Problem Solving Strategies

After reading Comprehending Math, I decided to ask students three essential questions while solving problems. Those questions are only a few that I took from Arthur Hyde's Braided Model. Those three questions help students to break down a word problem, understand it and develop strategies for solving. As a classroom teacher, you can turn these questions into a routine every time they come across word problems. Students can write down their responses or simply exchange ideas to help others lead to a solution. 

 

Here is an example:  The sum of three numbers is 98. The ratio of the first to the second is 2:3, and the ratio of the second to the third is 5:8. What is the value of the second number?

 

1) WHAT DO I KNOW FOR SURE?

Sample response: I know that the sum of the three numbers in 98. The ratio of the first number to the second is 2 to 3 and the ratio of the second number to the third is 5 to 8. 

2) WHAT DO I WANT TO KNOW, FIGURE OUT OR DO?

Sample response: We would like to know what the second number is. 

3) HOW CAN I SOLVE THIS PROBLEM?

Sample response: Since the second number is mentioned twice, I need to find the greatest common multiple of 3 and 5 and then represent the numbers as algebraic expressions. GCF (3,5)=15 so I can use the following expressions for each number:

Number one= 10x

Number two = 15x 

Number three= 24x

You can see that these numbers will satisfy the ratios mentioned in the problem: 

(10 to 15 is same as 2 to 3) and (15 to 24 is same as 5 to 8)

I will then add these three expressions 10x+15x+24x = 49x 

Since 49x = 98 x=2 and now we can tell the numbers are 20, 30 and 48 respectively. 

Singapore Math Experience

First, let's start with Singapore. You know that one of the highest math learners are in Singapore according to a study here. US being behind Singapore, some folks decided to bring Singapore Math curriculum into the United States. I believe that they did a great job. What makes Singapore Math so special is that:

• They don't have fancy, thousand-page textbooks.
• Their textbooks are simple, to the point, full of exercise and unlike their rivals not so much colorful.
• Their math goes in a sequential order so there are not much repetitions.
• Third grade math taught in third grade, no unnecessary repeats in later grades.

I think this is what Common Core people are trying to do right now. Other than those, Singapore Math has a different approach for teaching algebra, numbers and problem solving. You may see some of their work on Khan Academy as well. (Edit: They removed Singapore Math content from their website but they are still available on their Youtube channel)

 

Alright, I decided to use Singapore Math in my middle school classes because my students were missing lots of foundational skills which were supposed to be taught in elementary school such as long division or decimal multiplication. I decided to spend at least one class a week targeting those concepts but at the same time I didn't want to bore advanced learners.

 

So, I decided to test them all first to see which grade level they will fall into. In order to be able to do this, I have used Singapore Math Placement tests starting with 1A level. It says that on the website, if a student receives 80% or more, they can move onto a higher level test. A few students scored at 1A level and the others passed. I continued testing them until they score at any point below 80 %. Some students went all the way up to 4A and 4B level. These students were my advanced learners.

 

To be clear with the grade levels, do not assume that the middle school students are scoring at an elementary level. since they are not taught the Singapore way, it's quite normal for them to get wrong answers with the math questions they have never seen before. I have only done this to see where they belong according to Singapore Math curriculum and what level good be a good start for them.

 

Later on, I have shared them privately how they scored on the tests. Then, I have made copies of Singapore math textbooks in order to help them learn those concepts. They studied through the practice books and I have recorded their progress through those packets. This took me about two or three months in total but I have seen great improvement with some students.

 

For example, I had a very smart eighth grade student who didn't learn long division ever and I was able to teach him since he had to do lots of long division with those packets. At the end of the program, I had two types of students: The ones who liked it and the ones who hated it. I guess there were couple things missing at this cycle which I couldn't afford to do. Let me summarize the learning circle:

• They take a test and we identify students' level.
• Students start practicing (completing the packets with the teacher's assistance)
• Teacher gives them feedback on their mistakes and they learn from those mistakes [Yes, I skipped this part]
• Students fix the mistakes and they re-take the test they failed before.
• Students score more than 80% on the same test, so they can move on.
• Students scoring less than 80% means they need intervention.

By the way, I created a spreadsheet to keep track of which packet they have finished, what they got on the placement tests etc. When you put them all together, this was too much work but it gave me lots of new ideas to try:

Last year, I was teaching summer school where the students failed their math class and I had only fifteen days with them. Looking for what would be the best thing to work with them, I decided to implement Singapore Math curriculum. I did the same thing as above, except for one thing: giving them feedback. Since I had only five students, I was able to grade each packet and circle their mistakes, ask them go over again and fix them as much as possible.

