Tutorial: The
'Need-Levels-Choice'
Approach to Teaching Equations
An Engaging Approach Through Which To Teach Your Algebraic Method For Solving Equationgreater successs
- But With Far Better Results
- But With Far Better Results
Important
Before we get started, this tutorial is NOT about changing the algebraic method for solving equations that you teach to your students. Rather, this tutorial will show you a fantastically simple-yet-very-engaging approach that is (almost) guaranteed to make your method more successful, i.e., give your students more confidence, better understanding and greater success when teaching students how to solve equations.
Also Important: You are likely wondering “Is this going to be a whole lot of bla bla ..." Stay tuned ...
Fact: When we encounter a tutorial about something we’ve taught ‘a hundred times’ we are always sceptical - especially when it is from a provider we don’t know well. So you might be tempted to skim read this tutorial. This is understandable. However, skimming this tutorial may just be a huge mistake.
Don’t waste your time!
This might sound harsh, however … if you do not intend to work through this tutorial closely, then you may as well stop now. Either save the URL and come back when you have more headspace … or … throw it away. A cursory glance will only be a waste of your time. This one is an all or nothing situation.
Also, note that the text and videos contain different content - both need navigating.
Don’t waste your time!
This might sound harsh, however … if you do not intend to work through this tutorial closely, then you may as well stop now. Either save the URL and come back when you have more headspace … or … throw it away. A cursory glance will only be a waste of your time. This one is an all or nothing situation.
Also, note that the text and videos contain different content - both need navigating.
Really Important
Save the URL of this tutorial in case you want to refer to it later because it is not listed on the website.
In the article with the subtitle Why Student Understanding Needs To Be For The Majority of Lesson Time a case is mounted as to why we should strive to have students understand what they are working on. Having students understand - for the majority of all lesson time - the activities we give them to work through causes their engagement to skyrocket. This, in turn, opens the door to learning.
In the article with the subtitle Why Student Understanding Needs To Be For The Majority of Lesson Time a case is mounted as to why we should strive to have students understand what they are working on. Having students understand - for the majority of all lesson time - the activities we give them to work through causes their engagement to skyrocket. This, in turn, opens the door to learning.
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Teaching equations can be perilous!
The solving of equations is one of those topics that requires students to really ‘get it’. And with equations, students tend to either get it or they don’t. If they don’t get it, they switch off real quick. Unfortunately, this unit tends to result in many students switching off!
The way I see it, there are three, major, closely related reasons why students switch off during a solving equations unit:
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The Need-Levels-Choice approach you are about to witness tackles all three issues head-on. When the approach is implemented correctly, you should expect high student engagement, high student success and a desire in students to follow your algebraic method correctly.
During an equations unit the following two things need to occur:
During an equations unit the following two things need to occur:
- We need to teach students (at least one) algebraic method.
- We need to start students on easy questions before working towards more difficult questions.
Herein lies the problem!We have to begin with easy equations, and we have to teach students a method. But when we do these two things together, the process often backfires! Why? Because many students resist using our method when applied to easy equations. When we teach students our algebraic method for easy equations, students resist!
Most teachers will relate to the following: |
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- When first teaching our algebraic method most of us use simple, one-step equations, solvable by inspection, such as 'Find the value for m when m + 3 = 5'.
- We say something like “Follow this method for these easy equations so that when you face difficult equations you’ll have a reliable method to help you solve them”.
- But the students respond with "We don't need this! We know the answer is 2" … or … "This is stupid. Why do we need a method" … or … "I want to do it my way. I can see what the answer is!"
- This is the point in the unit from which we rarely recover. Instead of having students enthusiastic about solving equations, many switch-off. We aim for student success and engagement but end up with students who are frustrated and disengaged, or, at best, an outcome that is below potential.
Do you relate? If not precisely, do you suspect some of your students SHOULD be more enthusiastic by lessons 3-5 of your usual equations unit?
The #1 reason students resist learning our algebraic method
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Put yourself in the shoes of one of your students ...
This solving equations thing is new to you. The teacher writes up m + 3 = 5. You can see the answer is 2! You feel a touch of excitement - “Hey, I can do this!” But now the teacher is spoiling the party by demanding you follow some stupid method that, clearly, you do NOT need. The answer is obviously 2 - why do you need a method? Your conclusion? “This solving equations thing is nuts!” And the teacher thinks: "If they'd just do as I say for these easy equations then when they reach the more difficult equations, they'll see WHY I'm giving them practice using the method now. |
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Beeeep. WRONG!
The reality is that - at this early point in the unit - THERE IS NO NEED FOR A METHOD. The students are 100% correct in saying “we don’t need a method”.
