Lesson's With A Good "Hook"

Does Your Lesson Have Context?

When creating a lesson one of the important things a teacher needs to take into consideration is the level of engagement the students will have. Obviously, we want the students as engaged as possible. Now I know understand that many teachers find it necessary to have classes that they lecture and students take notes to help lay some ground work for the upcoming lessons. However, it is important for a teacher to always be critical of their methodology for delivering lessons. Furthermore, teachers need to make sure they are taking the time to get to know their students and decide what delivery would work best with this particular group of students.

When looking at the educators I follow on twitter I seem to see a growing trend of teachers becoming more theatrical in the delivery of their lessons. Below is a great example to check out:

20 Books BY Teachers, FOR Teachers to Inspire Your Teaching via #DitchBook author, @jmattmiller https://t.co/VEVScqRxr1 #tlap pic.twitter.com/5GPCQ9g5ZH

— Dave Burgess (@burgessdave) October 18, 2016

Retrieved From: capt_hook3.jpg

I wouldn't go as a far as saying I'm telling teachers reading this to buy a new costume for each topic and turn your classes into a fully interactive play (although that's kind of an interesting idea to for integrated curriculum with the arts). I am however, strongly encouraging teachers to look at how engaging their lessons are. For me this is can be as easy as devising a creative "hook" to your lesson to capture your students attention (i.e., Captain Hook)



In the bigger picture, the point I am trying to make is to make sure that lessons provide some kind of context to them. This makes is so much easier to answer the time old question "why do we need to learn this. " Adding context to your questions whether it's bringing in the latest viral video or making math questions about real life problems this question quickly begins to be asked significantly less.

Do you have a unique way to add context to your lessons? Feel free to add your opinions to the comments below.

Technology's Place In The Math Classroom

With the majority of my education having taken place in the 21st century it is easy for me to see what an integral role technology has played in the classroom. Almost as a minimum teachers are using projectors and slide presentations a daily norm in the classroom. But to what degree should or can the education system incorporate technology into the classroom?

I believe it is easier to address the what can be used in the classroom so I will do that first. Honestly, the options are quickly becoming endless. Initially cost and internet connectivity were combined a monstrous inhibitor to technology in the classroom. However, as technology progresses so does the ease of it's integration.  Numerous students have their own PED and are able to bring these to the classroom. This is just a starting point though; teachers are able to use free websites such as Padlet, Secretive, Google Classroom,  PollEV, Kahoo and countless others.

It is clear that teachers have many websites and programs that are easily accessible to them. The next thing to think about is which types/forms/means of technology should be used in the classroom? I think the easiest way to address this issue is to look at from the perspective of our student's success. If the technology helps create an inclusive environment, helps the student(s) achieve learning objectives or aids in maintaining the engagement of the student(s) I believe it is easily justified to be used.

Another way we can look at this is presented through this article from EdTech; a website that is based around the use of technology in an education setting. I recommend at least taking a look at this article but the website as an entirety is fantastic.

In conclusion; I truly believe that incorporating technology into the classroom can help a number of students. However, one important thing to remember is that technology should always be used as a compliment to the teacher not instead of the teacher.


Feel free to let me know how you use technology in the classroom or any of your opinions on the use of technology in the classroom. You can do this by commenting below

EDIT:

I found an awesome infographic today on one of my favourite Tech Based educator's twitter feed. Alice Keeler suggests that we should be moving anything that isn't better on paper to a digital platform as a means to upgrade it. I wouldn't go as far as saying that you should be filling out this flow chart every time you make a lesson and moving all of your content online. However, I do think it should be in the back of teacher's minds to be critical about the means used to deliver a lesson.  Thinking about whether this could, as well as should, be done through a digital platform is always an important Especially as we move more and more into the digital age. Check out the infographic below:

How Is This Better Than Paper? https://t.co/x4Bl6HEDzP pic.twitter.com/am8aeuEWW7

— Alice Keeler (@alicekeeler) October 31, 2016

Cheers,

Mr. Studenny

Gaps In The Classroom

Students often find lessons difficult to understand or keep up with. I'm sure a lot of my readers can look back on their time in grade 9 or 10 math and remember feeling totally and completely lost. That feeling when the teacher is talking about something and you have literally no clue what they mean. That feeling, if your like myself, leaves you stressed, anxious and incredibly uncomfortable. It is almost as though you are missing that one piece of the puzzle to complete it.

At this point of your read I encourage you to go to the following google drawings page and attempt to get get all the blue shapes inside the black square. Attempt to do so without manipulating the shapes orientation or size or using the red square to complete. (EDIT: Please when you're are done return the shapes to their initial positions at the top, not necessarily in the order they are right now)

You will quickly find that without the red square it is impossible to fully complete this challenge.

You can think that each of your teachers are giving you one piece of the puzzle that will let you create a final product. However, imagine one of your teachers fails to successfully give you the piece. No matter how much you try you can't complete the puzzle.

