Saturday 13 June 2015

Using student results to improve my classroom

One of the greatest challenges I have found as a new teacher is managing 7 classrooms with up to 32 students (around 200 students in total). I surprised myself by how quickly I learnt effectively all of the students names, however recalling their grades has been a bridge too far.

During class time I made assumptions of certain students based on their in class behavior and questions they have asked, only to check test results and find my assumptions have been incorrect.

To aid my awareness of classroom results, I have created 2 quite simple additional pages in the spreadsheets that I was loading student grades into already; a Reporting Page and a Classroom Map.

The "reporting" worksheet. This allows me to colour-code the results, Green for strong results, smoothing down to Red for poor results. (Below is an embedded copy of student results, with names changed to protect the identity of the innocent)

The reporting sheet allows me to filters for student ranking, so for any given assessment I can rank the students, and I can quickly see if any students that typically do well in assessments have performed poorly in a particular assessment (or vice-versa).

This has been extremely helpful when reveiwing the student results. For example I can see that Gertude, who typically gets mid 90% grades, achieved below 80% in the investigation, and Chanel with results around 80%, achieved 100% in the investigation.
This simple information enabled me to have two very meaningful discussions with each of these students as to the variance in the of the assessment.

In coming weeks I expect a similar level of insight into the student's first semester exams.

I have also been using the comment functionality of Excel, to record when I have sent letter to parents, or any other important items for students, such as competitions they achieved strong results in or long term absence.

Below I have embedded my student management worksheet
 (You are welcome to review in your browser or download a copy for yourself)



The second worksheet that I added was more beneficial to the earlier year levels. Using some vlookup function in excel, I have created a representation of my classroom, and linked it to the student grades.

This allows me to see the classroom hot spots (places with a lot of RED). This allowed me to pair students of differing ability levels, so they might provide some peer coaching. Additionally, where there are clusters of weaker students, I can ensure I am providing sufficient support and scaffolding of questions.

This may also provide some behaviour management benefits (and rearrange seating to redirect disruptive sstudents) but I am really aiming it to be an instructional tool (where do I need to provide help) and feedback mechanism (if the "green zone" is looking confused, I need to adjust the activity or instruction).
The above is a traditional classroom arrangement, but I do a similar arrangement for when my students are arranged in 5 large group tables. (This worksheet is included in my embedded Excel document, but the images do not embed, so the above is a screen capture of it).

I hope this might help any teachers looking to improve the way they use student results to provide tangible benefit to their classroom arrangement, or instructional method.



Sunday 7 June 2015

Visually Balancing Equations


When I am teaching students a new concept it quickly becomes clear when students have been taught what to do rather than why or at least how it works. Recently this situation become clear when performing Inverse Operations;
The students ask-
Why do we switch the sign when we switch the side of the equal sign? 
Why do we need to perform our Inverse Operations first on the addition, before multiplication? (We have just learnt the Order of Operations (BIMDAS/BODMAS)

I find that when students understand that they need to keep the equation balanced, that they develop a robust understanding of how inverse operations work, and why we can perform the operations we do.

Balancing equations is a pretty simple, and quite visual concept. I have seen a number of sites and games (mostly aimed at primary school level) using scales to consider how changing one side, needs to have an equal change on the other side.

But then I came across a different site. It had a simple, interactive and attractive site that invites students to be play and which flips the scales idea on its head.

Solve Me Mobiles (solveme.edc.org/Mobiles.html) uses mobiles (like those hanging above a cot) to balance the equations.


The site allows users to access a hundreds of balancing problems. Running from the simple to quite complex arrangements, with multiple variables and simultaneous equations. It is not intimidating, in fact some students thought it looked too simple (until they started trying to solve the more difficult ones).

On the face of it this is a very simple exercise. Guess the weigh of each shape, while animations of cloud and seagulls gently float by, and at first it is. The first level the students need to find 2 numbers that are equal and together equal 10...


