Video Game Thinking - Perseverence

Here ye, here ye: There are good things coming out of video games. Kids brains are quickly becoming wired to a new way of thinking, and it goes hand it hand with a time honored math strategy we call "guess and check."

Picture your beautiful blond-haired, blue-eyed 9 year old battling against an evil monster. Time after time her weapons are not strong enough and the character disappears from the screen. But magically, the character returns with one life gone, but ready to battle the same evil monster again and with new ideas for attack. In the end, your kind-hearted wonder either stops playing, completely looses all their lives or finds a way to defeat the evil villain.

Some math problems can be solved the same way, and we need to teach kids to harness their video game mentality and attack them like an evil villain. The guess and check math strategy requires a child to try out one possibility, check to see if it works, revise their attempt, check to see if it changes the outcome, and then continue to revise and check until the "answer" is achieved.

The hard part of the "guess and check" strategy is to keep kids persevering even when their guessing is wrong. We do not want kids to loose all their math lives or stop playing the math game. Video games have programmed kids to be okay with trying over and over again until they win, and now we need to re-program our students to keep going as well. Re-programming is key because students over the past 30 years have been taught that all math problems can be solved in "2 easy steps."

The classic guess and check question is:

Grandpa's farm has chickens and pigs. When Jenny went out to feed the animals she saw 80 feet but only 32 animals. How many animals were chickens and how many animals were pigs?

Here are some other "guess and check" questioning techniques:

- There are 24 kids in 3 grade with twice as many boys than girls. How many students are boys and how many are girls?

- How many different combinations of coins can you use to get 25 cents; fifty cents?

- List out a series of 6 numbers. Which two numbers can add up to 625? Which three numbers can add up to 625? Four numbers?

- Give all kids a geoboard and a set of specific descriptions of a shape (make a shape with 3 sets of parallel lines; make a 4-sided shape with one set of parallel lines). Students must continue to move the rubber band around until they have achieved a shape within the parameters. Walk around and continue to encourage students to check all descriptions before saying they are done.

- What is the longest perimeter of polygon that has an area of 25 square inches. In this activity, have students use grid paper or manipulate square tiles to determine their final answer.

- My favorite guess and check problem is Marilyn Burns Banquet Table question (link provided here). She also has a book Spaghetti and Meatballs for All to read aloud before completing the problem. http://mathsolutions.com/documents/0-590-94459-2_L.pdf

"Guess and check" has to be modeled by the teacher over and over until the teacher defeats the "being okay with my first idea" evil villain.

Fluency

The new standards have come out with fluency guidelines for grades K-5. The following are the new requirements for each grade level:

Kindergarten: Add and subtract within 5
1st Grade: Add and subtract within 10
2nd Grade: Add and subtract within 20 using mental strategies. *By the end, 2nd grade students must know all the sums of two one-digit numbers from memory.
3rd Grade: Multiply and divide within 100 from memory
4th Grade: Add and subtract multi-digit whole numbers
5th Grade: Multiply multi-digit whole numbers

I have noticed my students are doing fabulous mastering their addition facts. However, subtraction seems to always lag behind. Why? No one likes to subtract - everyone wants to add. The only time I find it exciting to subtract is when I am on a diet or determining the difference in the score of a sporting event. Most often, I use subtraction when balancing my bank account or getting change, both of which means I am spending money.

I took it upon myself to find subtraction activities and websites that go beyond simple flash cards and memorization.  My rules for fluency activities are the following:
1. The activity must require students to use strategies beyond memorization to solve the problem.
2. There must be a picture associated with the problem for K-1 or struggling mathematicians.
3. Students must be able to see how the facts are connected together. For example, 4+5=9 which means 9-5=4.

This is a great website for a lot of subtraction games. I really enjoyed the different levels of: 

Speed Grid Subtraction

There are a lot of activities on this page. However, I find that Math Mahjong best fits my rules for fluency activities:

Sheppard Software

Addition and subtraction work together to create a very thought provoking game. 

Circle 21

Where Did Patterns Go?

I have heard several elementary teachers say, "Wait a second - I don't get to teach patterns anymore?" Their smile quickly turns sad and a long gaze appears dreaming of colorful patterns filled with cute shapes and designs. Yes, gone are the days of carefully planned color-coded calendars in AB, AAB and ABB patterns. 

Eureka, patterns still exist!  Mathematical practice #8 states: Students should look for and express regularity in repeated reasoning. Because it is stated in the mathematical practices, every K-12 student should be solving problems by looking for patterns. 

However, we have to change our schema of patterns. In the past, we gave students a pattern, and they had to identify the next item or create a rule for the pattern. Going deeper meant students created a new pattern with an existing rule.

Now, we need to have a different approach to teaching patterns. Patterns are used to solve problems. I use the pattern of odd and even a lot in my classroom math discussions. Early in the year, there are many discussions of "What does odd mean? What does even mean?" This concept then leads to the next question, "What happens when you add two odd numbers? What happens when you add two even numbers? If you want an odd total, what are your addends going to be?" (Yes, I make my students use the word addend). 