One of the biggest struggles as a teacher is to determine where students gaps in their knowledge and understanding is and how to combat this. This struggle with putting the puzzle together gives a small insight into how students struggle when they have gaps in their education. With this in mind it is entirely reasonable for these students to not be able to meet the standards in classrooms.

So how do we determine which students have gaps and what those gaps are? 

This is defiantly the big question for teachers with regards to students who are underachieving. There are a number of techniques that teachers can use to help identify these gaps:

1. Diagnostic Assessments: before diving into new material taking the time to establish a baseline and make sure students understand all prior material that is necessary to move forward. 
2. Observing Conversations: a carefully trained ear can allow a teacher to pick up on subtleties in vocabulary and other communication skills that suggest gaps. 
3. Analyzing Answers: working through a students thought process can tell the teacher a lot about how they approach problems and what their gaps or strong suits may be. 
4. Ministry Support: the MOE provides resources to help address gaps students face. These can be found through the website Edugains. 

To conclude; it is imperative that teachers take the time to identify students who have gaps in their knowledge and furthermore, take the initiative to close these gaps. Through this process our teachers will be able to provide tools to certain underachieving students that will help them succeed.

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Are you a teacher that has a strategy they use to close gaps? Feel free to share in the comments.
Are you a student who has faced a similar struggle? Feel free to share our story or insights in the comments.
Do you have any questions? I strongly encourage you to ask! 

Differentiation in The Math Room

In the classroom all of our students are unique and it is the teacher's obligation to treat and teach them as such. One of the more difficult aspects of teaching is making sure that your lessons are accessible to all students. The last thing you want to do is create barriers between your students and understanding.  It is easy to think of equal opportunity, accessible lessons and barrier free classes as taking the time to work with students who are achieving at a lower than average standard. This is can be problematic as you are no longer giving the attention to students who are gifted that they deserve. Take the following picture posted by @barrierfreemb on twitter as an example:

Equality vs. equity vs. the removal of systemic barriers #accessibility #DisabilityMatters pic.twitter.com/NBU3HwYfMU

— Barrier-Free MB (@barrierfreemb) May 12, 2016

The problem in this illustration is that the illustrated characters can't all see the ball game. In the first segment you see the characters each have an equally sized box; representing equality for all. Next we see that the boxes have been modified and individualized for each of the characters allowing them to all see; representing equity. In the final segment you see that the barrier that was put there in the first place being modified to allow all characters to see clearly without the need for boxes; representing the removal of systemic barriers.

When I look at this illustration I can so clearly see the connection to a key concept we've been recently introduced to that aims at creating an accessible lesson. The concept is to have your lessons built with a low floor and a high ceiling. This means that students who are achieving at a lower standard can access the same work that students who are achieving at a higher standard can.

One of the means of creating a low floor/high ceiling lesson is using techniques such as open ended questions as well as parallel tasks. Both of these aim to have students able to work on the same curricular expectations with the same task goals but at their own individual level. It is important to note this doesn't only benefit students at low and high standard achievement levels but also all the students in-between.

If you're new to creating open questions (like I am) it can be quite difficult to develop them yourselves. The important parts of open questions are that any student can access them.  An example could be asking students:

"How many apples are too many for a family"

instead of:

 "You are part of a family of 7. You each eat one apple per day 5 days a week. Apples last for one week before they go bad. How many apples should you buy for your family?"

Having this open ended question allows students to make it personal as well as control the complexity of it. One student may think of their family and easily say 20 apples are too many for my family. Another student may look at it more in depth by deciding how many people are in the family, how many apples they eat a day, if everyone eats an apple, etc. 

Marian Small, is very experienced at developing these type of questions. It is defiantly worth following her on twitter and her "good question of the week."

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Feel free to comment if you are currently working to use open questions in your classrooms.
Do you use them in math or other subjects?
What do you do to break down systemic barriers in your classroom to ensure you lessons are accessible to all?
What are you thoughts on equality vs equity?

Using Manipulatives for Pattern Recognition in Mathematics

Helping students understand the relationship between patterns and algebra can be an abstract progression. Using manipulative to help students visualize the patterns can be an incredibly useful tool. If teachers can start getting students to visualize the progressions of certain patterns and develop their skills in visualization the transition into algebra will be much smoother.

The following pattern is an example of this type of relationship:

Photo by author.

When I look at this pattern it is easy to develop an algebraic expression to determine the relationship. The expression n+4, where n=term number represents this.  Although it is easy to develop this expression it is important to take the time to look at this relationship and see why this expression makes sense. If we can have students focus on the fundamentals of developing this expression. If we can have students look at the diagrams and determine which parts are growing and which parts are consistent they can easily see relationship. Recreating these patterns with manipulative gives students the opportunity to visualize the progressions. The green triangles remain constant at 4. The purple square increases by one for each term; starting at one. 

The exciting part of this is that with repetition and practice students will be able to identify more complex problems and how they relate to linear relationships. 

