What are these stupid strategies kids are learning days? Why can't they just learn the #@$#* way I learned it?

Wow! This turned into a huge post. I apologize! You may want to break this reading up into several sittings.  Sorry! I have included the slides that I share so you could read the slide and then, if interested, read the details below it and if not interested, just skip ahead to the next slide. 

I chose to start my blog reawakening with this question because I get this question a lot from parents...not all parents but many. It's imperative that we have parents on our side when we are teaching in a way that is often different that the way they learned. If parents understand that these changes are good, then they are more open to them.


In order to help with this, I hold parent nights so that parents can come and learn more about the pedagogy of our curriculum.  They are encouraged to bring in their children with them. (Preferably no more than one child per parent) Some of these sessions take place where I work (CARC) and others have taken place within a school that has arranged for me to hold it there.  Typically, I set each session to be grade specific or a very small span of grades. This helps narrow the examples and activities that are provided and to focus of our conversations.

Here is the link to the Google Slides I use/adapt. You have my permission to use/adapt this presentation to meet your needs!

Let's see how a typical parent night runs.

Everything written below in normal text is something that I say during the workshop. If it is in italics, then it is something I do or notice.

--------------------------------------------------------------------------------------

The parents arrive, some with their children and some without. They all have different expressions on their faces when they come in. Some are excited to be here. They are ready to learn and to have conversations around math. Others look like they are ready to bolt. It is obvious that they have not built a positive relationship with math. Others look like they are here to challenge everything. They don't like the way that their child is being taught and have come prepared to put an end to that. The rest of the parents are somewhere in between.

During our time together, we will be looking at math in a variety of ways. Everything we do follows the philosophy of the current Alberta Mathematics Program of Studies. However, your teacher may be teaching strategies that are different that the ones we do today.

We are going to explore strategies that may be new to you. When you see them or hear them, keep an open mind. Ask yourself, do they make sense to you? Have you ever seen them before?

We are going to have an opportunity to make connections between what you learned in school and how your child is experiencing math now.

At the end of tonight, I hope that you feel like you have a better understanding of the philosophy of the Mathematics curriculum.

We only have 1+ hr together which means that our time together is just a teaser. We could spend days and days on these ideas.

Each of these questions was posted on the screen one at a time so that they could focus their discussion.

Question 1: Parents, turn to your child and ask them this question.  Listen carefully to their responses. If you don’t have a child here tonight, write this question down so that you can ask them later.

Question 2: Parents, tell your child one thing you think THEY are really good at in math.

Question 3: Parents, ask your child “What is one thing you feel you really struggle with in math?” Again, listen carefully to their responses.

After conversations: You may or may not have been surprised about some of the answers shared during this conversation.  Often, we have different beliefs about our strengths and areas for growth. Have this conversation several times throughout the year.  Expect the answers to change over time.

These two questions show up separately.
Question 1: Parents, do not answer this question out loud. When you were in school, what was your least favorite subject?

I talk with a lot of people around the world and often ask them this question. What do you think most would say? Pause Unless they are a high school math teacher, university math professor, engineer or in another math related jobs, many adults (but not all) have told me that math was their least favorite subject. Why?

Many people were shown algorithms and procedures and told to follow them blindly. "When dividing fractions, invert and multiply. Don't ask why." Often when asked how the algorithm works, they were told just to follow it. Some people had no issues with the algorithm. They could follow it. Many who could follow it also understood it while others followed it blindly but could get the answer. However, many people need or want to understand how it works. Without that understanding, they couldn't follow the algorithm.

People often identify their memorization skills as the reason they are good or bad at math. If you have all your basic facts memorized, you were often perceived as good at math. If you didn't have them all memorized, well...you obviously weren't good at math.

How fast were you at finding answers? Could you do it in your head? If you thought slower than others, if it took you more time to find an answer, if you needed paper to solve it, you were often perceived as being bad at math. Speed became a division at math.

If you were good at running algorithms, following procedures and memorizing basic facts, you were successful in math which made you feel like you were good at math. If you weren't good memorizing, you probably felt you were bad at math.

Question 2: What area in math do you think people often identify as being a huge issue? Algebra is often identified as the biggest issue for many people. Even though we use it all the time, people don't see it expressed in variable form very often so they assume they are not using it. Algebra in symbolic form can be intimidating. People have told me that they don't understand how there can be letters in math, or why the value of those letters change. They "learned" algebra by jumping to abstract concepts too quickly rather than exploring it concretely first.

It is through our experiences with math that makes us feel that we are either good at it or not good at it.

