8/12/2015 5 Comments 4 Major Benefits of Inquiry Lessons & How to Use Them to Help Your Math Students Thrive
1. Inquiry enhances independent problem solving skills.
Inquiry-based learning teaches students how to find patterns, figure out properties, and discover new rules of mathematics. They slowly learn how their brain actually progresses through the idea to get them from "lost" to "ohhhhh, I see what the pattern is." After this becomes second nature, they will be more ready to attack future unknown situations.
The critical thinking skills that are required to ask questions that will lead to discovery are learned and acquired. They develop through practice, just like any other skill. Students must practice the inquiry process, just like we as teachers must practice sitting back and letting them struggle. It's not easy, but begins to feel more natural over time. As students get more and more accustomed to the inquiry structure that you use, they will slowly strengthen their own skills and gain independence in problem solving. Here's an Algebra example: I always teach exponent rules with guided inquiry. We work through the patterns and write out all the variables and cancel or expand until students develop product rule, power rule, and quotient rule for themselves. Then, when we get to the negative exponents later in the unit, their skills with this process have grown to the point that they know how to come up with their own concrete examples. They know how to look for patterns. I have them develop their own sets of rules for negative exponents.
Work towards the skills that will lead your students to persistence in problem solving.
2. Discovery leads to deeper understanding of a specific concept.
After discovering a mathematical property on their own, students will truly understand the concept behind the rule. Instead of following a set procedure, they will understand WHY a rule works and HOW it was developed.
Let your students build a concept, not just follow a given process. It's very rare that I give a formula as a part of notes. I like to have students find a formula for themselves. One example is for surface area of a cylinder. I have a dissection lesson for classes to "dissect" a cylinder "specimen." They have to discover for themselves that the length of the rectangle is equal to the circumference of the circle, and then go from there. Most middle school students across the world REALLY struggle with truly understanding this formula. They have a hard time visualizing the base and why circumference plays a part in this formula. However, after this hands-on lesson, the students really "get it" and never forget how the rectangular face wraps around. You can read more about this lesson in my Cylinder Dissection blog post. I do a similar structure for discovering circle theorems in High School Geometry. Students draw their own chords and have to tell ME how arcs, tangents, central angles, and inscribed angles are related, instead of me telling THEM these theorems. 3. Students discover a new level of math confidence & self-motivation.
When students feel the pride that comes from discovering a theorem, property, or formula for themselves (just like a mathematician does!), they suddenly gain a new level of confidence in their own math abilities.
I have noticed students have a sudden willingness to try a new challenge or approach a different type of problem instead of giving up. Kids believe in their ability to apply knowledge from one situation to another. I feel like this has given my students huge advantages on standardized tests. After I started incorporating more and more inquiry learning, the kids got more and more comfortable with being exposed to an unfamiliar problem type. 4. Retention increases HUGELY when concept mastery replaces memorization.
This is so important to note, and one of the benefits that I rarely see advertised by supporters of inquiry learning. Here's the thing:
If a student develops a formula, rule, or property for himself, then he understands on a deeper level where it came from. He won't have to memorize it at all.
The student can reproduce the formula at any time because he "discovered" it. This is especially true if it was done in a hands-on way. During a test, or later in life, the development of the idea is what will help a student recall how a property works or how to re-create the formula. So, here's how to make it happen in your classroom:
Some tips as you start to incorporate more inquiry learning, and give your students these benefits -
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There are two main ways to get your class working hands-on with Geometry concepts. Try manipulatives, software, or a combination of both.
Check out Geogebra for a great tech-approach to inquiry learning. To use the software in a lesson, have students create the diagram (or use a template). Be sure all measures are displayed. Then, as students manipulate the points, lines, and angles, they can observe how the measures change in relation to one another. For example, to discover properties of angles along a transversal, your students can quickly sketch a pair of parallel lines on the screen. Then, after drawing the transversal, they can label all angles and have the software display the measures. They will notice congruent pairs right away. Then, as they drag the transversal and change the diagram, the angle measures will keep updating. The students will see that certain pairs of angles are always congruent and certain pairs are always supplementary. Have students write these observations in complete sentences. I often have my classes write their rules in an "if___, then ___" format. I also have them give their own examples.
If you do not have access to technology, or prefer to follow it up (or mix it up) with a hands-on activity, the same properties can be discovered by hand. Have your students trace an angle, then slide it down the transversal to overlap perfectly with its corresponding angle. They can discover Corresponding Angles Postulate, and then move on to make observations about Alternate Interior & Exterior Angles.
The key is really just to avoid GIVING a theorem or property any time that you can. When students discover it for themselves, they can remember it, understand it more deeply, and apply it more smoothly in the future. You can use patty paper for this, but I usually just cut up tissue paper or tracing paper.
You can also have your class measure the angles with a protractor. They can draw a few diagrams and record angle measures and observations when the lines are parallel and compare these to similar diagrams where the lines are not parallel.
Be sure that each student records observations in complete sentences and then develops a property also written as a sentence. I do a similar setup for teaching vertical angles. Using a small piece of tracing paper, the kids draw a pair of intersecting lines. By folding different ways, they can see pairs of congruent "overlapping" angles.
I use an inquiry-based introduction for Triangle Theorems as well. For Triangle Sum Theorem, there are plenty of options:
1. Use Geometry software to sketch a triangle and display its measures. Find the sum of the interior angle measures, then drag one vertex to create a new triangle. Find the sum again. (Repeat) 2. Use a protractor. Draw a few different triangles with different classifications (right, obtuse, etc.) Measure the angles and find the sum for each triangle. (There will be some error with this method, so I have students do plenty of examples and notice that their sums are all approximately 180 degrees.) 3. Use cut-up paper triangles and have students line up the vertex angles to create a straight angle.
I do Exterior Angles Theorem in a similar way.
A few tips:
Looking for more detail or more examples??:
Here are links to some of my Geometry specific inquiry posts to get you started - 1 - How to actually structure an inquiry-based lesson plan 2 - The specificbenefits of an inquiry approach 3 - Questioning strategies for inquiry learning 4 - Discovering Congruent Triangles 5 - Discovering Impossible Triangles 6 - Discovering Surface Area (middle school) 7 - Discovering Segment Addition Postulate Or, click any of the images above to purchase worksheet packs and materials to accompany your lesson. Have you subscribed? I'll send you great stuff!
To Read Next:
A Downloadable Guided Inquiry Lesson for Grades 6-12 - Great for Gifted or Math Clubs
This lesson can be inserted anywhere throughout the school year and is perfect for students in a gifted program.
It would also be great for those last days of the school year, when exams are over, but you want to do something purposeful. Get your students thinking critically about place value and the base ten number system by comparing it to another system. Start by introducing the Mayan Number System. This system uses base 20 and is great to work with because the zero acts as a place holder, just like our own! After introducing the lesson, group students into pairs and hand out the Number Cards and worksheets.
Have students practice assembling two-digit and three-digit numbers using the cards.
The activity is great in pairs. You will hear some awesome math talk about place value and digits. It's so fun to see your students thinking more deeply about a fun new math idea.
Extend the lesson by asking students to try another system. Have them use base 8 (with standard numerals) to write numbers from 1 to 100. Click here to download the files for the Mayan Number System lesson. Enjoy!
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