mention here that our emotions are very closely linked to our ability to learn. This has been scientifically proven, but I’m sure most of you have had experiences where you were stressed out and went blank on a test or were desperately trying to cram for a test/interview but failed to commit what you needed to memory.

To use this to help your child best, ensure that the math you’re doing at home is fun, not a chore or punishment of any kind. Flashcards and math worksheets can often be seen as boring and feel very punitive for kids and so even though they practice daily, they may not improve much. This can be fixed by making a game of the math and doing the activities I mentioned in this blog as a family with a focus on growing your brains.

If your child does enjoy flashcards and worksheets but is using ineffective strategies or just memorizing, again, the benefits will be limited. They can absolutely practice using flashcards/worksheets but should still be using strategies as this is what builds number sense. Check out these cool flashcards you can print for free (at the end of the paper – although I recommend reading the paper as it’s a great read if you want to know why we need to do more than memorize).

 

Better than any flashcard or worksheet is spending a few minutes daily engaging in math conversations with your children.

Have fun!

Parents – How to Help Your Children to Learn & Enjoy Math Part 1


In today’s post we will be exploring how to connect reading to math, math in the home, and math out in the ‘real world”.

 

Parents are often wondering how to best support their kids at home in math. I’m writing a 3 blog series dedicated to just this! If you are a teacher, please feel free to pass this along to the parents of your students.

As we transition to teaching math more conceptually, teachers aren’t the only ones left a bit mystified. I believe that parents are the most important partners of teachers in their children’s education. I would love to see all parents and teachers working collaboratively to help students succeed and enjoy math! This is why I do a lot of ‘Parent Math Nights’ at schools and pre-schools as a way to invite parents into the conversation and provide them with the reasons why teaching math is changing to incorporate way more conceptual understanding and visuals. Every time I do these parent nights I am inspired by how committed parents are to learning all of these new ideas so that they can best support their kids.

I’ve written a lot about WHY we need to teach math conceptually, so if you are looking for more information please check out these past posts (“new math”, “Seeing is Believing”, “Math Class Make-Over”). In a nutshell, teaching conceptually means to teach WHY the math works as well as how it works. A quick example is to think of a procedure like adding 234 + 28. You were probably taught to line them up to the right, which is a procedure.

We want students to understand that we are adding ‘like terms’ or same place values and using base 10 blocks helps them to develop this understanding so when they do ‘line them up’, they are making sense of the procedure and could even use other procedures that make sense to them. Also, I’ve written a lot about growth mindset and truly believe it is the very first thing both teachers and parents can focus on to improve students’ math learning. If teachers, parents or children have fixed mindsets about math, then their ability to learn it will be reduced. Developing a growth mindset is essential to becoming a good mathematician and math student. See here for more on growth mindset.

There is significant scientific research that shows that our beliefs about our ability to learn have a large impact on our achievements. We want to teach kids that they can learn anything they want – this is having a growth mindset. It will likely take time, effort and often a lot of struggle and failure, but
they can learn what they want. Kids usually have growth mindsets about things they are passionate about so you can relate it to their passions to help them understand. For example, if your child loves to play hockey, you could remind them how hard just skating used to be for them, but with time and practice, skating is now a lot easier.

 

 

I will be referring to mathematical habits of mind throughout this 3-part blog series for parents. Some of the mathematical habits of mind that we want to foster in children are: curiosity, collaborating to solve problems, resiliency, resourcefulness, making connections and understanding why things work as they do.

 

This 3 part series is broken down into the following posts:

1. Seeing the math is already all around us and learning how to engage in informal fun everyday activities.

2. Websites, along with suggestions for use, that will ignite children’s curiosity and mathematical reasoning skills.

3. Games that you can play (or that your kids can play together) with your children that will help them to develop fluency and mental math skills.

So, let’s jump into today’s post: Seeing the math in everyday life! We will be exploring how to connect reading to math, math in the home, math out in the ‘real world’.

Reading and Math:

Most parents I know read to their kids each night as part of their bedtime routine. This is SUCH a great routine that makes more impact on students’ success than you may think and reading often with your children in their first year of school still has positive effects when they are 15 years old! (check out this study from the OECD)I’d like to add that even reading to infants has been proven to increase their language abilities in childhood – so it’s never too young to start!

Luckily there are a tremendous number of math books so that when
reading stories together, you can also be exploring mathematical ideas.
Click here for a list to get you started. However, you don’t need to search out
specific math books because there is math in ANY book you read. Here are
some suggested questions that you can pose to your kids to help them
find the math:

1. “How many feet are there on this page?”

2. “How many leaves do you think are there on that tree?”

3. “How many kids are in this picture?”

4. “Are there more girls or boys in this picture?” “How do you know?”

5. “What is the biggest animal on this page?”

6. “Which child is the tallest?”

