Resonance

Resonance: Richness or significance, especially in evoking an association or strong emotion.

Occasionally I come across blog posts that strongly resonate with my beliefs about education. Here are 3 examples that have evoked strong emotion in me lately:

1. Why all teachers should be hero teachers by Alice Leung

Quote 1: “For me, teaching is not “work”. Like many other teachers I have a great passion for teaching and live and breathe it.”

This resonates strongly with me because I have always loved teaching kids. I will be sad if I have to retire due to ill health. It is a great gift to be able to help young people learn.

Quote 2: “We need the teaching profession to be made up of  teachers who collect data on how effective they are teaching and how effective their students learning; teachers who constantly seek ways to improve their practice; and teachers who reach out to the global profession of teachers to share best practice and support others.

I believe that reflecting on our teaching practice is of paramount importance in becoming a better teacher, and it naturally follows that looking for ways to improve is necessary.

2. Maths needs better PR at school by Kerry Cue

Quote: “Maths is not visible in schools. Other subjects have their selling points.

Languages other than English have FOOD.

Geography has VOLCANOES and TRAVEL.

English has PLAYS and FILMS.

History has BLOODY WARS and TYRANNTS.

Drama has a school MUSICAL or PLAY.

Art has, D’uh, rooms full of amazing ART.

Science has BAD SMELLS, EXPLOSIONS and DAVID ATTENBOROUGH.

How can we make maths more visible and more fun in high school?

Be AUDACIOUS, my little mathspiggies.

Think BIG and then even BIGGER again.

Here are 12 ways of making Maths more visible in your school.”

I can’t agree more Kerry. Maths needs a good PR job. Our enthusiasm for the subject as well as making it more visual and hands on will help more students come to love and appreciate the beauty of Mathematics!

3. The Coming Apocolypse by Adrian Camm

Quote: “Whilst politicians and journalists would have you believe that our education system is a “disaster” because of the latest comparative results in international tests where Australia children were beaten by students from 26 countries, this ignores contextual and cultural considerations and is really a misuse of student performance data. It neglects the humanistic side of education and does nothing more than turn children into a number – what the data doesn’t tell you is that high scores can often signify relatively superficial thinking and the ‘hidden’ reality of the fact that the measure affects that which is measured.”

Spot on Adrian – it’s almost like if you can’t measure it, then don’t do it. Some of the great learning moments in a class are not planned for, not found in VELS or on a Naplan test.

What blog posts have resonated with you lately? 

 

Risk your Quadratic skills

My last post about this great revision game was “Risk your Algebra skills“.

In Year 11 Maths Methods, we have been learning about Quadratic equations. Like most classes there is a wide range of abilities. Some kids get quadratics and others struggle. “Completing the Square” is like learning Chinese to some. Finding the meaning of the discriminant is harder than trying to store your luggage at a Russian railway station!

But I will help these kids experience success.

In Bob Sullo’s excellent book “The Motivated Student“, he states that: “All behaviour, from birth until death, is purposeful, engaged in so that we can meet five human drives:

• To survive and be safe and secure
• To connect and belong
• To achieve power and competence
• To be free and autonomous
• To play, enjoy, and have fun” (page 38)

“Rather than cultivating an environment of fear, build a culture of success. Adopt the following three key messages, articulated by Saphier and Gower:

• This is important.
• You can do it.
• I won’t give up on you“. (page 13)

I have articulated these last 3 statements to my students and I’m pretty sure they believe me.

So tomorrow we start revising Quadratics and the students are looking forward to Risking their Quadratic skills (I have planted some seeds!) This time round I have changed one important thing:

Instead of me allocating their FACTOR based on past assessment, they have chosen their own factor on a scale from 1 to 6. However this number is open to peer approval. Luke had no hesitation in nominating a factor of 1 and of course no one objected. When it was Megan’s turn she nominated a factor of 4.1. Her peers were very certain that this was way too high and reversed it to 1.4. Megan came back with 3.9 and finally settled with 2.9.

I think that this method empowers the students to realistically assess their progress on a particular topic.

Their nominated factors are:  1.0, 1.4, 1.5, 1.7, 1.9, 2.0, 2.9, 3.1, 3.4, 3.5, 4.0, 5.9

Here is my game sheet.

Stay tuned to see how the students risk their…..

Introduction to Year 8 Integers

I glance at the classroom door nervously (after 35 years teaching?!?!). My new year 8 class should be arriving in the next few minutes. Will they be as good as my year 8′s last year, which was my favourite class?

Lee Blake, et al (2009)

I have already put some notes on the board: a definition of integers and representation on a number line. Pretty basic start and then a practice worksheet P8 from “Motivating Maths“.

The kids arrive and we start to get to know each other. I give 2 students star notes for showing eagerness by talking to me in the yard yesterday.

I want kids to get into a good working routine so we talk about:

1. My job is to teach, your job is to learn.

2. You must make mistakes to learn (so one boy says: “so we should write 2 + 2 = 5?).

3. Good work habits egs. punctual, prepared, get straight to work.

Enough talking, so students copy notes and do worksheet.