But as they start to become more complicated the tools the site provides becomes valuable.


Students can click and drag the mobile, to create equations.
Once they have the equations, they can subtract(or eliminate) items which naturally happen on both sides.
The site also allows for prime factorisation, with factors also able to be 'eliminated' from both sides (effectively dividing both sides)
Through these operations the maths comes naturally and visually allowing students to solve the equations.

The balancing of equations can then be expanded through moving into simple simultaneous equations, when there are multiple bars, and increasing number of objects/variables.


This structure then allows for substitution, again through natural drag and drop approach. This allows the user to isolate variables to solve.

The students quickly took to the problems, with flexibility for some students to pick a range of difficulties to match their ability.

The lesson flew by, with my time as the teacher, simple offering leading questions to students as they find themselves on a bump, before jumping up to the next level.
"Are you sure you have all of the possible equations from that set up?"
"If the left arm is balanced with the right, the left arm must be half of the total?"
"What could you substitute to isolate an object?"

I found that I needed to direct students towards the correct vocabulary, but whether they were eliminating variables, or "flicking bits", they understood the mechanics and the limitations.

As we summarised the lesson, we found that different students were applying a range of strategies to solve the puzzles, with some focused on equations, others applying a halving logic, and others aiming to isolate each object.
This really highlighted how important communication and willingness to try new approaches was.

I created 2 mobiles (one challenging {solveme.edc.org/?mobile=2726} and one impossible{solveme.edc.org/?mobile=2741}) and shared them with the students, and as an extension opportunity I suggested they create one challenging and one impossible mobile, and provided a discussion board so they could share them. The discussion and the learning continues as they explore why some may be impossible to solve.

Thursday 4 June 2015

Solving equations physically

I enter the classroom, with a bag of cash, a small digital kitchen scale and a glint in my eyes.

I don't need to even need to ask the question, the students ask for me.

"How much cash is that?"

Without skipping a beat, I put the coins into a cup and put it on the scales...

3320 grams

Well there is a tricky problem. How many coins does it take to weigh that much?

The students split into 4 groups, each with 2 cups with difference selection of coins in each. We weigh each cup and then after subtracting the weight of the cup (5 grams), the students developed equations to represent the weights.

Let "a" be the weight of 5 cent coin, "b" for 10 cents coin and "c" for 20 cent coin.
4a + 5b + 2c = 310 grams
3a + 2b + c = 210 grams

The students attempted to discover the weight of each coin, through application of a range of algebraic techniques.
Given the 3 variables and only 2 equations, they find it impossible to solve, until eventually one group shares with another group, and the class as a whole understand that sometimes, the answer requires asking someone else.

Finally some answers start to emerge... however there are still differences from groups. Once all groups have had a chance, I get each group to submit their answers and we create a simple table on the white board.

A students calls out, "We should average them"

(I hadn't planned on that but what a brilliant idea)

"Great... how do we do that?" I innocently inquire.

"Sum them, then divide by four" The chorus replies.

So I add another row, for Class Average, as the students call out the numbers.

How could we check?
Well who makes these coins?
Lets look up the Royal Australian Mint
(http://www.ramint.gov.au/designs/ram-designs/5c.cfm).

Despite the questionable quality of the scales, minimal quantity of coins and potential for algebraic mistakes the class average arrive within 0.2grams for each coin. I think to myself, well there goes my discussion on sources of errors, but one student notices that a group has consistently predicted nearly a gram too high for all of the coins. What could that be? The students happily provide suggestions, and the list creates itself.

With time vanishing, and students generally feeling positive, I don't feel like I even need to answer the original question. Instead it is time for some reflection...

1) What did we just do?
2) What skills did we use?
3) What new did I learn?

I circulate to get a feel for how students went. The response was clear. The more capable students had been working through the problem and developing their ability, however the lower ability students required considerable scaffolding. The activity simply led to frustration for the lower ability students.