This was very helpful since I saw the students actually improving their scores and learning the basic concepts which they never learned before (such as reading time, converting customary units and measurement). Everything seemed to be alright but we only had fifteen days so it was a little short to gain a great amount of success.

Overall, I still love the Singapore math curriculum but I would rather have students start with this curriculum in their first grade and become fluent with their foundational math skills. If you have any ideas, suggestions, you can share them here.

Math Game Night Ideas

Image by April Bryant from Pixabay

If you are thinking about organizing a math game night, here are some ideas for you: 

Math Challenge:
Students sit around like in a spelling bee contest. They go up on the stage and answer the questions by doing mental math.

Round 1: This round consists of questions 1-10 time tables problems.
Examples: 5 x 4 = ? 7 x 8 = ?

Round 2: This round consists of two digit by one digit multiplication problems
( 11x 1 to 19 x 10)
Examples: 12 x 8 = ? 14 x 5 = ?

Round 3: This round consists of two digit by two digit multiplication digit. ( 11x11 to 19x20)
Examples: 25 x 20 = ? 17 x 12 = ?

For this round, a multiplication table will be distributed to participants prior to the competition. In case of a tie, students will be asked harder problems.

Game 24:
Student sign up for the competition. Game will be performed as a tournament. In each round, two students compete against each other and the winner goes to next level. In each round, students are to answer three questions. 

Jeopardy:
First option:
In Jeopardy, there will be four players competing against each other. Every student will represent their homeroom. 

Second option:
Four students will be selected randomly from the audience. Student sign up before the game and a raffle takes place in front of the audience. After the raffle students go up and compete against each other.

Are you smarter than a seventh grader?
A group of 11the graders compete with a group of 7th graders. Questions will be from all subject areas of 7th grade. 7th grade students will be picked by the teachers. 11th graders need to sign up.

Millionaire:
The winners of the game show will be able to play at the millionaire. During the game they are allowed to ask the audience, call an outsider, or go 50/50.

Classroom Discipline 101

I am going to recommend you a great resource which is worth a lot more than it costs. Craig Seganti is  an experienced teacher especially in urban schools with the toughest students you can ever imagine. I have purchased his e-book and read it thoroughly. I will strongly recommend his product not only for new teachers but also everybody else. It's only $39.95 and you can download it instantly.

Why do I recommend it: Is because I have used his classroom rules, his techniques and followed his other strategies which worked out quite well in my class. I have also seen a couple of other teachers using similar strategies and they were also successful. Here is the link, check it out:

http://www.classroomdiscipline101.com/

Never Yell at the Students

Image by ashish choudhary from Pixabay

Students do a lot of things to drive teachers crazy. There will be moments where it's very hard to control yourself in those situations. Yelling at a student never gives you power; instead it takes power from you and gives it to the child. Yelling means: I don't know how to stop you or how to control this class other than yelling. Yelling also makes a person stressed, tired, and eventually the teacher wishes to quit his/her job. Even at times when the kids can be very annoying, you need to be able to control yourself. 

Khan Academy

I don't know if there is anyone out there who hasn't heard about Khan Academy yet. I am a big fan of Khan especially the Practice part. I have used Khan Academy videos for personal development and recommended students to watch them. I have created student accounts for my math club and monitored their progress throughout the year. One of our seventh graders went all the way up to trigonometry and he is still practicing. I love the sequence and pacing in math since students cannot learn advanced topics if they don't have the foundational skills.  http://www.khanacademy.org/

 

First Day of the School Toolkit for Teachers

Image by Dorothe from Pixabay

In order to start your first day smoothly, you may consider following some of my advice here:

• Obtain a student list from the administration.
• Place a sticker on each desk and number them.
• Greet students at the entrance and introduce yourself.
• Tell each student where to seat. (You can simply tell them: Go to Desk number 4. You will see there are numbers on the desks)
• I have seen some teachers prefer to write students' names on the desks.
• Seating chart could be made alphabetically. You can adjust it later on.
• If possible, show the seating chart on the board by using an LCD projector or a smartboard.
• Prepare a first day assignment, preferably a short survey about the student.
• After they settle down and complete their first assignment; distribute your syllabus.
• Now you can talk about your course outline, classroom rules and expectations.

I looked around and see if there are any templates ready to go. Following websites have some files you can download or at least give you an idea of how to prepare them: Seating Chart Template, Student Survey, Syllabus Template.