If, in your head, you said math was your least favorite subject or if you feel like you are bad at math, the good news is that you were NEVER bad at math.   You just weren't taught the way you needed to be taught in order to understand it. And that's what we are trying to do in schools. Teach math in such a way that it makes sense to them rather than through rote memorization. 

There are three things teachers want you know about their mathematics classes. The first goal is for your child to love and understand mathematics.  Both goals need to be attained for future success. If a kid understand math but never loves it, they won’t think about all the opportunities they may have in their future that could involve mathematics.  For those that love math but don’t understand it, there may come a time that they dislike math due to their limited understanding. And we want kids to keep as many options open as possible and the reality at this point is that some students fear of mathematics prevents them from being as successful as they can be or pursuing certain areas of study

Secondly, you are going to see a lot of concrete manipulatives in your child's class. Tools such as base ten blocks, integer tiles, unifix cubes, cuisenaire rods, and other tools help students build a concrete understanding which allows them to make connections to abstract representations. The use of manipulatives or other materials does not mean that the mathematical understanding is any less, and often it means the opposite.  If a student can understand an algorithm AND explain that with the use of manipulatives, they have a stronger foundational understanding of the concept.

Math class is no longer sitting in rows, working on worksheets. It is an active learning process. They will not be talked to for a period of time and then sent home with a ton of homework to practice what they heard. They will be doing activities and group work along with some individual work. They will build mathematical ideas using manipulatives. They will talk to people about their understandings and strategies. Some of the activities may spill into their outside of school life and will hopefully engage family or friends.

I hear a lot of people complain about the "New" math. The math has not changed. They still need to learn to add, subtract, multiply and divide. They will still learn math in school. However, the WAY your child is taught math will not be the same as the way you were taught.  And change isn’t a bad thing.  There will still be times that some things seem familiar, but there are other times that things will look or sound different.  What we hope you will do is encourage your child to work on mathematics, to ask your child to explain what they are doing and why, to involve your child in as many ways as you can think of that involve mathematical thinking (ie grocery bills, filling up with gas, counting out money) and tell your child that they are capable and can be a successful mathematical thinker.

Two questions are posted on the screen for everyone in the room. These are adjusted based on the grade level. Choose one question to solve in your head. Do not use paper or a calculating device other than your brain. Hold a closed fist in front your chest while you are thinking. When you have solved it, put up your thumb. If you have time and can think of another way to solve it, put up another finger.

I give enough time so that almost everyone has at least one thumb up If both of you have your thumbs up, please explain to the other person exactly how you figured out the answer. I should hear things like, "First I did this and then I did that."  Parents, you will go second. If you are still thinking, go ahead and finish thinking before sharing. 

Participants are given time to share their thinking. When it looks like everyone has had a chance to share their thinking...  Let's share your thinking with the rest of the group. Who would like to explain the strategy they used or their partner used to solve one of the questions on the board?

Someone shares their thinking. I ask questions to clarify their thinking for others and make sure that steps aren't skipped. Throughout their explanation, I am recording their thinking on the board.  Did anyone else do it the same way? Cool. If that makes sense to you give me a thumbs up. If that makes no sense to you, give me a thumbs down. If that makes some sense to you, give me a thumbs in the middle. Who did it a different way?

The traditional algorithm will always be shared by a parent. Sometimes they are embarrassed that they used it. Others are proud. Is it ok for students to use the traditional/standard algorithm in school?Yes! There is absolutely nothing wrong with using the traditional/standard algorithm. It is absolutely a strategy that works.

We run through several examples So, we have heard many different ways to solve those two questions. Who's strategy is correct?

Participants always respond that all of them are correct. If you only walk away with one understanding from this night, I want it to be this - there are many ways to add numbers. The "grade 3 outcome" says that students must be able to add "3 digit" numbers. It doesn't say how they must do it, just that they must be able to do it. They must master a strategy for adding numbers but what they master may or may not be different than the one we are most familiar with and that's ok.

There are many different strategies for adding, subtracting, multiplying and dividing.  There are the traditional methods we learned in school but there are also many other strategies students are exposed to like the ones shared today. You may find your child using strategies that are very different from the ones you learned and that’s ok. We want children to understand that there are many strategies but…

They don’t need to master all of them for a particular concept.

There is no right or wrong strategy as long as the strategy is efficient and effective for your child. It might not be the most efficient strategy available but it may be the most efficient one for them at their level of understanding at this moment in time. With experience, students will develop more efficient strategies.