But the real tragedy in the above scenario is this: students lose some trust in us - they don't trust us when we say "use this method". They are then more likely to refrain from implementing the method according to our requests, and when they reach the 3-4 equations will unnecessarily struggle.
The reality is that - at this early point in the unit - THERE IS NO NEED FOR A METHOD. The students are 100% correct in saying “we don’t need a method”.
But the real tragedy in the above scenario is this: students lose some trust in us - they don't trust us when we say "use this method". They are then more likely to refrain from implementing the method according to our requests, and when they reach the 3-4 equations will unnecessarily struggle.
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Creating a NEED TO LEARN is key
If we want our students to learn something, then we need to create in them a need to learn it. Saying “I’m teaching you this now because you’ll need it later” doesn’t cut it.
Enter to The Need-Levels-Choice approach to teaching equations (with your method). The Need-Levels-Choice Approach mostly applies to the first 2-3 lessons. However, by using this approach during those early lessons, you should expect students to be: |
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- Exuberantly engaged.
- Understanding what they are doing.
- ‘Begging’ you to show them your method for solving equations.
Then, after those initial lessons, students will be much more willing to follow your method closely as they tackle the more difficult equations.
Watch the video below to see the Need-Levels-Choice approach explained and in action.
Disclaimer: The classroom footage is a bit grainy but suffices to convey the message.
After watching the video … Keep this in mind
Had the classroom footage been taken when I was teaching my own classes (before I left teaching to develop PD full-time), you would have seen super-engaged students solving equations with a great deal of enthusiasm. The footage used for this video was from a salvage lesson. The class had experienced one lesson of something similar to this approach, but the lesson ‘bombed’ and I agreed to show the teacher the correct version of the Need-Levels-Choice. Given the students’ poor experience in the previous lesson and the fact that I was unfamiliar to them, the students were much less enthusiastic than was my usual experience.
The Need-Levels-Choice will save you time!
(Two-three 40-min lessons of time in an 8-10 lesson unit)
(Two-three 40-min lessons of time in an 8-10 lesson unit)
Students new to solving equations will, during a typical unit, take 5-6 lessons to reach the point where they are encountering equations that require four and five steps to complete.
However, with a correctly implemented Need-Levels-Choice approach, students typically reach the 4-5 step equations during their third lesson. This is a saving of 2-3 lessons! It is achieved because students are more engaged, understand the process and are gaining a great deal of success.
The Printable Notes
A set of printable notes are included here.
Five levels of equations - example
Download this example set of 5 levels of equations for use in the Need-Levels-Choice Approach, or use it as a guide to making your own.
However, with a correctly implemented Need-Levels-Choice approach, students typically reach the 4-5 step equations during their third lesson. This is a saving of 2-3 lessons! It is achieved because students are more engaged, understand the process and are gaining a great deal of success.
The Printable Notes
A set of printable notes are included here.
Five levels of equations - example
Download this example set of 5 levels of equations for use in the Need-Levels-Choice Approach, or use it as a guide to making your own.
Unpacking Need-Levels-Choice - 4 keys that make the approach a winner
The Need-Levels-Choice approach:
Note that Need-Levels-Choice is also ideal for revising equations as well as teaching equations to students who coped poorly with the unit in previous years.
- Has equations arranged into LEVELS which is key to enabling the approach to work.
- Creates a NEED in students to learn your method when they encounter the first 'brick wall' - the level 3 equations (2-step-not-solvable-by-inspection).
- Gives agency to students from the beginning of the process through offering students CHOICE of a method when solving the level 1&2 equations ("You can use whatever method you like to solve these equations ... ").
- Gives agency to students by providing them with CHOICE re the equations they solve and choice re their speed of progress through the levels.
Note that Need-Levels-Choice is also ideal for revising equations as well as teaching equations to students who coped poorly with the unit in previous years.
Video #2: Making the algebraic approach understandable for students
We all have our favourite method for solving equations. I'm not here to tell you to adopt a different algebraic method. However, it’s often enlightening to see other methods in action. The algebraic method demonstrated in the video below is, I believe, fairly standard. However, a deliberate attempt has been made to demystify the algebraic process for students.
In the video, I demonstrate some of these demystifying strategies that aim to allow all students to make sense of the algebraic process.
In the video, I demonstrate some of these demystifying strategies that aim to allow all students to make sense of the algebraic process.
De-mystifying the algebraic process - The Main Points
The main points of Video #2 are summarised at the bottom of this Google Doc.
PD that contains more tutorials like this one
If you like this style of easy-to-implement tutorial and are looking for PD that will make a difference in your classroom check out our courses on the All Courses Page.
If you are looking for positive departmental change, check out the Teacher Teams Page.
If you are looking for positive departmental change, check out the Teacher Teams Page.
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