While having a problem solving activity, for groups running over a whole lesson allowed the high performers to shine through persistence and application of logic, it had let some lower abilities coast. Perhaps they had seen something new, or perhaps they will recall the activity in future discussion, but they didn't feel ownership over the solution.

This lesson was great, but next time I need to be more aware of when students are letting the stars of the team carry the rest.

As a final thought- I was glad that I weighed the coins initially. It gave me an easy way to check that all of the coins had been returned (which they were).

Monday 1 June 2015

Team Quiz for Trigonometry Revision

Two weeks of Trigonometry can cover a lot material, but how much do the students remember?
As high performing year 11 students completing the Maths Methods course (One of Australia's more challenging Mathematics Secondary Curriculum). These students are already quite motivated and engaged in the subject however as the teacher I really need to understand what students are understanding and can apply.
So it is time for a class quiz, but let's make this one fun...

I put the students get into teams of 2-3 students. Each team uses a laptop to log into Socrative.com, where they join my room. I ask that each team include the name of all team members, but this is only for the teacher to know, because teams are allocated a colour, which they will see more of shortly.

Once students have entered a name, they find out their team colour and begin answering questions...


As the students submit their answers, they receive immediate feedback, with the correct answer (and an explanation of the solution if loaded in for that questions).

Perhaps more engaging for the students is the Space Race going on the Big Screen. Every team has a rocket ship (assigned by their colour), starting on the left of the screen and slowly proceeding across to the right. How do they move their ship? Simply by getting the questions correct.


The timing of the questions is up to the students, however they quickly become curious of who is that Teal team that is winning, or Lime team which started slow, but is going faster now!

The students have a range of strategies, noting that in this quiz there are only 20 questions, and 35 minutes to complete it, getting each question correct is perhaps more important than getting them completed quickly.

What is the teacher doing during the frenzy of the quiz? Moving from group to group, I get insight into the problem solving approach of the students. Encouraging all team members to attempt each question, then to compare answers prior to submitting. This allows students to learn from one another, while picking up on errors.

When the timer ends (manually by the teacher) then we can get an immediate insight into the results.

Names are usually shown on the left. They have been hidden for student privacy

As a class we seem to have some misunderstood question 6, so I click on the question to discuss as a class.


I can immediately see that 9 groups got this question correct, so I call on them to explain the correct answer. One group quickly draws up a unit circle to show the angle in relation to Cosine (as the x coordinate), then another group disputes the answer by showing a Cosine wave, showing the value on the y axis.

Seeking teacher mediation, I explain that both approaches are correct and how they reach the same result. The discussion results is numerous 'ahhh's of realization from students, particularly some of the lower performing groups. It seems many understood Sine better than Cosine, which this quiz brought out.

We move onto the application questions, many included images as part of the question. This demonstrated the students needed additional time on problem solving involving various trigonometry rules.

Looking through the questions, (such as question 12) students simply missed the units. However the later questions received lower average (as would be expected as the questions became increasingly complicated.


One group got Question 20 correct (and another got very close), so we worked through the question as a class so we could understand the thought process, involving attributes of pentagon, Cosine Rule & Area of (non-right angled) Triangles.

After the lesson I was also able to check which students have achieved 50% or lower results. I raised my concerns with those students to suggest additional study to ensure they maximize their results. These students appreciate the private communication and consideration from their teacher.  

While setting up this quiz took a little time (mostly extracting good questions from a range of textbooks) having this insight into student's strengths and weaknesses was precisely what I needed to target revision and be confident in proceeding to the next topic. This quiz will now be available for future quizzes (and other teachers can also access the quiz in Socrative.com with SOC:14918462)

I find Socrative.com's Space Race is a fun way to get students actively involved in a quiz, and allows immediate listing of which students can solve which questions.
Socrative.com also allows for teacher paced or individual student paced quizzes, with or without immediate student feedback, but Space Race is my personal favorite.