Photo by author.

After practicing pattern recognition and developing algebraic expressions students can begin to relate these activities to graphing linear relationships. Take the pattern to the right for example. While recreating the patterns students will be able to develop the algebraic expression to be 3n+4. The difficult part in this example would be seeing that the centre square is also part of the fixed triangles. It would be through the practice that students would become accustom solving this. 

Photo by author.

From here, students can use manipulatives from the patterns on graph paper to visualize the growth.  Next they can track the progressions and relate the this growth back to the algebraic equation. This lays the frame work for discussions surrounding graphs as well. The relation between term 0 and the y-intercept is is easily seen. Extrapolation is also evident while using this method. 

Why Are WE Scared To Estimate?

My instructor brought up a great point the other evening about students struggling when asked to estimate answers to basic mathematic questions. (L. Surrturmm, personal communication, September 14, 2015) This really got me thinking and the more I thought about it the more I could relate to the issue at hand. Through this post I hope to shed some light on the reasoning and a possible strategy to correct this.

retrieved from: http://images.clipartpanda.com/estimate-clipart-math_estimate.gif 

I want you to think back to an experience I'm sure most of you all had in a math class. We've afll been given a math question asking us to first estimate the answer than compute it after to see how close we were. For example:

Question:

"If Jenny gets  $.47 for every Apple that she sells how many dollars while Jenny have if she sells 30 apples per day and works 90 days in the summer?"

Answer:
Estimation:___________
Computation:_________
Show your work:

_______________________________________________________________________

Now if you were like me I'd be more concerned about making sure my estimation was as close as possible to the correct answer because I was worries that the teacher would think I didn't have a good understanding of the content if it was far off. For that reason my approach to this question would be to fill out the show your work section first, then the answer. Finally I would put a number not far off of the correct answer as my estimate.

Looking back on this and trying to understand why I'd (I wanted to say children but that wouldn't be accurate because I'm not sure I'd be any less of a culprit to than I was back then) approached this question this way I came up with a couple reasons:

• I was caught up in the idea that I always had to have the correct answer.
• I was worried the teachers would be disappointed in me if the estimate was far off.
• I didn't understand the importance of developing strategies related to estimation.

Now that I've given this a bit more thought with an education, development lens I'd like to explain an option of how I'd have wished I'd approached this question:

First I'd highlight the important parts:

"If Jenny gets  $.47 for every apple that she sells how many dollars while Jenny have if she sells 30 apples per day and works 90 days in the summer?"

Next I would round the numbers to something more manageable:

-90 days in the summer would become 100 days.

-30 apples per day could remain 30 apples/day.

-$.47 for every apple would become $.50/apple.

From here I would say 30 apples/day for 100 days is 3000 apples. Then I'd think if Jenny makes 1/2 of a dollar per apple she would have half as many dollars as she sold apples. That would be 3000/2 which is an easy 1500. 

Making my estimation become; $1500 for Jenny over the summer.

________________________________________________________________________

If we look at this suggested process for estimation it resulted in an answer that was only a few hundred off and a 15.4% error - which if we consider the fact it took hardly any mental math to solve is pretty impressive. 

If we take the time to encourage students to think of ways to answer simple questions, like this apple problem, through basic reasoning and utilizing estimation we will be developing their adaptive learning skills.  In my opinion this is one of the best ways to set the foundation of have students thinking outside the box and develop creative solutions to complex problems. 

Our first steps to move students in this direction is slowing down our lessons and providing basic techniques creating manageable problems. We want to give the students the opportunity to make educated guesses. Once students start developing some skills and strategies for estimation then introduce more complex, challenging problems. 

________________________________________________________________________

Feel free to comment and let me know you opinions on estimation.

• Did you have any experiences similar to the one I outlined?
• Did you have an experience very different from this one?

Intermediate/Senior Physical Education and Mathematic Education

The posts I have been uploading thus far have been based around education in general.  As an intermediate/senior teacher candidate with teachables within Mathematics and Physical education I figured it would be beneficial to introduce myself in regards to these.

First of all; my name is Mr. Studenny and I am a teacher candidate at Brock University's Faculty of Education.  My first teachable is in Physical Education and my second teachable is in Mathematics. As a teacher candidate I plan to bring a combination of the skills I have learnt through these domains to the classroom.  An area that has really sparked my interest through my undergraduate degree has been in creating an engaging inclusive environment for my students. I find that the creation of a sense of community in the classroom can totally change and shape the learning environment in a very successful way.

I am particularly interested in how students react positively to a classroom that has a strong sense of community. I feel this helps engage and motivate students. Furthermore, it also sparks initiative and creativity in them. I view each an every one of these traits as a fundamental important characteristic of an engaging, successful classroom.

I can not wait to apply these principles to the physical education and mathematics curriculum.  I completely understand the struggles these will bring during the next few years of my professional life. I'm excited to face these challenges and see where they take me.

Cheers,

Mr. Studenny