Instant Feedback Part 2

So we all agree that giving students feedback on their work is important. (see this post) AND the fast you can give it, the better.

Using technology is an easy way for students to get feedback. Most apps that students would use to practice fluency and new skills gives them immediate feedback.

Most new math textbooks now come with online access for students. Even if most of your students do not have access at home to the internet, you can still give them to option to complete homework online.

However, not every one has access to technology. I am extremely lucky to have 10 working computers and 10  ipads in my room which we use on a daily basis. However, not every classroom has technology and there might not be an app or activity online that covers what you are doing. There are still activities students can do.

Fill in a Riddle

There are several resources where students solve a riddle by completing math problems. We use Pizzazz books on my campus and there is basically practice sheets for every concept we teach. As students solve the problem, they find their answer. If the answer isn't there, then they know they made a mistake. 

QR Codes

There are so many ways to use QR codes in your classroom. You will need a device that has a QR code reader on it. You can have task cards where students do the work and then scan the code to check their answer. You can add QR codes to the end of a worksheet where students check their answer.

You can have card sorts where students have to match cards where each card has one half of the QR code and then when they match the card they put the QR code back together. If it scans, the answer comes up correct. If the QR code doesn't scan, then it isn't the correct answer. Just google QR code math activities ( or any subject) and see what comes up.

Color by Number

Even middle school students will color. This is similar to the riddle. The students solve a problem and if they find their answer on the picture, they know they are correct. With this, along with the riddle, students can easily get the riddle and picture by copying. Make sure to require students to show their work.

Graphing Picture

To practice graphing, mystery pictures provide lots of practice and students can see by the end if they have a picture or just a jumble of points. These mystery pictures do not just have to be ordered pairs. There are some that make students solve a problem before getting the ordered pair. For example, (-3+-4, -5+2) is the ordered pair (-7, -3).

What other ways have you found that help students see if they are on the right track?

CAMT 2016

I was selected to present at the Conference for the Advancement of Mathematics Teaching next summer. I am so excited and now I am nervous.

My session is on Thursday June 30 at 10 am. My room will hold 180.

One Hundred Eighty.

I will have a microphone. I am nervous and anxious. I have 8 months to plan and change plans and plan some more.

My topic is on Writing in Mathematics. Something I've tried to be better at in my classroom this year. The students find it difficult at first, but they get better with practice and scaffolding.

So, if you are at CAMT next summer, come see me!

Thanksgiving

Happy Thanksgiving.

I hope you will have a relaxing day today.

I am sure that I am not alone is saying this: I love this time of year. I love the smell, the weather, the time off school. It is the time of year when all my brothers and sisters come on town...its amazing. It is 6 weeks of awesomeness.

I have so much to be grateful for. This has been a great year. I graduated with my Master's and moved into our new house. I got to spend time with my little girl and husband.

When I was a teenager, I had teenager problems (who didn't.) To make myself feel better, I would list everything I was grateful for. I haven't done it in a while because while I have adult problems, I have a better perspective of what life is about. But I still have much to be grateful for.

My small family of my husband and daughter
My big family.
The gospel of Jesus Christ
My house
My career
Books
Television
Internet
A community of teachers
Christmas
Sleeping In

I could keep going, but it is time to get started for the day. To end, here is my little girl.

What are you grateful for today?

Instant Feedback Part 1

As part of my master's program I had to do a large research project. I researched whether using technology in the math classroom would improve student attitudes about math and increase their confidence in math. I used student surveys before and after a unit using our online mathematics textbook to track changes in student attitudes and confidence.

The survey asked students to strongly agree to strongly disagree with statements like "Math is difficult for me" "I know I can do well in math" "Learning math is enjoyable", etc. After comparing the results from the pre and post survey, there were no significant changes expect for one statement. "Math is difficult for me." Students went from agreeing with that statement to disagreeing. I gave them an open ended question on the post survey to tell me what they liked about the online textbook. They responded that they liked the feedback and help it gave.

They said:
"It provides a video to help me understand"
"It tells you when you do something wrong"
"It gives more chances"
"It gives you similar problems until you get it right."

I came to the conclusion that students benefited from the instant feedback they received on the website. Because they were instantly able to tell if they got a problem right or wrong, they were able to find mistakes and correct them. A majority of my students were able to see proof that they did understand the concept and felt better about their ability to do math.

