Intellectually Needy

Intro

"So does this bore the heck out of you?" a student asked me.

The problem is that this was after two days of doing the Barbie Bungee Jump activity. The fabulous Barbie Bungee Jump. (Cf. Julie and Fawn) I was assisting a very nice and competent substitute teacher.

Coming on the heels of Christopher Danielson's and Chris Lusto's #globalmath session on building intellectual need, it was clear that most of these students did not have it. Nor were they looking for it.

This is a good school with good students and good teachers. What's going on, or not going on? My first brief observations:

1. Students were given all the steps to follow. Being told to do a, b and c and then doing a, b and c is not engaging.
2. There was no hook. How much of a hook depends on the lesson. This one could have used the video, a discussion about bungee jumping, etc. Going straight into 'here's what you do' gives no chance for wondering. Even if it's what the students want or are asking for.
3. There was no expectation that this was worth their time or could be interesting. There is always time to start, but this might also be about developing a culture of inquiry. Students need to learn that this is what math is, and this is what math class is like or could be like.

Recount:
Day 1: Students were given a worksheet with a table, told how to assemble the rubber bands and washers and to collect data for 1 to 6 rubber bands. Then graph all of their data and freehand a line of best fit. This is the beginning of a functions unit that will end with linear functions. Then they were asked to make a prediction for how many rubber bands they would need for the drop. We didn't have the actual heights, so they predicted for 3 m. Mostly, their prediction method was pick a number that was bigger than 6. 20 seemed nice to them, though some went with 18, since 6 rubber bands was close to a meter. Two groups found the average increase per rubber band.





We weren't clear about how to do the drop in the stairwell. We didn't have a set (or maybe even one) tape measure for long distances. Two teachers wound up determining 3 drop spots and measuring the distances, between 3 and 3.5 m.

Day 2: (After a snow day and a PD day.)
The students coming back were not much more enthralled than they were Day 1. I shared how this was the start of a functions unit, the math idea of having a rule to go from input to output. I tried to phrase the question as given the input of how many rubber bands, could they predict how far it would drop. (Not much traction, as there were already instructions on the screen.) The substitute gave each group their drop height. The two groups that had figured out the averages used this to make quite specific predictions, and one group made the complete table that this would generate. At the last second they cut 2 rubberbands off of their total, to allow for the length of the disk and acceleration. They were worried that it would be traveling faster at the bottom and that would make it stretch more. Two other groups adjusted their number a bit, but without reasoning that they could share.

We proceeded to the stairwell and groups took turns making their single drop. 2 hit the floor, including one of the more mathemaical groups, 2 got about 70 cm away, 1 was more than 1 m, and the group that had made the table got to within 10 cm. Went back to the classroom, shared the results and had the winning group describe their efforts while few listened. I talked with the mathy group that hit the floor about what went wrong. Basically they felt math failed them. Double checking their work I saw the problem was that they were computing for the wrong drop height! Their calculation would have put them quite close.

So What?
The students were pretty happy. Better than a typical math class, playing with rubber bands, leaving the classroom. The sub was okay with it, as students were mostly in control and made it through all of the steps. I felt like we missed an opportunity.

So what would you change about the lesson? What would add/create/inspire intellectual need in what is a (potentially) great activity?

Post Script:
Excellent discussion! I just want a few of the shared links to be more visible here. But many people put great thinking below so don't skimp on the comment reading.

• Timon: http://www.101qs.com/1563-barbie-bungee Barbie Bungee video
• Ruth: http://cohort21.com/ruthmcarthur/2013/02/02/freestyle-barbie-bungee-no-steps-required/ her blogpost sharing an open-ended/low structure approach
• Pieter: http://www.researchgate.net/publication/222209242_Analysis_of_a_fatal_bungee-jumping_accident sad accident analyzed
• Julie: (blogspot ate her comment) follow up post http://ispeakmath.wordpress.com/2013/02/02/barbie-bungee-follow-up-be-careful-when-using-the-recipe/
• Robert: http://robertkaplinsky.com/lessons-learned-in-implementing-problem-based-learning/ expands on his four C's

Intellectually Needy

Intro

"So does this bore the heck out of you?" a student asked me.

