The Galileo website is an awesome starting place for teaching with inquiry. They have articles and resources to learn about inquiry-based education as well as plenty of research.
Start on the home page, then check out the full set of classroom lessons and examples. They have plans for specific high school, middle school, and primary school math investigations.
You can also download the Focus on Inquiry eBook, read more about what inquiry means, learn how to construct essential questions, and much more.
NCTM offers a set of math resources on the Illuminations site. One of my favorite features here is the enormous library of virtual manipulatives. You can allow your students to drag around the virtual algebra tiles, discover triangle congruence theorems, and shade equivalent fractions (and that's all just pulled from the first page of manipulatives!) This set is perfect for classrooms with computers or ipads.
There are also some fantastic lessons. They're sorted by grade level. Check out some lessons for grades 6-8 or 9-12. There are lessons for younger kids too.
The brain teasers are also fun and would be great warm-ups. There are plenty available.
I use GeoGebra to make exploration easy in Geometry class. Students can sketch a figure into the software (parallel lines intersected by a transversal, centers of triangles, tangent lines, etc.). GeoGebra allows them to easily display angle measures, drag points around, and notice properties by observing what measures change and what measures stay the same. There are endless possibilities with this, especially if you are trying to incorporate a little discovery-based learning.
Download the free software for your classroom or check out the teacher pages that are packed with worksheets, samples, and ideas for lessons that use GeoGebra.
Desmos is the new way to do all your graphing and plotting. It's ideal for Algebra investigations. Use this site to allow students to transform functions and create fun or artistic graphs.
Try the graphing calculator or browse the teaching resources and activities that are available. You can also check out videos that show some of the many uses of the desmos calculator.
5. Inquiry Maths
As an inquiry fan, I have loved the Inquiry Maths site for a long time. The question prompts are perfect ways to get students thinking critically about math concepts.
Take a look at the question prompts in each category on the left sidebar. There are tons of great Number Prompts, Algebra Prompts, Geometry Prompts, and Statistics Prompts.
I also recommend checking out their assessment framework and tips for writing your own prompt.
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Here's what Dawn, an Algebra teacher says about using warm-ups: "When I teach completely different preps back to back, I survive on the daily warm-up routine. Students automatically start working, and I pause and get my plan for the period straight. Warm-ups have changed faces over the years in my classroom. From a daily word problem to 5 quick prerequisite problems, all were highly beneficial, but all took preparation. At some point it’s hard to be awesome every single day and still have a life outside of school. I needed a routine that needed no prep."
If you are not convinced to try warm-ups, check out Mrs. E's blog post: "Bellwork Keeps Me Sane."
Once you decide to incorporate a warm-up or bell-ringer into your daily routine, decide what format would be best for your class.
Here are 8 totally different ways that you can kick off your math period. Try a combination of a few of these ideas to get a well-rounded, but consistent warm-up routine.
1. Number of the Day / Function of the Day
I love this new warm-up idea from Algebra Simplified - "After reading an excerpt from a wonderful book on math teaching (that I cannot find to reference), I adopted the Function of the Day. No prep needed; just write a function on the board.
Students write 8 true facts about this function (I don’t even collect it; we discuss their responses). For example, the function today for my Algebra IB students was x-2y=4. Students gave me the linear form, the x & y intercepts, the slope, the equivalent equation in slope-intercept form, equivalent equations using scalars, a perpendicular line, a parallel line, and a random point on the line in function notation.
Two weeks ago they couldn’t even tell me the standard form of a linear equation. All of these concepts taught in a previous math class have been refreshed solely from this warm-up routine and debriefing of student responses. Don’t tell them, but the functions are going to get progressively more complex." - Algebra Simplified
2. "Writing in Math" Question Prompts
3. Problem of the Day/Week
4. Video Warm-Ups
5. Test Prep
6. Review of Prior Knowledge
7. Introduction to New Content
8. Joke / Riddle
Julie from Secondary Math Solutions shared her newest warm-up strategy: "I tried something different last year and just had a joke posted when they came in.
