Why Make the Distinction?
Have some of your students already mentally "ruled out" a major in mathematics?
It is pretty common for high school students to make judgements about mathematics in general based on their experience in math classrooms throughout their education (which makes sense - can't blame them!). Obviously, the math they have been exposed to is limited to the topics in K-12 curriculum and is limited to the teaching styles that are common in early, middle, and secondary education. However, a student can become completely turned off to mathematics without ever even getting a peek at certain fields within math. Don't let your students give up on a future in a mathematical area they have never even heard of yet! I experienced this myself, and was so lucky to have one last math class during senior year of high school to knock some sense into me. I had disliked math all along. Because of scheduling changes, I ended up taking one last class even though my math credit requirements were already satisfied. The last minute peek into higher level math got me so interested that I chose a major and career in Math! I ended up going into math education. Without that class, I would never have discovered my LOVE for math. I have also experienced this as a teacher. Sometimes, when students get a glimpse into theoretical or applied math, they realize that they truly do not hate all math. Before your students leave high school, give them a peek at the options that lie ahead. Be sure that they are aware that there are fields within mathematics that may interest them far more than the math they have studied so far. It may just make the difference for someone who truly is meant for a career in math and does not yet realize it. Some topics for discussion:
After they do a little research, have your students make a quick chart with examples of Theoretical and Applied Math topics. Have each student determine which area they might prefer to study. Here is a worksheet to guide your students in this short project. Another option is to work as a whole class and collaborate to make one huge chart on the board. Enjoy! Click on the images to download. Worksheet Included to Guide Your Class Research and Discussion
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Are you having trouble making your lessons student-centered?
Prompts for inquiry-based learning can help guide your instruction and give students a chance to investigate for themselves. Start small. Take a look at a lesson in which you normally begin by giving a formula, rule, or property. Your lesson may typically sound like this: "Here is the formula for ___. Let me show you how to use it, and then we will practice." Now, instead of giving the information, allow the students to develop the formula for themselves. They will remember it better, understand it more deeply, and be able to apply it. The great news about adding guided inquiry questioning is that it can sometimes be done with ZERO extra teacher prep. Try this format instead: "You are going to develop and use a formula today." Kick the lesson off with just the right question and then sit back. Offer materials or samples as needed. The students will do the work, and you as the teacher will simply decide how much help to give each student or group. Try to resist the temptation to participate too much! Here are some sample prompts. Remember that instead of GIVING information, you are asking the class to use what they know and test cases to come up with a pattern or rule. Give a prompt that fits your objective and then give plenty of time for students to think and work. I like to have students work in pairs.
Here are some inquiry-based questioning samples to write your own prompts within a lesson: 
Do you feel that you do not have time to give for this type of lesson? Give it a try and you may notice that it is worth it. If your students develop their own formula for surface area, you will need fewer practice problems afterward, and you will spend less time reviewing. They will understand the formula and reproduce it without forgetting. The time saved later will balance out.
When students have completed an investigation, give them some time to reflect and write up their conclusions. Try questions formatted like this: 
To get more detail about how to actually structure a guided inquiry lesson plan, read the additional posts below.
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12/12/2014 7 Comments Higher Level Thinking in Mathematics
I want to share a few of my recent favorite strategies for getting math classes thinking more deeply about concepts.
Let's get them really wondering about what makes the math work! The first one, writing in sentences, they really do not like (sorry, kids!) but it works so well and is SO important. The other ideas are ones that the students really do enjoy and request. I love to see a class really engrossed in trying to figure something out and ENJOYING IT!!
Writing Prompts
Writing in complete sentences is the key to incorporating writing in math. This is always a struggle. You will have to tune out the complaints that "This is math class; Why would we have to write in sentences?".
When questions are worded the right way, you can succeed with getting your students to write out real answers. Here are some samples (from my Pre-Algebra Question Pack) - Try writing a few test questions or Warm-Ups that sound like this:
Turn the Tables
Flip your questioning around for a few minutes, and ask students to supply you with the information that is usually given. This works a little like Jeopardy, where you offer what is typically the final answer. I like to ask for TWO DIFFERENT questions to keep students thinking hard. You can do this in a whole class setting or even use this type of problem on a quiz. Sometimes I include extra criteria to guide the responses and keep students from taking the easy way out. Here are some samples:
"Always," "Sometimes," or "Never" True? free template
Here are some sample statements to give you an idea. This type of activity works for any subject.
Is the statement always true, sometimes true, or never true?
This works well with partners. They will make sure to test every case they can think of to see if a statement can sometimes be true. 
This strategy is the absolute best that I have seen for getting students really thinking and discussing a concept. I ask individuals or pairs to determine whether statements are "Always True", "Sometimes True," or "Never True." This type of questioning goes so much farther than a standard true/false question. High school teachers, textbooks, and tests do this sometimes, but I like to incorporate this at the middle school level as well. Getting kids used to this type of thinking early is so beneficial!
I developed some activity sheets with statements. To make it a little more fun, I added coloring. Students color each circle according to the directions and end up with a pattern for quick checking. Classes really seem to love this, and the higher level questioning and thinking that you can hear as they test cases is amazing! Here is a link to the pre-created puzzles in my store. If you would like to make your own, here is a FREE template to download. inquiry-Based Learning
Remember that one of a teacher's most valuable tricks is.....
... the PAUSE... Get your students intrigued, and then sit back and wait. Do not always give the answer. At first they may be surprised that you are withholding information, but resist the urge to always tell. When students figure out a concept for themselves, they remember it better, and they understand it better. Try some of the wordings below: "There is a formula for surface area of a cube, but I am not going to tell you what it is. Now that you know what the term "surface area" means, use the nets in front of you and develop a formula." "There is a formula using distance, rate, and time. You need "d," "r," "t," "=," and one basic operation. Think it out with your partner using this word problem about driving at a rate of 25 miles per hour. See if you can write a formula that works and seems reasonable. Then explain to the class." "Now that I have explained zero pairs to you, use the manipulatives on your desk to model the integer addition and subtraction problems on the worksheet. Then write a set of rules for adding and subtracting integers based on the patterns that you observe." Read more about inquiry strategies using the links below.
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