The problem is that this was after two days of doing the Barbie Bungee Jump activity. The fabulous Barbie Bungee Jump. (Cf. Julie and Fawn) I was assisting a very nice and competent substitute teacher.

Coming on the heels of Christopher Danielson's and Chris Lusto's #globalmath session on building intellectual need, it was clear that most of these students did not have it. Nor were they looking for it.

This is a good school with good students and good teachers. What's going on, or not going on? My first brief observations:

1. Students were given all the steps to follow. Being told to do a, b and c and then doing a, b and c is not engaging.
2. There was no hook. How much of a hook depends on the lesson. This one could have used the video, a discussion about bungee jumping, etc. Going straight into 'here's what you do' gives no chance for wondering. Even if it's what the students want or are asking for.
3. There was no expectation that this was worth their time or could be interesting. There is always time to start, but this might also be about developing a culture of inquiry. Students need to learn that this is what math is, and this is what math class is like or could be like.

Recount:
Day 1: Students were given a worksheet with a table, told how to assemble the rubber bands and washers and to collect data for 1 to 6 rubber bands. Then graph all of their data and freehand a line of best fit. This is the beginning of a functions unit that will end with linear functions. Then they were asked to make a prediction for how many rubber bands they would need for the drop. We didn't have the actual heights, so they predicted for 3 m. Mostly, their prediction method was pick a number that was bigger than 6. 20 seemed nice to them, though some went with 18, since 6 rubber bands was close to a meter. Two groups found the average increase per rubber band.





We weren't clear about how to do the drop in the stairwell. We didn't have a set (or maybe even one) tape measure for long distances. Two teachers wound up determining 3 drop spots and measuring the distances, between 3 and 3.5 m.

Day 2: (After a snow day and a PD day.)
The students coming back were not much more enthralled than they were Day 1. I shared how this was the start of a functions unit, the math idea of having a rule to go from input to output. I tried to phrase the question as given the input of how many rubber bands, could they predict how far it would drop. (Not much traction, as there were already instructions on the screen.) The substitute gave each group their drop height. The two groups that had figured out the averages used this to make quite specific predictions, and one group made the complete table that this would generate. At the last second they cut 2 rubberbands off of their total, to allow for the length of the disk and acceleration. They were worried that it would be traveling faster at the bottom and that would make it stretch more. Two other groups adjusted their number a bit, but without reasoning that they could share.

We proceeded to the stairwell and groups took turns making their single drop. 2 hit the floor, including one of the more mathemaical groups, 2 got about 70 cm away, 1 was more than 1 m, and the group that had made the table got to within 10 cm. Went back to the classroom, shared the results and had the winning group describe their efforts while few listened. I talked with the mathy group that hit the floor about what went wrong. Basically they felt math failed them. Double checking their work I saw the problem was that they were computing for the wrong drop height! Their calculation would have put them quite close.

So What?
The students were pretty happy. Better than a typical math class, playing with rubber bands, leaving the classroom. The sub was okay with it, as students were mostly in control and made it through all of the steps. I felt like we missed an opportunity.

So what would you change about the lesson? What would add/create/inspire intellectual need in what is a (potentially) great activity?

Post Script:
Excellent discussion! I just want a few of the shared links to be more visible here. But many people put great thinking below so don't skimp on the comment reading.

• Timon: http://www.101qs.com/1563-barbie-bungee Barbie Bungee video
• Ruth: http://cohort21.com/ruthmcarthur/2013/02/02/freestyle-barbie-bungee-no-steps-required/ her blogpost sharing an open-ended/low structure approach
• Pieter: http://www.researchgate.net/publication/222209242_Analysis_of_a_fatal_bungee-jumping_accident sad accident analyzed
• Julie: (blogspot ate her comment) follow up post http://ispeakmath.wordpress.com/2013/02/02/barbie-bungee-follow-up-be-careful-when-using-the-recipe/
• Robert: http://robertkaplinsky.com/lessons-learned-in-implementing-problem-based-learning/ expands on his four C's

Mathematical Concept Wall - More Examples!