One of my favorites was "what do you call friends that like math"? Algebros!! And from there we would go straight into checking the homework."
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A recent study has proven that success in math is strongest when both halves of the brain work together.
So, we have started adding art into STEM curriculum, incorporating more project-based learning, and allowing creative thinking through inquiry.
Here's the reasoning behind the theory, plus how to maximize the benefits of right and left brain crossover for your own students.
Right Brain Vs. Left Brain
You are probably already aware of some of these distinctions between the left brain and right brain:
But are you aware that your own teaching style probably favors one side of the brain more? Lecture, research, notes, and quiet independent work are classroom features of left-brain teaching and learning.
Math is also a logical and analytical subject with a left-brain tendency. So if you are teaching math through lecture, notes, and practice, you are neglecting your students right-brains!
Here are a few ways to add a little more "right-brain-ness" into your class:
The right and left hemispheres of the brain communicate through the corpus callosum, a fiber bridge that crosses between the two sides.
Any time you can encourage interaction between the hemispheres of the brain, you strengthen this connection.
Click the images to explore these brain-friendly products.
Physical exercises that cross the midline can strengthen the nerve-cell pathways between the two sides of the brain. The midline is an imaginary line drawn down the center of the body. An exercise in which the left hand crosses to the right side of the body is an example of a cross-lateral exercise.
This type of physical movement helps the brain hemispheres to communicate across the corpus callosum. This benefits your students because it helps to coordinate learning.
We already know that students need to get up and move every 20 minutes or so. During that time, try a couple of cross-lateral exercises to force the two sides of the brain to communicate.
"When you cross your midline in exercise, you get a boost in brain alertness, creativity and memory!"
-Alison Beaver (article here)
Incorporate Right-Brain Friendly Options
Have you ever noticed that a lot of kids who like Algebra and do really well in it tend to struggle when they start Geometry the next year? Also, quite a few kids reach Geometry and suddenly like math class for the first time. They had difficulty in Algebra, but in Geometry, math suddenly makes sense to them.
Some people do well in both, and have a good balance between right and left brain learning, but I think that a lot of the students who enjoy Geometry are often the more artistic & spatial learners. They thrive in a right-brain-centered environment.
(Previous Post: Learn more about the learning styles of your own class of students here.)
Try to mix up characteristics of the two categories, or use choice boards that offer options from both categories.
I like to include options on choice boards such as:
Compared to taking notes or giving an oral presentation, these types of tasks offer more communication between the two sides of the brain.
Surprising Benefits of Coloring & Doodling
You may have heard about the recent trend of adult coloring books.. It has been discovered that the simple act of coloring helps to activate the brain.
Coloring can improve memory, learning, and retention. It even offers the additional benefit of stress relief. The relaxation that comes from coloring decreases activity in the amygdala, which is the part of the brain affected by stress.
It is possible that this is partly due to an unconscious reminder of childhood, a time of lower stress. Whatever the reason, this got me thinking about using coloring to reduce math anxiety. It is great to add just a touch of coloring (in a purposeful way) to a math activity. This can help students to relax and focus while still learning.
I read through a really interesting study in which people listened to a recorded conversation. Afterward, they were asked to recall the names of people in the conversation, and those who were doodling as each person was introduced were able to learn the names more easily!
It turns out that doodling (like coloring) requires just enough brain power to keep you from daydreaming, but not enough to distract you. It actually increases focus!
(article from TIME)
Here are a few ways I add just a touch of coloring into math activities to keep both sides of the brain active during the learning:
Click the images to take a closer look at these items.
My next thought is something like doodle notes - I will have to add that to my long list of projects. I bet the kids would do really well with something like that.
Now Here!: "Doodle Notes" for Math
Edited to add: I've put together the first batch of doodle notes, as promised. Check them out by clicking the images below.
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