So what does it look like when a student has mastered a strategy?  If a student has mastered a strategy, then for that student, the strategy is efficient, effective and explainable. If it is efficient, the student can use it to find the correct answer in a reasonable amount of time. Although there is no time limit, I think about a minute would be a fair time estimate. When a student is first introduced to a new strategy, it might take them 10 minutes to use it to answer a question and that's ok. They just haven't mastered it yet. Through more experience with a particular strategy, they will usually become more efficient at it. What is efficient for a grade 2 student to add numbers will look very different than what a grade 6 student may use. Efficiency increases over time and experience.  If a student has mastered a strategy, then for that student, the strategy is effective, it must get you the right answer every single time. Sometimes students make up a strategy that flukes into the right answer but doesn't work in any other situation. So, it must be effective every single time. If a student has mastered a strategy, then for that student, the strategy is explainable. They have to be able to explain why the strategy works, why they chose that strategy to use for this particular question and whether it will work for really big numbers and really little numbers.

We have to remember that many of us were taught math focusing on learning the traditional/standard algorithm. If we felt we were successful in math, we often were able to learn those algorithms easily and feel comfortable using them. We have had many years of experience working with that algorithm. If you were one of the adults who, in your head, said that you don't feel like you were good at math in school, you may have said the algorithms and procedures didn't make sense to you. Alberta Education dictates the outcomes we must teach, such as "adding three digit numbers", but they do not tell us how to teach those strategies. That has always been up to the professional judgement of teachers. Nor does it dictate which strategies students must use. That is up to the student.

At this point, we engage with a math activity that is specific to the grade level of students who are attending. For example, if it's grade 5, I will show them how to use base ten blocks to build a conceptual understanding of 2 digit by 2 digit multiplication then work through representing that as an array model. I will be sharing these activities in later blog posts.

So what can you do at home to help your child see more success in math? Play games! Board games, dice games, card games, etc. It’s better to play for a short amount of time but more often than playing for a long time once in a while.

It's important to understand the difference between a game and a practice activity. "Games" that don't require any kind of strategy are simply tools for practicing basic facts. For example, roll two dice and multiply them together to get an answer fits in here. These aren't games. These are pounding a nail in over and over until the nail is embedded in the wood. Children need some of this but it doesn't need to be the main focus in order for them to master those facts.  

A game requires some sort of strategy. Being strategic will help them build deeper mathematical thinking. They need many opportunities with this.

So let's take a look at some examples of games that we have played in the past.

 The card game war.  Is it a practicing activity or a thinking game?

War is definitely a practicing activity. There is absolutely no strategy involved. You simply flip over cards and figure out who is larger. It's about practicing comparing numbers. One person doesn't even have to think if they rely on the other person to decide who is bigger each time. So how do we turn War from a practicing activity to a strategy game"?

• Divide a deck of cards so that each player receives one suit of cards.  (ie. You get all of the Clubs) Place the rest of the cards back.
• Players fan out their cards so they can see them but the other player can not.
• Players each choose one card to play and place it face down in front of them.
• When both players are ready, they flip their cards.  Highest card wins. If there is a tie, players replace the card back in their hand.
• Cards that have been claimed go into a discard pile.  Not back in their hand.

Participants are given a few minutes to play "War...with a Twist".

Variations:

• Player A takes all the red cards. Player B takes all the red cards. Each player chooses two cards for each round.  Decide at the beginning of the game which operation will be applied.

Variations:

• Player A takes one black suit AND one red suit. Player B takes the other black suit and red suit.
• Black cards are positive numbers.
• Red cards are negative numbers.

Bump Games are something I have added to my classroom over the past few years. First, I'll teach you how to play and then you can decide if they are a practice activity or a strategy game.

Instructions: Player 1 rolls the two dice and add together. For example, I roll a 1 and a 3. What do I get? 4. This is Alien Bump - Multiplication by 6. What do you think I will multiply the 4 by? 6. What is 4 multiplied by 6? 24. I cover the alien beside the number 24 using a tile (or a coin, or a bingo chip - whatever you have at home.) Do not cover the number 24 otherwise you won't be able to see it. Make sure to put it on the alien.  My partner rolls. They get a 2 and a 5. She adds those together to get 7. Then she multiplies 7 by 6 to get 42. She places her different colored tile on the alien beside 42. We keep going back and forth one at a time.  What happens if I roll a 7? My partner has already covered the 42! I bump her chip off and give it back to her and then cover the alien beside the 42. What happens if I roll another 4? I'm already on the 24! This time, since I am already on the spot, I get to put my tile on top of the number 24, claiming this spot. Now that I have a tile on both parts of the spot (the alien and the number), it can't be bumped off! Play until someone uses all their tiles or the entire board is covered.