Here's some more examples of my students' Mathematical Concept Wall cards - some of them are just brilliant! To see my original post on the idea see http://mrcollinsmaths.blogspot.co.uk/2013/01/mathematical-concepts-wall-for-want-of.html

Year 7:

The Universal Panacea: TIME (#BlogSync)

January 2013 sees the 1st month of the #blogsync initiative set up by a series of bloggers via Twitter. The #blogsync is a central hub where all blogs on a common topic are shared amongst a community of bloggers/teachers/educational gurus. To see all of the posts on the below topic click the following link ==> http://share.edutronic.net/

The 1st topic is: "The Universal Panacea? The number one shift in UK education I wish to see in my lifetime".

Having thought about the 1 universal thing that I feel could remedy UK education there was only really one answer based on my experiences so far... TIME!

If only we, as educators, had more time.

More time to plan our lessons - not just your 'bog standard' lessons but 'all singing, all dancing' lessons. Lessons that will blow our students' minds. Lessons that will grab our students attention from the minute they step through our classroom door to the minute they have to leave. Lessons that will take into account all of the multifaceted things we, as teachers, have to take into consideration when teaching a group of 30+ students. I know that I spend far too much time at the weekend and of an evening planning lessons as best as I possibly can for my classes, but even then I still find that some lessons end up being planned within a limited time frame.

Last year, when completing my GTP, I read many books that knew full well that teaching becomes a massive prioritisation task - what needs to be done now and what can be left for later. They also knew that you can't spend hours planning each lesson as there's just not the time in the day/week/term to do so. So, the suggestions of certain books is to give each class one 'all singing, all dancing' lesson a week. However, as noble as this seems that still means the majority of your lessons that week will just be 'ordinary' and surely that is just not 'outstanding'. It may be realistic, but not 'outstanding'.

More time isn't just needed to plan lessons either. There's marking to complete. There's reports to write. Parents to ring and get the support from. Resources to create and share with colleagues. CPD to complete and reflect on. E-mails to send and answer. After school revision sessions to run. and so on and so on. If we're to do all of the things we're expected to do in the current time frame we are given to do it, it's no wonder that corners end up being cut and essentially all these jobs are just done to the level required, rather than the level possible.

So, where can this extra time come from? Can we even get it from anywhere? Unfortunately my name is neither Bernard nor do I have a magical watch to freeze time...

...imagine if we all had one of these watches. How amazing would it be to, in the middle of the lesson, stop the clock and just take 5 minutes to reflect on what is happening around us. To freeze everything around us would enable us to: look at each and every student's book to see what, exactly, they had achieved so far in the lesson, to reflect on how we had just taught what we had taught - did I do a good enough job? Have I left anything out? What do we do next, what are our next steps? Is there something happening in the room that, perhaps, I wasn't aware of whilst helping the student I was previously helping? Could my TA do with a bit of guidance as to who to support next in the lesson and how best to do this? All of these questions are things that we have to take snapshot judgements on in the flow of a lesson. I know I often forget to say certain things (mainly giving out homework). Sometimes I find time just runs out in the lesson - we get so wrapped up in what we have been doing that the bell goes and you realise you've got to let them go to their next lesson - they possibly don't want to leave, you definitely don't want the lesson to end!

However, in realism, this isn't going to happen in my lifetime. So, is there a realistic solution?
I used to teach, last year on my GTP, a year 8 class for a 'double' period. This period lasted for 1 hour and 40 mins and the students were often given a 5 min break in between the 2 periods as that was when the normal lesson changeover would be taking place. Now, initially when I took over this class I was slightly daunted by the fact I would have a double period with the class and that I'd need so much more content for my lessons. However, what I found is that we were able to do so much more given the extra time and I treated the lesson as that - a lesson. Not a double lesson but an extended lesson with a short break in between. The break allowed my students to take a breather and for me to assess where we were from the first half and where to go in the 2nd half - adapting my planning where necessary. I think this structure worked quite well and there could be something there to build on?