I am kept busy answering questions and marking books.

I challenge the more capable students, who finish their tasks quickly, by rolling 6 dice on their table and asking them:

“How many bears, how many fish?”

Students remain fully engaged (except for student X, who has to be moved after a warning).

With 10 minutes remaining I give out their first assignment: LOOKING FOR PATTERNS. I will be interested to see which students are keen enough to start it for homework. The first page will lead into next weeks lessons on “Adding and Subtracting Integers”.

So my challenge is to teach, motivate, and engage these students so that they will form a positive attitude towards learning maths in the future.
I am looking forward to that challenge. Stay tuned to see how things go?

4 More Sleeps

The summer holidays are nearly over. As usual I can’t wait to get back to school. I have had the time to do lots of reading (fiction and mathematics) and to do some planning for this years classes. But nothing beats being in the classroom with kids.

Shelley Wright at Wright’s Room, has been a consultant for the last 12 months. I quote the following from her blog, which expresses my feelings perfectly:

“Everyday since I have left my classroom, I have missed it. Everyday I have missed kids. I miss their energy and enthusiasm, their optimism. Their quirks. Their struggles. Their hugs. I miss the energy and noise of a school. And even though I work in classrooms, those kids are never mine. They always belong to someone else.

Beyond this I miss pushing the envelope, trying what’s new. Innovating. Failing. And learning in the most intense way I have ever experienced. I love taking risks, problem-solving the glitches and the intensity it requires of my brain. It makes me feel alive”.

So 4 days or 96 hours or 5760 minutes or 347600 seconds. Hurry up please!

What If ?

Andrew Mathews Cartoon

These two little words are very powerful in teaching and learning Mathematics.

An Open Ended Question can easily lead to an investigation by simply saying:  ”What if …….”

I encourage students to give more than one answer to an open ended question because:

1. I want them to THINK and do more Mathematics; and

2. I want them to stop thinking that Maths problems always have ONLY one answer.

EXAMPLE QUESTION

Trevor from Tatura gets a pig for his birthday. Since it’s ok in Tatura to have pigs, he wants to build an enclosure for it in his back yard. The perimeter of his enclosure is 30 metres.

WHAT MIGHT ITS AREA BE?? WHAT WOULD THE LARGEST AREA BE??

Many students will assume a rectangular enclosure, so the teacher may have to scaffold by asking: “What if the enclosure is some other shape other than a rectangle?”

The first question is open ended because many answers are possible depending on the shape chosen.

WHAT IF the dimensions of the enclosure are all integers?

WHAT IF  IN LESSON DESIGN

The power of Maths teachers blogging is in the sharing of ideas. This often results in a teacher taking another teachers idea and asking “What if………………..

Example 1

Rebecka Petersen‘s post: Math History – We’re all learning here, was read by Karen Fouss. She thought – what if I do the same thing with quotes? See her post titled Guilty Pleasures.

Example 2

In my previous post: Teaching in 2013 – I can’t wait, I adapted Paul Bogush’s script to make it more relevant to me.

So I wish that 2013 continues to be an excellent year for sharing ideas via Math blogs; and lets ask WHAT IF? often!

Multi-Dimensional Learning and Assessment

Two major concerns I have with Mathematics teaching are:

1.  Too much time is spent in Maths classrooms on skills practice.

2.  Assessment is too heavily dependant on written, end of topic tests.

Fortunately, these concerns are well addressed in my holiday reading:

Assessment in the Mathematics Classroom: Yearbook 2011, Association of Mathematics Educators

Chapter 2 outlines the S.P.U.R. approach. The first example given is:

The 4 questions illustrate the 4 elements:

1.  SKILLS

2.  PROPERTIES

3.  USES

4.  REPRESENTATIONS

I quote from the text: ”We suggest that each of the previous questions is an appropriate assessment item for teachers to use when students are studying decimals. Each provides different insight into what students know about the concept. Together, they provide a more robust view of students’ depth of understanding than would be obtained from an individual item”.

My new years resolution is to use a wide range of teaching and assessment methods this year. Hence I am looking forward to reading these chapters:

Chap 2:  Using a Multi-Dimensional Approach to Understanding to Assess Students’ Mathematical Knowledge

Chap 3:  Assessing Problem Solving in the Mathematics Curriculum: A New Approach

Chap 4:  Assessing Conceptual Understanding in Mathematics with Concept Mapping

Chap 5:  Using Journal Writing to Empower Learning

Chap 6:  Implementing Alternative Assessment in the Mathematics Classroom

Chap 7:  Open-Ended Tasks and Assessment: The Nettle or the Rose

Chap 8:  Using ICT to Improve Assessment

Chap 13:  Implementing Self-Assessment to Develop Reflective Teaching and Learning in Mathematics

I recommend this text to you as a practical, up to date guide to assessment in the Mathematics classroom.

Also see the NSW Board of Studies website which outlines 3 main approaches to assessment:

I welcome any comments regarding how you assess students in your classes!