Odd and even patterns also come up when counting coins and telling time. Students quickly realize that the pattern still exists when you are counting by 5. I wait patiently for this moment to occur in my classroom. "Mrs. McEldowney, when I count nickels, the ones digit goes 5, 0, 5, 0. That is odd, even, odd, even! How cool is that?" My follow-up question then becomes, "Well, if the pattern works with counting by 5, does it also work when you count by 4? count by 7?" 

The following is one of my favorite pattern problems. I recommend spending about 5 minutes each day for several days until all of the questions have been sufficiently dissected.

Magic V's

I recommend only trying to tackle one question per day. It is amazing to watch students manipulate numbers to figure out the pattern. I leave it on the board for the whole day so students are constantly reminded to think about the question.

Once you get started with this one, it is hard to stop. What patterns did your class notice when solving the problem? 

Math Practices

Let's welcome the new Common Core Standards, which are once again filled with content and process skills. What used to be called math process skills are now referred to as math practices. There are ten math strategies and processes that can be incorporated into any math question. The best part is that these ten strategies are the same for Kindergartners through graduating seniors.  Also, these math practices should be the lens through which you view the content standards.

This year, I have fully embraced math practice strategy #5 - Using appropriate tools strategically. Students, and not the teachers, need to be using the tools more strategically.

In the past, I thought I was doing well by exposing my students to many different manipulatives and tools to solve math problems. Many mornings were spent filling individual baggies for each student and lessons would often start with, "Pull out your base ten blocks..." I have challenged myself to have the students take more ownership of the tools. This started by changing my math center.

This summer, I made all new labels for my containers. Each label has a picture for those students who still struggle with reading. Removing the lids has led to an increase in student usage because the materials in the containers are visible.

The next goal was for students to get what they needed without prompting.

It started the first week of school by modeling whole group questions such as, "How am I going to solve this problem? Are there any tools I can use?" Then, students would go and get the recommended tool and I modeled proper usage.

Continuing this strategy, I moved to asking the students to come up with a list of tools they could use to solve the problem. Several students moved straight to drawing pictures as their tool. Other students continued to use manipulatives. The class would do a "gallery walk" to find all the different tools used. The lesson often concluded with, "Which tool do you think was most effective?" 

The next step was my favorite because it involved several awkward whole class moments. I posed a problem and then proceeded to stare blankly at the students. Finally, I would exclaim, "I just don't know where to begin. What should I do first? Let's just guess." My patience set in until a student would say, "No, no, no. Why don't you try using ______?" Cartwheels and clapping would ensue, the problem would sometimes get solved. If the chosen tool did not help to solve the problem, the process would begin again and would continue until we knew we had the best possible answer. I watched as students started to own the tools.

At this point in the year, most students were very comfortable using tools to solve a problem. There were still individual students who did not grasp the concept. These students needed individual attention which started with, "So tell me what tools you have tried to use to solve this problem." This tiny clue was often the key they needed to unlock the problem solving mystery.

It is now January, and my students have finally reached independence. Yes, it took that long, but it was well worth every long and painful moment. Any time a math problem is discussed, students are free to get any materials they deem necessary to complete the question. During a recent principal observation, my students grabbed 5 different manipulatives and they were all beneficial in solving the problem. I did not waste any class time handing out materials or making baggies of counters prior to the lesson. I call that success.

Teaching Math

When you ask an early childhood teacher why they entered into the profession, the two most common answers are "I love kids" and "I want to teach a child how to read." Personally, I have never met a single teacher who said, "Wow, I can wait to teach a child how to add!" Earlier in my career I would have given the "I love kids" answer. However, as the years progress I find myself getting really excited about teaching math. 

There has been an evolution with teaching where teachers have become comfortable creating rich language arts, science and social studies lessons. When it comes to math, the mentality is to turn to page 348, go through the bold words the textbook company has told you to say, and hope it takes the 60 minutes required to spend teaching the subject. As teachers, we have turned math instruction into isolated skill sets solved through specific rules.

But math is so much more than a set of rules, procedures or memorization of facts before moving on to the next skill. Math is teaching a child how to think. Math is getting stuck half way through a problem, finding a new angle of attack and sticking with it until you know the answer is correct. Math is getting excited because you found a pattern in the clock time or date (my class had a party on 12/12/12 because we figured it was not going to happen until 1/1/2111 or 1/1/2101 which ever way you look at it). Math is critiquing another individual's work, realizing they solved it a completely different way, and yet finished with the same answer as you. Math can be fun!

The new content standards sitting on the laps of teachers has the ability to provide this type of thinking, a mentality that has been missing from the vast majority of elementary classrooms. Once you have come down from the pain of deconstructing these new content standards and realize a lot of content has been stripped away, come find me and I can share so many wonderful ideas which you can incorporate with your students on a daily basis. 

Hopefully, we can change this image of American math education. 

Exxon Commercial