Alternatively, we could have an afternoon a week free. I know some schools finish early on a Friday in order to complete CPD or as extra PPA time. I feel that it would be feasible to extend the Mon-Thu school day to 4pm and then have this afternoon free to complete marking/planning, go on courses, speak to and share ideas with colleagues etc. Would it solve all my time problems, of course not - but it may give that extra bit of time needed to make a significant difference to the quality of each of the tasks a teacher is required to do?

I'd be interested to here form anyone who does have a half day one day a week for planning purposes etc. Does it make a difference?

I'm sure I'm not the only one who would like to see teachers given more time to complete the job we are employed to do, as to whether it is feasible is another question.

Curse You, Nate Silver

OK, not really. I am a big fan of the Silver one, and his application of quantfied reasoning to realms rife with superstition.

But his Super Bowl Analysis got me wondering about the data. He uses a stat called SRS, Simple Ranking System, from pro-football-reference.com. They have a nice linear algebra explanation of it on their blog. Mr. Silver used this stat to consider whether good defense or good offense was more conducive to winning. By looking at the top 20 in each category, he concludes defense is the key. Or more of a key than offense.

Always fabulous and frequently mathy Foxtrot.

I got to wondering about the differences. Maybe what mattered was your offense to opponents defense, or vice versa. I started putting his data into a spreadsheet, but because teams are rarely exceptionally good at both (exceptions 68 Colts, 96 Packers), there wasn't enough data. I was surprised to find that Pro Football Reference is free and an awesome resource for data. So I started filling in a spreadsheet, figured I'd tumblr it and people could fill in the rest if they were interested.

I got hooked, which is why I say, "Curse you, Nate Silver."

Turns out my idea about the differences was only mildy predictive. I took NFC Offense - AFC Defense and compared to AFC Offense - NFC Defense. ("How is that different from NFC Total SRS  - AFC Total SRS?" I would ask students if I had them this semester.) Here's the Google spreadsheet.


There's definitely some things to notice there. My next thoughts were to compare defenses, offenses, and finally to look where those two agree.


Bad news for Baltimore. When a team is favored in defense and offense, they've won about 3/4 of the time. So Raven fans you should be getting 3:1 odds when most people are feeling it's pretty close. Looking at these numbers, you could consider it the 4th or 5th biggest upset should Baltimore win. No 68 Jets or 07 Giants, but significant.

What do you notice about the data?

January 31, 2013

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Which Super Bowl is this, again, dear?

Another pop quiz!

What do the Queen of England, the Super Bowl and the United States Constitution have in common?
 

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January 30, 2013

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January 29, 2013

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January 28, 2013

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Pearson Teaching Award

 

Finalist Sanjeev Taneja Receiving Certificate from Former International Cricketer Anil Kumble



 

January 25, 2013

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Biography of Tirthaji in Hindi

Prof.Shriram Chauthaiwale sends us this beautifully written Biography of Tirthaji in Hindi.On the cover it has a colored image of Tirthaji which I am seeing for the first time. The Book also has a poem by the author to remember the 16 Vedic Math Sutras.

Interested in a copy ?  Mail me at gtekriwal@vedicmathsindia.org

Consorting with consortia

Common Core sets the standards, and two consortia, PARCC and SBAC, will write and grade the tests that assess whether those standards were attained.  It’s a very cosy, profitable arrangement where the heaviest burdens and risks fall on the educators and students.

UCLA’s National Center for Research on Evaluation, Standards, and Student Testing (CRESST) has published this month a report called On the Road to Assessing Deeper Learning: The Status of Smarter Balanced and PARCC Assessment Consortia.

The report gives a general stamp of imprimatur to ongoing progress (what did you honestly expect?) cloaked in the usual hedged language:

Study results indicate that PARCC and Smarter Balanced summative assessments are likely to represent important goals for deeper learning, particularly those related to mastering and being able to apply core academic content and cognitive strategies related to complex thinking, communication, and problem solving.