BENEFITS OF FEEDBACK 
Other research also finds that using technology with feedback improves student attitudes towards math. Feedback gives students a chance to improve and then reflect about what they are doing. They correct misconceptions before it becomes solidified. It tells students mistakes are okay and can be learned from and fixed. Students feel like they are improving when they fix mistakes and learn from them in time to not repeat it on the next problem.

We give students feedback when we grade, but it is not instant enough. If students take a test, they go home and most forget about what they were thinking while taking it. If feedback is instant, they remember their thought process, their strategies, etc, and are able to see what worked and what needs improving.

Technology isn't the only way to give instant feedback to students. Later, I'll share some other ways to give feedback to students.

• Cavanaugh, C., Gillian, K.J., Bosnick, J., Hess, M., & Scott, H. (2008). Effectiveness of interactive online algebra learning tools. Journal of Educational Computing Research. 38(1), 67-95. 
•  Kim, J., & Jung H. (2010). South Korean digital textbook project. Computers in the Schools, 27(3), 247-265).
• Zerr, R. (2007). A quantitative and qualitative analysis of the effectiveness of online homework in first-semester calculus. Journal of Computers in Mathematics and Science Teaching 26(1), 55-73. 

Thinking Blocks

Here are FOUR! free apps that require students to use strip diagrams (bar models) to solve problems. Each app has a different focus, addition, fractions, ratios, or multiplication. These are also available on the Math Playground Website. 

Your students might need some coaching on how to use a bar diagram. strip diagrams are a helpful way to see the relationship between quantities. I wish that I had bee shown how to use strip diagrams in school. Especially for ratios. 

Each app has different levels that get progressively more difficult and use different types of situations. 

The students are given feedback as they place each part of the strip diagram. If they get it wrong at first, they are prompted with question to think about to help them. 

Not every student loves this app, but it is helpful for them to practice making bar diagrams to model situations. 

My Favorite No

I love when student analyze their mathematical errors. (Which is why I liked this activity)

This is another way to have students analyzing errors when the teacher pictures her favorite wrong answer.

Sometimes a students has the perfect wrong answer because it leads to so much rich discussion with the class. Then every one has the opportunity to learn from a mistake.

Scientific Laws and Scientific Theories

While I have students after school waiting for buses to dismiss, we watch education related videos. Sometimes we watch CNN Student News and sometimes we watch Ted Education videos. This is their new one this week. If you believe a theory graduate into a law, you need to watch this.

In my Science Teaching for Middle Grades class I took in grad school, we discussed this topic a lot. Most people have misconceptions of what a scientific theory is and think that it will one day "graduate" into a law. (Which is what I thought at one point in my life.) A theory in science is not like a theory in other content areas.

So when people here things like the Theory of Evolution or the Big Bang Theory--they hear theory and think there is not enough evidence to support the theory to become a law so it should not be given too much weight. Not the case. 

Having a scientifically educated population is important for our future and our children's future. Teachers need to make sure they understand what they are teaching. Many elementary teachers are not given proper training in science teaching--or the time to teach it. I love teaching math and I think it is extremely important to my students futures that they understand the basics of it--especially financial literacy and reading graphs. An understanding of science affects who we vote for, what policy are leaders create, what gets published in textbooks, etc. 

Unfortunately, most schools are not going to provide the training to make sure that teachers know what they are teaching. It is up to teachers to research, read peer-reviewed articles, have subscriptions to journals, and ask when they don't understand. This way they are doing everything they can to provide the best lessons for their students with the most accurate information. 

Blog Posts I Love-Part 4

We are getting closer to solving inequalities when we get back from Thanksgiving break. My students still confuse the > and < signs, and then we add the "or equal to" and they get even more confused! Dana Boucher from Math Coach's Corner write about these signs and then relates them to a number line.

I feel like my students are a little more snappy with each other. We are all ready for Thanksgiving break but I want them to be comfortable working with each other. This Edutopia post talks about creating a classroom culture with laughter. I would like to try a few of the activities once a week.

From Math Coach's Corner again--Using Data to Plan Remediation. My data drives my instruction, especially my small groups. This post was a good reminder of what data should be helping you with. It reminds me of standards based grading, instead of traditional grading.

I need more comfortable shoes for work. I look forward to Thursday and Friday--not just for jeans but for tennis shoes. So here are 30 brands of shoes that are teacher friendly.

