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If you don't know what the discovery method is, let me give you a quick summary of the basics.  With the discovery method teachers create an opportunity for students to DISCOVER mathematics (formulas, algorithms, connections, etc...).  This is basically opposite of a teacher standing in front of the classroom and TELLING the students the mathematics.  The discovery method leads to a greater understanding of mathematics and also builds students' confidence.  Here are 4 tips to implements the discovery method in your classroom. 

1. Open-Mindedness Environment:  Since students are discovering what works and what doesn't work failure is bound to happen.  In fact, you want failure to happen, because students will learn what does not work.  However, students hate failing, because they do not want to look inferior to their classmates.  This is especially true once students hit middle school, where students protect their image fiercely.  If you don't set up an open-minded classroom, many students will rather not try than try and fail. 

Setting up an open-minded classroom needs to start from day 1.  It's a culture you need to establish and live in your classroom.  Talk to your students about how mistakes are opportunities for growth.  Even displaying student's mistakes (without names) and taking time to learn what mistakes were made is a great strategy, because your students will see how learning really does happen from mistakes. 

2.  Guided Task:  You need to give your students a guided task.  Guided tasks often have more than one answer, are approachable for all levels and have room for continued challenge.  A simple example might be, "Create a prism with a volume of more than 230 cubic meters and less than 200 cubic meters."  A challenge you could add on to this question is a condition of surface area as well. Let your students have a productive struggle. 

3.  Teacher Assistance:  Teacher assistance is absolutely essential for successful discovery. Teacher assistance is NOT lecturing nor is it telling students what to do. Teacher assistance IS walking around the room and asking questions to the students.  The questions may look like "Explain to me what you are thinking."  "Explain to me this step that you did right here."  If students are stuck, "Tell me what you do understand" or "Tell me what part you don't understand." Guide your students but do not spoil the discovery process.  

4.  Conclusion:  Since the point of the discovery method is that students discover something you need to make sure to bring it all together to verify that ALL students have actually discovered what they need to discover. Also, if your guided tasks have multiple solutions or multiple ways to arrive at the solution you need to discuss this.  One way that I have done this in my classroom, is when students are working and I'm walking around I make notes of the different ways students are solving the problem.  I then have groups present different aspects of their process.  I usually don't have time, nor is it necessary, to have groups make a huge presentation of their whole process.  You just want to highlight the important points with the goal that all students make the discovery that you need them to make, such as an algorithm or formula.  

Once I implemented the discovery method in my classroom, retention of the material increased because students could connect the mathematics to experiences


Adding and subtracting integers can be a tough concept for middle school math students to comprehend.  Especially if students have been taught that subtract always means to get smaller. I wanted to share some tried and true successful ways to teach students how to successfully add and subtract integers. 

1)  Use number lines:  Number lines are essential when introducing adding and subtracting with integers.  I always found it easier to give students a paper with a bunch of number lines on them  to speed up the process of teaching.  Having students draw number lines for each problem can take a lot of time.  Another thing that I have done was to give students one number line in a protective sheet.  Then they use a draw erase marker to draw on the number line for each problem.  They can just erase the arrows after each problem.  Also, students love dry erase markers...so they always creates extra engagement.

2)  Teach subtraction as adding the opposite, then have students rewrite subtraction problems into addition problems.  For example, 5 - (-3) changes to 5 + 3, because you add the opposite of the second number.  Another example, -4 - 6 changes to -4 + (-6).  Having students circle the second number also helps those struggling with distinguishing between the subtraction sign and the negative sign.  You might need to remind students that when there is no written sign such as in -4 - 6, then 6 is positive, but then you will flip it to a negative.  

3)  Lots of practice with basic numbers:  Don't jump to adding and subtracting large value integers until they have a really good conceptual understanding.  Do lots and lots of number lines and rewriting subtraction into addition. 

I created some FREE ADDING AND SUBTRACTING INTEGERS STATIONS for you! Click here to get yours now!


I know I'm not the only one who wishes all school was cancelled on Halloween and the day after Halloween. So much excitement in the air and so much sugar in their bodies, makes it hard to teach.  I want to share some tips that have worked for me to effectively teach during the holidays.

1) Routine
Keeping your routine is the most effective strategy to having a successful day during an exciting time of year.  Start class the same way you always start class.  Transition from activities the same way you always transition. End class the same way you always end class.  Keep your routine, and the students will be more likely to keep their routine.   

2) Keep your Expectations
Acknowledge the excitement of your students, but let them know that you expect the same behavior as any other day.  Don't budge on classroom management. I love the idea of "work hard then play hard."  I would often take the time to teach this to my students, and reinforce this concept on days when they especially needed it.  

3) Fun and Engaging Activities 
Even middle school students love to do fun holiday activities.  I think it's ok to do holiday activities, but it is important to keep them standards based. You definitely don't want to waste a day of teaching, but you can be creative and teach the standards while recognizing the holiday. 

I was at the beginning of my teaching career when the "turmoil" over the common core standards was in full force.  My state had changed their standards to the "Utah Core Standards," but they were really the common core standards in disguise.  They were trying to avoid the terminology "common core" and all the political problems it was causing, but the truth was that the state recognized that these were quality standards, and it would benefit the students in my state if they were implemented.  

Before the 1960's arithmetic was the majority of what was taught in math class.  Then the United States entered the space war with Russia...the USA was determined to become the best.  As a result, the "new math" was introduced.  The "new math" dove into matrices, trigonometry, geometry, and more all on a very conceptual level.  The "new math" eventually received a lot of push back as many people thought it would be more beneficial for students to learn a little about a lot of math.  The curriculum then changed to "a mile wide but an inch deep."  At this point, math became less conceptual and more algorithm based.  The students that naturally had good math reasoning were still pushed along and entered Calculus during high school, but every one else started to get left behind.  This became evident when they entered college. The basic level math classes at the the Universities were full and many students were struggling.  

It was clear that the standards were failing many students.  Purely conceptual wasn't a solution, and purely procedural didn't work either.  The new standards were created with the goal of valuing conceptual and procedural.  With these new standards, the hope of many educators is to not lot students get left behind.  To allow all students to succeed. First, teach at a conceptual level so students can reason through the mathematics and perhaps even discover an algorithm.  Encourage procedural fluency, but only after they have mastered conceptual understanding.  

With these ideas in mind is how I create all of my resources.  Valuing both conceptual understanding and procedural fluency.  If you are interested in some math assessments that assess both conceptual understanding and procedural fluency you can click on the links below. They are also editable for use year after year. 

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