Any challenges in implementation, the report foresees, will not be substantive but rather ``technical, fiscal, and political’’.

The CRESST report sounds one note of caution: ``Absent strong representation in the new assessments, students' deeper learning likely will be compromised.’’  Therein lies the rub: will the ``assessments call for deeper learning and reflect 21st century competencies’’?  (CRESST report, p.5)

As we at ccssimath.blogspot.com are also interested in the assessments being developed by PARCC and SBAC, we thought we’d follow CRESST’s lead and release our own status report.

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January 24, 2013

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January 23, 2013

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മാത്സ് ബ്ലോഗ് ഒരുക്കം - മലയാളം

സാധാരണ രണ്ടു ദിവസത്തെ എങ്കിലും ഇടവേളകളിലാണ് മാത്സ് ബ്ലോഗ് പോസ്റ്റുകള്‍ പ്രസിദ്ധീകരിക്കാറ്. ചില പ്രത്യേക സാഹചര്യങ്ങളില്‍ സര്‍പ്രൈസ് പോസ്റ്റുകളും പ്രസിദ്ധീകരിക്കാറുണ്ട്. റിവിഷന്‍ പോസ്റ്റുകള്‍ക്കായുള്ള വിവിധ വിഷയങ്ങളുടെ പഠനസഹായികള്‍ ഒരുക്കി ഡേറ്റ് നിശ്ചയിച്ചു ഷെഡ്യൂള്‍ ചെയ്യുകയാണ് പലപ്പോഴും ചെയ്യാറ്. ഈ മാസം ആ പ്ലാനിംഗ് വിജയകരമായി നടത്താന്‍ സാധിച്ചില്ല എന്നത് ഒരല്‍പം സന്തോഷത്തോടെ(?) അറിയിക്കട്ടെ..

ഈ വര്‍ഷത്തെ എസ്.എസ്.എല്‍.സി റിവിഷന്‍ പോസ്റ്റുകള്‍ ക്ഷണിച്ചു കൊണ്ടുള്ള സ്ക്രോളിംഗിന് ലഭിച്ച അഭൂതപൂര്‍വ്വമായ പ്രതികരണമാണ് ഈ സന്തോഷത്തിനു കാരണം. ഒട്ടേറെ പഠനസഹായികള്‍ അതുമായി ബന്ധപ്പെട്ടു ലഭിച്ചു. ഒരു ദിവസം ഒരു പോസ്റ്റ് എന്ന നിലയില്‍ പ്രസിദ്ധീകരിച്ചാലോ എന്ന ചിന്തയിലാണ് ഞങ്ങളിപ്പോള്‍.

മലയാളം വിഷയവുമായി ബന്ധപ്പെട്ട പോസ്റ്റാണ് ഇന്ന്. മലയാളത്തിലെ വിവിധ പാഠങ്ങളുടെ സംഗ്രഹം ഉള്‍ക്കൊള്ളുന്ന ഈ പഠന സഹായി ഒരുക്കിയിരിക്കുന്നത് കാസര്‍ഗോഡ് ഷിറിയ ജി.എച്ച്.എസ്.എസിലെ രമേശന്‍ സാറാണ്. ഇതു തയാറാക്കുന്നതിനു വേണ്ടി രമേശന്‍ സാര്‍ എടുത്ത പ്രയത്നം ഈ പഠനസഹായിയിലൂടെ കണ്ണോടിക്കുന്ന ആര്‍ക്കും മനസ്സിലാക്കാവുന്നതേയുള്ളു. മലയാളം അദ്ധ്യാപകര്‍ കണ്ടു വിലയിരുത്തുമെന്നും വേണ്ട തിരുത്തലുകളോ കൂട്ടിച്ചേര്‍ക്കലുകളോ കമന്റിലൂടെ നടത്തുമെന്നും സര്‍വ്വോപരി ഇതു കുട്ടികളിലേക്ക് എത്തിക്കുമെന്ന പ്രതീക്ഷയില്‍ ഈ പഠനസഹായി നിങ്ങളുടെ മുന്നിലേക്ക്...
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January 22, 2013