Follow Me on Pinterest

I took a break from Pinterest but now that it is almost Thanksgiving I am looking back over all those fun craft ideas I pinned for the Holidays. We are about to have our first holiday season in our brand new house and I am really excited to decorate. Pinterest is where I store all my ideas for what to make.

If you are interested, follow me on Pinterest!

Visit Randi's profile on Pinterest.

I also have two boards that I use to store teaching ideas. One for math ideas and one for general teaching ideas.

Follow Randi's board Math on Pinterest.

Follow Randi's board Teaching on Pinterest.

Create a City--Coordinate Graphing

This was another project my students did. They had to create a city. I have seen this idea floating around Pinterest for a while. Like the last project, I liked how this had students word backwards then what normally do when practicing graphing. 

The requirements were to have at least four buildings, and one needed to cross the x or y axis. They had to tell me the corners of each building and name at least one point inside it. The could decorate it however they wanted and as much as they wanted. I know that some students don't enjoy being forced to be artistic. I hated that in school. 

Here are some colorful examples. 

Create a picture-Coordinate Graphing

I gave my students a project a few weeks ago and I love how it turned out. Instead of giving them coordinates to make a picture, they drew a picture and then gave me the coordinates. I was not sure what I would get out of them, but I was impressed. I want to tweak how I present the project to the students and once I do that, I'll share what I gave the students. 

They had to include at least 60 coordinate pairs, have at least 5 shapes, and graph in all 4 quadrants. 

Dr. Who anyone?

Kakooma

Another free app to share.  It is not super easy so my students who like a challenge enjoy it. 

Kakoom was created by Greg Tang, who has lots of resources on his website.

The app has changed since I first downloaded it. I like the look of it now, but students do have to create an account before using it. All my ipads in my classroom have the old app so I do not have to worry about that. But if I did, I would just create one account and sign into each ipad app with that account. It is not easy to get signed out, so you wouldn't have to continue to do it.  

This is the description of the game. Students can practice multiplication, addition, and addition of negative numbers. The negative integers is my favorite part of the game because there are few integer operations practice games out there. 

The accounts are to keep track of points. Students can play practice rounds or play live with other students from around the world. 

Blog Posts I Love-Part 3

Part Three of Blog Posts I Love that I ran into this week.

This lesson uses Green Eggs and Ham as an introduction to variables and solving equations.

I made a promise to myself a while ago to not read posts about people complaining about being a teacher. Recently, there have been several blog posts in my twitter/facebook feeds about teachers who resigned because they were unhappy with the direction education is heading. Over at Venspired, Krissy Venosdale writes about how she will never resign.

There are a lot of things in education that I want to change. But there are also a lot of good things that happen every day. Also, if we want things to change, it starts in the classroom. I will do my best to make the changes in my classroom and be an influence to teachers and students around me.

I want to remember to show my students this way to subtract by thinking as subtraction as the distance between two numbers. It would eliminate a lot of problems/mistakes that come with regrouping. It wouldn't always be the most efficient way to subtract. From Math Fireworks

Over at Show Your Thinking, she uses a color coding system to grade. Instead of putting number grades on a paper, students use the colors to see what they did and didn't understand.

Order of Operations Errors-Order of Operations Error Analysis Activity

We've been working on Order of Operations this week and my students have the Order part down, but it is the Operation part they need some help with. 

I did an activity where I asked students to purposely make a mistake when evaluating the expression. Then the class had to find their mistake.

Order of Operations Error Analysis

My students LOVED this. It went over so well and they all wanted to go up several times to try to stump their classmates with the tiny little error they made. 

Eventually, I found 3 students who had evaluated the expressions in 3 different ways and then had the class explain their mistakes. 

They made mistakes with the exponents, solving in the wrong order, ignoring grouping, not regrouping when adding and subtracting, etc. It shows that they know what type of errors are common and will hopefully be on the look out for it. 

I have a station that I will pull out next week where the students will get an expression solved two different ways and will have to sort them into correct and incorrect. That station is available in my store. If you have it, make sure to re-download it because I made some updates to it. 

I Read Books

I have hobbies. 

One of them is reading. I love a good book and right now I am on a reading kick. And I want to share the good books I've read.

Here are some books I've read this year that I would recommend. 

I saw the movie poster, my cousin said it was good, so I read The Martian. In 24 hours. I really liked the science and engineering in it. It was a realistic book. Then I watched the movie which I really enjoyed, but my husband did not. 