 

You get the point….math is literally all around us, we just need to open our eyes to it! Better yet, ask them to come up with their own math questions about a book, or page or idea.

Math at Home and in Nature:

We often think of math as calculations. This is arithmetic and it is an important part of math but there is so much more! We know that students who understand math visually and who develop their visual parts of the brain are more successful in math. So, let’s SEE the math at home and in nature.

Shapes
– look for all sorts of shapes in: nature, pictures, toys, books, puzzles, cars, parking lots, buildings, etc. Name these shapes if you can and look at how rectangles come in so many forms – they can be long and skinny or almost like squares. Many kids think that triangles are only triangles if they have 2 or 3 equal sides because most toys and books only show these types of triangles so they would benefit from seeing all sorts of triangles including scalene (triangles with no equal sides).

 

You can also start to talk about the attributes of shapes. How many sides – what are sides? How many points or corners? Parallel and non-parallel sides, etc.

 

We want to nurture children’s innate curiosity –so ask them what they wonder about. How many sides does a circle have? Can a shape have more than 5 sides? Kids often wonder some pretty profound things, some of these ideas they can figure out or look up while others might require some further math learning.

Categorizing

This is a mathematical process as it helps us to make sense of things so you can ask your kids to sort their toys or a pile of blocks, dominoes, cards, etc. in any way they want but they have to describe their ‘rule’. Better yet, make it a game! They categorize their toys into 2 or 3 piles and you have to guess their ‘rules’ for each pile. You can incorporate this into cleaning up their room by asking them to put away all of their toys into ‘like groups’ (however they define this – stuffies, dolls, trucks, etc.) and younger children can work alongside
an older sibling if needed (collaboration!).

 

Measurement

measuring lengths, weighing, and estimating measurements are another facet of math that we often forget about. If you have a scale, practice guessing how much things weigh and then weigh them (how much do YOU think a carrot weighs?). Kitchen scales are great tools for this, especially for food items or lighter items. Using measuring cups and spoons, kids can explore volumes of containers. You can ask them what they think holds more a tall skinny container or a short fat one (think capers jar versus tuna can). Here’s a fun one you can do with popcorn: take a piece of paper and roll it into a tall cylinder and then with another piece of the same size paper roll it into a shorter cylinder.
Tape them shut and then ask your children to predict which one will hold
more popcorn or will it be the same? It’s the same size paper so many
predict the capacity will be the same….carefully fill each with popped
popcorn and then measure the amounts that fit into each with a measuring
cup…try it out and see what happens.

 

Baking and Cooking

– Involving your kids with cooking and baking is a great way to see the math in everyday life. Cut a piece of celery into 10 pieces – what fraction is each piece? Does it matter if they are the same size? Even if you don’t know all the answers, it is valuable to pose the questions. Baking is especially valuable as they are getting used to using measuring cups and understanding that when we need ¾ cup we can use ¼ cup 3 times or we can use ½ cup + ¼ cup….great learning here, especially understanding why this works! If you are doubling or halving recipes, even better!

 

Shopping

If you are kids are with you at the store, this is another great opportunity to make a game out of math. Have the kids estimate the total cost of all of the items and see who gets closest. If your kids are quite young, you can start by asking them to round the cost of any one item to the nearest dollar by asking them to consider which it is closer to (is $2.45 closer to $2 or $3? How do you know?) – By the way, we want to do this with meaning, so have your kids determine if it is below or above the half-way mark, rather than tricks like ‘if it’s five or more round up’ (which only works in base 10  and doesn’t help students to develop understanding).

 

 Math in Nature:

I have to at least mention the math in nature in this post! There are some pretty cool ratios and patterns, such as Fibonacci’s series that can be found in nature. The Fibonacci series starts with 1, 1, 2, 3,.. and can be continued by adding the previous 2 values to find the next value. So after the 3 comes a 5 (3 + 2), then 8 (5+3), …you can keep going as long as you want! The spirals you see in the pictures below follow this series! Nature is also a great place to look at quantities and shapes! How many leaves are on a tree? How many blades of
grass in a yard? These are BIG numbers that kids often have trouble understanding unless they can SEE what they might look like :).

 

These are all very general examples but I wanted to open your eyes to the possibilities and to help you see how you use math daily, even when you don’t think of it as math. If your child gets frustrated remember to remind them that struggle is an important part of learning. In fact, if they aren’t struggling, then we aren’t challenging them at the right level. We want kids to engage in productive struggle and so we need to reframe struggling to understand something from being viewed as bad or to be rescued from, to being a normal part of the learning process. Along with teaching and modeling the growth mindset, this creates resiliency. (Important side notes: if the problem is way too hard, this is NOT productive struggle. Additionally, you want your child
to have success, along with struggle, so they enjoy playing these games
with you.)

Stay tuned for the next post where I’ll give you some websites and activities you can do with your children! Remember to be positive about math, its uses and the struggle to figure things out.

Have fun learning with your kids!