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Elegi Pemberontakan Para Berhenti

Elegi Pemberontakan Para Berhenti
Oleh Marsigit

Elegi ini sengaja dibiarkan terbuka. Pembaca dipersilahkan untuk membuat Comment, Tesis, Analisis, atau Sintesis, perihal apa saja baik secara Formalnya maupun Substansinya jika Elegi ini diteruskan. Siapa saja yang terlibat, apa yang dibicarakan, kemudian referensi yang mungkin digunakan. Apa hubunannya dengan Elegi-elegi terdahulu. Apa juga

മാത്സ് ബ്ലോഗ് ഒരുക്കം - ഐ.ടി - 1 (With English Version)

അല്പം മുമ്പാണ് ഷാജി സാര്‍(ഹരിതം) ഈ മാതൃകാചോദ്യങ്ങള്‍ ശേഖരിച്ച് അയച്ചു തന്നത്. പലരും പലവട്ടം ചോദിച്ചതായതു കൊണ്ട്, പിന്നെ സമയവും നാളുമൊന്നും നോക്കിയില്ല. അങ്ങ് പ്രസിദ്ധീകരിക്കുന്നു.
IT Theory Questions Malayalam Medium | English Medium
Prepared by Shaji sir & John Sir

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Prepared By Shaji Sir, Haritham

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Prepared by Mathew Mullamchira,St.Mary's GHS, Cherthala

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Prepared by Younus Saleem M,Nibras English Medium School,Moonniyur , Chemmad

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Prepared by മുരളിമാഷ് ജി.വി.എച്ച്.എസ്സ്.എസ്സ്. വട്ടേനാട്, പാലക്കാട്

Click here to download IT Theory Model Questions - English Medium
Prepared by Younus Saleem,Nibras English Medium School ,Moonniyur

Std X Malayalam Medium Theory Questions Prepared By IT@School

IT Practical Questions & answers Prepared by Jose Abraham Sir

Mathematical Concept Wall - Examples!

My Mathematical Concept Wall is coming together nicely. I have all of my year 7 cards to put up still and my Year 10s will be introduced to this soon too.

Here are a few examples of the work my students have produced so far and an overall look at the 'wall' (a work in progress)!

 Here's how the 'wall' is taking shape!

 A few Year 8 attempts!

Here's one of my Year 9 class' Pi pictures!












For more info on my Mathematical Concepts Wall see my previous blog post here. Also, see a fellow Mathematics teachers' blog with their Mathematical Concept cards they have been doing with their classes at http://mrcavswalloffame.wordpress.com/ - you can follow Mr Cavadino on Twitter too @srcav

What to do with Mock Exam Data!?

The start of the new term brought with it the start of a new year and the chance to refocus my attention on certain classes and procedures I have in place. It also saw me finish teaching the Edexcel METHODS in Mathematics Unit 1 content to my Year 10 class.
Monday this past week I had one of my school's NQT sessions. The session was on using data effectively and what to do with the information about your classes you have at your disposal. At lot of the things discussed in this meeting I was either already doing or had done in the past but needed a timely reminder of them.
The 1st week back after the Christmas/New Year break saw my Year 10 class sit a mock Unit 1 paper. Having then marked all of these papers I started to think about what I should now do with the results from this mock and how I would best support my students improve on their results and achieve their target grades. Here's what I've been doing over the past week...