Astronaut Mark Watney becomes standard on Mars after his crew thinks he is dead. He has the science the crap out of the supplies he has in order to stay alive until he can (maybe) get rescued. I was on the edge of my seat reading this. 

I think this is THE mystery book of the year. I was number 250 on the library wait list so I was surprised when I got an email saying it was ready for pick up. I was expecting to have to wait a year to read it. 

Rachel takes the same train every day and every day she sees the same couple in their house. She has created a story around this couple; she's named them and begins to feel like she knows them. Until she sees something about them that she only could have noticed. She goes to the police and become entwined in their story. 

This is like a Beauty and the Beast retelling. The dragon comes once every 10 years to a village and takes one girl to live with him. The dragon is responsible for keeping the dangers of the Wood away for the price of one girl who will serve him for 10 years. Agnieszka fears her best friend will be chosen, but is surprised when she is chosen to leave her family, friends, and village to serve the Dragon for 10 years. 

I cannot say enough how I LOVED this book. It is very fantasy, which is not usually what I like, but this was so good. 

I love Mindy Kaling. Of the few TV shows I keep up with, The Mindy Project is one of them. I loved her first book Is Everyone Hanging Out Without Me? and I've been excited to read this book since I heard she was writing it. I think she is funny, down to earth, and honest. I love the message that she gives about being true to yourself and not taking constant reject as a finality. 

What books have you read would you recommend? I am always adding to my ever growing to-read list. 

Order of Operations

I am starting order of operations with my students tomorrow and Tuesday. I prefer not to just jump into algorithms with students without hooking them in or giving them some kind of real-world reason they are learning a new skill. 

Before teaching, my understanding of order of operations was the some people made some rules, decided that multiplication had to be done before addition and we all just blindly follow. Who "they" were was unclear to me. 

When we teach order of operations by just giving an expression and asking students to evaluate it, that is essentially what we are teaching: We are saying that these are just some rules you need to memorize. 

However, as I tell my students, in the real world there aren't signs that make you solve a math problem before you enter a room. Or you don't have to prove you can multiply before you take your driver's test. Instead, math comes up and you have to be able to take all you have learned and decide what is useful in that situation. 

So instead of telling students the order of operations, I introduce them to real life situations and ask them to write numerical expressions that tell the story with numbers. Then I ask them to evaluate those expressions using the knowledge they have of where the expression came from. My students learned order of operations last year without exponents, so they are not completely new to it.

I have created a presentation on Google Slides that will be the lesson I do with my students. 

Use it if you would like. If you would like to make changes to it, go to File and then Make a Copy for yourself to save to your Google Drive. 

Prime Factorization

The students started prime factorization this week. 

I was unfortunately sick on Wednesday and ended up missing school that day. It was the first unplanned absence I had in 5 years. It was agonizing on Tuesday night trying to predict if I would feel better the next day. There were many cons to calling in. Mostly, the students would miss a day of new instruction. I had an emergency sub basket all ready with work for them, but it was just practice. Also, I would miss our class picture. In the end, the sickness won and it is good I did stay home. I ended up losing 5 pounds in one day to being sick. I was miserable. 

So my prime factorization lesson seemed rushed as I was trying to make up for a lost day. But I tried to vary the activities the students did, and gave them time to talk about the math. 

We started the lesson with reviewing what prime and composite numbers were. We talked about definitions, debate over which numbers were prime and composite and watched this video.

In one class, we had to talk in length about the difference between a multiple and a factor. 

Then we added a page to our notebook about prime factorization that looked like this. 

The tree flips down and there is another practice factor tree underneath. The students then got a practice sheet to work on with their group which we then checked. 

Afterwards, I gave everyone a dry erase marker and they practiced making factor trees on their desks while I went around checking and asking questions. 

Some common mistakes I saw were wanting to make the prime factorization smaller. Like taking 2x3x5 and wanting to collapse it to 6x5. We would go back to the definition of prime factorization and ask ourselves if all the numbers were prime. Also, some students just did the factor tree and thought they were done. I had to remind them that the factor tree was the process, not the actual prime factorization. 

Next, I will pull students in small groups and practice so I can really who has it and who needs more help. 

One station I will have next week while I pull students in small group is this Prime Factorization Match Up with QR codes. I try to have many of the stations that my students do include instant feedback. I am actually much better at grading this year than I have been in the past, but it is still not same day grading. Students need to know if they are doing it correctly. This way, they can check right away. Plus they'll have an ipad which they still think is cool.