Teaching in 2013 – I can’t wait

At this stage of the summer holidays I get restless. I want to be back at school. I can’t wait to meet my new students. Will they be keen and excited to be back at school? Can I inspire them to love Maths like I do?

To fill in the time over the holidays, I spend more time doing online PD than any other time of the year! Part of this time is using Google Reader to catch up on my favourite blogs.

For example: BLOGUSH. Paul Bogush’s post ….every other teacher gives some great advice to a first year teacher: What will your first words be to a new class?

What about an “old” Maths teacher in his 35th year of teaching? Adopting Paul’s script, it might be something like this:

(leaning over desk, both palms on table, dead serious, start with neutral voice that allows you plenty of space to get loud, soft, serious, pause, speed up)

Let’s start…

I have a confession…

I am so scared.

I

have been teaching

for 35 years….

and I have loved every day!

But soon, my teaching days

will be over.

But not only am I scared…

I am ridiculously excited.

Because some students

in this class,

will learn to love Maths

like I do.

Someday when they have left school,

they will think

that’s where my love of Maths

started.

I hope this year will be just as awesome for you

as it will be for me.

Ready?

Now the first thing I learned in teacher school was to do attendance and learn names so I that make sure that if your name is Alice I don’t call you Bob…of course if your name is Alice and I call you Bob you probably have bigger problems than just me not remembering your name.

Who’s Benjamin Sumpter?
Hi Ben…
Ben what’s one thing I should know about you?

The key to this approach is making a connection with the students, as well as keeping it interesting. Then perhaps they will engage more in their learning and perhaps even draw pictures like:

Salute the King

TUESDAY

Home group before lunch. Nothing planned!

Looking for inspiration.

Google search: “Group Card Games”.

Result: How to Play the Funniest Card Game Ever.

Rules: Deal all the cards face down. It is better if everyone has the same amount of cards, but it is not mandatory. The object of the game is to get rid all your cards. The first person to do that is declared the winner.

Every player must now, one by one, turn over the top card on their pile without looking at it first and place it in the middle of the table. As soon as the first person to reveal an Ace, King, Queen or Jack, here is what EVERYONE in the group must do:

Ace- Stand up
King- Salute
Queen- Put hand over heart and bow (remaining seated)
Jack- Start clapping.

The last person to salute loses this round and gets all the cards from the pile. The game continues, cards are being placed in the middle of the table, Oh an Ace! Everyone must stand up! The last person to stand up, once again gets the cards from the pile. Game continues and oops! a Jack, everyone must start clapping.

In home group the kids enjoy the game. There is lots of interaction. Some kids choose not to play “nicely”. Lots of social skills to be developed here. Very worthwhile me thinks!

WEDNESDAY

Idea: Could “Salute the King” become a Maths game?

Rules:

1. As above but for 2 – 4 players and take out aces, kings, queens and jacks.

2. Total the cards flipped over and then:

A Square Number	STAND UP
A Multiple of 5	SALUTE THE KING
A Multiple of 3	HAND ON HEART
30 to 39	CLAP HANDS

The game was a big hit! Students wanted to play again after lunch. “I want to beat you Mr. T”, Rhys said.

And Rhys did by improving his mental addition speed and learning the square numbers; and multiples of 3 and 5.

Note that if the total is 33, then you put your hand on your heart (not clap hands) because it has a higher importance.

Try Salute the King in your class, and leave a comment about how it went and any modifications you made!!!!

Mathematicians are People, Too

From my bookshelf comes a very easy to read book about the history of Mathematics. Mathematicians are People, Too is a delightful book written by Luetta and Wilbert Reimer (1990).

The stories are interesting, well written, and have great  illustrations. The reading level would be appropriate for many secondary school students and some upper primary school kids as well.

I particularly like the first story about Thales, titled “Pyramids, Olives, and Donkeys”.

Thales of Miletus – illustration by David V. Black

Chapters from the book could be read to a whole class, or set as a reading – comprehension assignment. Here is my assignment for Chapter 1.

I highly recommend this book to teachers to help give their students a greater interest in, and hopefully a love of Mathematics.

Happy Lines

I am always on the lookout for good maths problems. Problems which make students think. Non-routine problems.

Some students are reluctant to engage with problem solving because it puts them out of their comfort zone. Therefore give encouragement. Give problem solving strategies (Maths Toolbox). If absolutely necessary give hints (scaffolding?).

I recommend that you checkout “Introducing the Maths Toolbox” by Kevin Cummins.

Here is a problem that I used with my Year 10 General Maths class today. It is taken from:

USA Mathematical Talent Search
Round 1 Problems
Year 22 | Academic Year 2010{2011
http://www.usamts.org

I introduced the problem by explaining what a happy line was. I drew the 9 dot square grid on the board and my students quickly told me that it had 8 happy lines. So far so good.

When I gave them the 3 x 9 grid many students eagerly set about finding all the happy lines. The first problem was that most students did not understand the difference between a line and a line segment. They counted the 45 degree lines but missed the other angled lines! Some very good discussions and new discoveries evolved.

My biggest challenge in this situation is to not give in to “Teacher Lust”.

Read about how “Problem solving empowers children“.