The first thing I did was to, on the front of each students paper, put a sticker (kindly given to me by my Mentor after discussing the assessments) with the students target grade and their grade from the paper itself. This made it very clear to the students how far they were off their target or whether they had achieved their target grade on the paper.
I then, taking the spreadsheet created by my mentor that she sent out to the whole department, typed in each students marks on a question by question breakdown basis. This allowed me to see, as a class, the questions that on the whole were done well and those that needed some further teaching. It also allowed me to put in a VLOOKUP formula to calculate the students' grades based on the grade boundaries for the paper. Then, in a discussion with my mentor following this analysis she recommended I work out a 'value added' column to see how far off/on/above targets the class were.
Having then completed a question breakdown analysis for each student I was able to see which questions I needed to take the class through as a whole and I did this with the class in the lesson that I gave the students their papers back. I gave them their papers with their grades, an AfL sheet which stated each question, the topic covered by that question, marks available and then a column for the students to rate their RAG for the question, write in the marks they got on each question and then a column for 'actions'. The 'actions' column was for them to think about how they are going to improve on the questions they did wrong. In addition to given them these AfL sheets I then went through with them the 2 questions on the paper that stood out as being done poorly as a class - this was the manipulating algebra questions (a lot of factorising). This made me think about how I had taught this topic originally and why the topic hadn't stuck in the students minds - was it because I hadn't taught it well enough? Was it because we covered that topic nearer the start of the school year and they'd just forgotten it?
I then told the students, for homework, to do 1 of two things. The first (following feedback from the NQT session) was to complete a survey I had set up for the class on www.surveymonkey.co.uk to give their honest opinion on our lessons so far this year, their grades, what they felt needed improving, what was going well, what activities they liked best in class etc. The second was to go to my YouTube Channel (mrcollinsmaths) and watch the solution videos I had created from their mock paper for the questions they did not answer correctly.
I will then discuss with them the results of the survey (some of their responses are as useful as they are brutally honest) in our lessons next week.

However, I did not feel this feedback was effective enough and wanted to focus more individually on questions the individuals needed to work on in the class - perhaps the questions they should have got right but didn't for whatever reason. So, I went back to the spreadsheet and filtered out the results by their marks. This then put the top of the class at the top of the sheet and the bottom of the class at the bottom. From this filtering I was then able to group the students by their results.
I then aimed to do a group work lesson whereby I sat students according to their results in the mock paper. The interesting thing about doing this was that when I was grouping the students into groups of 6 (the top 6 students being in group 1, the second 6 students being in group 2 and so on) I was starting to notice patterns in the questions they got incorrect or scored low marks on. Pretty much in each 'groups' case there were one or two questions that these students all got wrong. So I decided that I would differentiate the tasks for each group based on these questions they all got incorrect. This then meant that in the 5 groups I had set up each group had 2 tasks to work on relating to 2 questions they got wrong in the mock paper. There was a clear level of increasing difficulty to the questions as you went from group 5 to 1, with a few overlaps in the groups. For example group 2 and 3 had 1 task that was the same (forming expressions and solving equations) and group 1 and 2 both had a factorisation task. I used tarsia puzzles and pre-prepared worksheets for each group so they could all support each other on the tasks.

Here's the resources I prepared and how I set up my room:

I gave each group a magic whiteboard www.magicwhiteboard.co.uk to work on and whiteboard pens/resources were on each table at the start of the lesson. The groupings were up on the board as the students came in and my number tiles were on the tables to direct them to the appropriate group. I explained at the start of the lesson why I had set the groups up in the way I had and that my intention was that each student was able to answer 1/2 questions from the mock paper at the end of the lesson that they weren't able to in their actual assessment. As the lesson progressed the great thing I found was that the top 2 groups were, for the first part of the lesson took care of themselves and were able to get straight on with the tasks they were given. This allowed me to go straight to groups 3 and 4 initially and give them support at their table so they were able to complete their tasks. Group 5 were busy at this point cutting out their tarsia puzzles and this allowed me the time to get to the other groups. When I finished explaining to groups 2 and 3 and covered any questions they had they were then able to get on with their tasks. I sat with group 5 and checked they knew what they had to do  (HCF and LCM) before then going to group 2 and 1 and giving them my input to move them on to the harder of the tasks they were given, this for group 1 meant going through factorising quadratic equations (coefficient of the x^2 term > 1) at the IWB (I purposefully sat them at the front for this reason).
At the end of the lesson I got students to revisit their AfL tracker sheets from the lesson before and fill in whether they felt more confident on their RAG scale and whether they now knew how to do the tasks they were set. I could see progress in the lesson as the groups had either completed their tarsia puzzles or completed their w/sheets, moved on to other tasks given at the IWB etc.