Give participants time to play.

There are many different Bump Games that you can play.

So, is a Bump Game a practice activity or a strategy game?

Bump Games do not require ANY strategy.  It’s complete luck. This is a good way to introduce the game however.  Once they are familiar with the process, then switch it up! Make it more challenging.

Variations:

• Add an extra die. Ex. When the game asks for TWO 6 sided dice, give them THREE 6 sided dice. 
• Roll all THREE dice.
• Player chooses which of the TWO dice he/she will use.

Variations:

• After rolling, player may add ,subtract, multiply or divide the two dice to get a number that is useful.

There are many games that you can play to help students practice basic facts but still allow for strategic choices.

Parents, it is extremely important that you never say "I am/was bad at math". Women, this is especially true for you. Research has shown that when a mother tells her daughter that "I was bad at math", the daughter's belief about their own ability drops and as a result, so does their achievement.

It is ok to say, "I don't understand this...yet" or "I didn't learn this way. Please help me understand."

Your child is going to come home using strategies that you may not have seen before. That's expected and it's ok if you don't understand them right away. Ask your child to explain it to you. Remember though, they may not have mastered it yet so be patient. Remember that they will often explore the strategies using simple examples and then move on to more complex questions. I don't know how many times I've seen a strategy presented on Facebook using an over simplified example. Adults get upset because you would never use that strategy on that particular example. Please keep in mind, we only do that when introducing a strategy. We are not saying it makes sense to use that strategy on such an over simplified example. However, it helps students explore the strategy before it they have a chance to use it with more appropriate questions. Try that strategy out yourself.  Remember, it might not be your most efficient strategy and that’s ok. If you are stuck, google it or ask your child's teacher to help you understand it. I will be creating blog spots exploring many different strategies and how they can be introduced, moving from simplified questions to more complex questions.

There are many opportunities to work with numbers at home. At this point, I share activities that are appropriate for the age level of the students in the session. Baking is a popular one for all age levels. Giving children two few forks to put out at supper and asking how many they are short. Counting toys. There are too many to list here.

My "dumping grounds" website contains some of the activities that I have created for different grade levels (based on Alberta Curriculum), strategy games and practice activities that you can access to help your child. Videos are slowly being added for many of the ideas as well. Feel free to use this to help you understand and explore math!

One final reminder: My goal is to help my students build deep, conceptual understanding, through concrete experiences and making connections to abstract representations. They are still expected to master basic facts. They will still learn how to add, subtract, multiply and divide. They are just not doing it through rote memorization, flash cards or mad minutes.

--------------------------------------------------------------------------------------
When the session is over, parents always come up to me to talk about their math experiences and how they connected with the math in this session.  Here are some comments that I always receive, regardless of the grade levels I focused on or whether they believed that they were good or bad at math.

"Why wasn't I taught this way? If I had been taught this way, I would have understood math!"

"When I came here tonight, I didn't understand why my son was drawing boxes to add. Now I understand." [This was after I showed them how to add using base ten blocks]

"I always thought I was cheating. I couldn't do math the way the teacher showed me so I had to figure out my own way of doing it. Now, I know I wasn't cheating."

"When you said that I was never bad at math...that I just wasn't taught the way I needed to be taught in order to understand, that opened the world to me. I'm not stupid! I can learn this."

"My child might use a strategy that's different than I do and that's ok!"

"When's the next Parent Night?I want to learn more math!"

Parent nights have evolved so that parents who have participated in this beginning "theoretical" portion come just for the new activities and parents who are new to the event come earlier to learn the "theoretical" part as well as all of the activities.

When parents have an opportunity to experience and understand what is going on in the classroom, they will support you. I believe that it's imperative that they have an opportunity to participate in a parent night the first few weeks of school. This will set the stage for the rest of the year. I encourage you to create a class website where students create videos explaining all of the strategies you explore. What does it look like to solve a question using concrete materials? What does it look like to solve it using each of the different strategies they have learned? What a great assessment tool for students as well? Do they understand their chosen strategy well enough to explain it to someone who has zero understanding?

Wow! Did you make it to the end of this post! Great job! That was a lot of reading. I won't be making all of my blog posts that long. I won't be able to keep up with my one post a week if I do that every time. :) 

If you're not too exhausted from all that reading, I have a Reflection Question for the you:  What opportunities have you provided to help parents understand the strategies that their children are exploring in class? I would love to hear about them in the comments below!

If you have any questions about how I ran parent nights that I didn't address, please feel free to ask! I will respond to all questions as best as I can. 

Have a fantastic day and I will see you in a week!

Sandi