Here's a pic of group 5's completed tarsia on Prime Factor Decomposition (their 2nd task)...

The class worked well throughout the lesson and I feel had I not done this differentiated group work lesson that the students wouldn't have had sufficient feedback from their mock paper and wouldn't have known where they went wrong with at least a few of the questions. This also meant that they would now, if taking the paper again, would pick up more marks than they originally did, therefore improving their score.

The final thing I have thought about doing is, again after discussing the class with my mentor, set up a 'focus group' of those students who are significantly below their target grade. I already have students in a seating plan according to their target grades - in the hope that students on similar targets support each other achieve their similar goals, but also need to focus some more of my attention on 3-5 of the students that need an extra boost to achieve their targets.
I have informed the class of extra support sessions from me after school that are available and will be discussing this week with those students that are in this new 'focus group' about attending these sessions and will also aim to get their parents involved as I know they are supportive and will encourage them to attend the sessions.
I will blog more about this class in the future, after I have fed back the survey results, had a few of the after school sessions and thought more about how I can revisit some of the unit 1 topics whilst teaching the unit 2 content of the METHODS in Mathematics.

Rule Book

Last week I did a bit of private tutoring with one of my tutees I haven't seen in a while. She's currently revising for her Mathematics GCSE exam that she has in March (well the 1st paper is 28th February)! After we had gone over lower and upper bounds, direct and indirect proportion, bearings and a few other things she showed me the 'rule book' that she had been keeping over the past month or so to revise more effectively.
Now, as I used to work in the school in which my tutee is studying I know of one of the Mathematics teachers there that uses these 'rule books' with all of his classes in KS4 as an effective way of them keeping revision notes and examples of questions. Each week he'd check these books to see that the students were using these. However, my tutee doesn't have this teacher for Mathematics and so I was massively impressed that she had decided to do one off her own back.

In the book she had a separate page for each topic/different type of question, all pages were numbered and at the back of her 'rule book' she had an index to easily find certain topics to revise from. I thought this was brilliant and I am now wondering as to how I could introduce this in class and whether or not students would use it as well as she is? Would it be something that I'd have to check on a weekly basis? Would these checks and the compulsory nature of me insisting the students kept these books then have a negative affect on them wanting to keep them? Should they be something that the students themselves would have to WANT to be keeping rather than something I would be telling them to do? All questions I'd have to consider and I may well contact my previous colleague to see how best he uses them with his classes?!

Here's my tutees' rule book...(I don't know who Sam is - maybe he appears throughout the book to explain concepts etc?)

 Here's some of the notes she's made inside - looks like Pythagoras' Theorem in 3D!

Here's the index pages - notice how she's almost made 100 pages already!!












The only thing I asked her was if anybody had checked the notes/examples she had written in her book. She said that they hadn't so far as it was just something she had been keeping to help her revise! I thought that this may need to be done so that she was certain that everything in there was accurate (I'm sure it would have been). If introduced in class these would, at some point, need marking or at least looking over by me. I could see these being used in conjunction with a class exercise book. The 'rule book' would be used for students to take down notes at the start of the lesson - just one example, key formulae/definitions etc, and then exercise books could be used for practise questions, workings out, homeworks etc. Mark the homeworks as they are given and completed and then mark the 'rule books' once a week/fortnight?

I'd be interested to hear if any Mathematics teachers are using anything similar in class and how best they have been implemented? Do the students take to these well? Do they use them proactively? Tweet me @mrprcollins or reply below!

Socrative

Last week, just before the school day started, I was setting up my lessons for the day and getting all of my resources printed off and cut up etc when my HoF came into the room to ask to borrow one of my Year 9 books to show my topic trackers in the subject leaders meeting. After we spoke about these and how I use them he happened to notice one of the resources I was planning to use that day - the DfE Standards Unit S2 resource on evaluating probability statements. Having recently taught the same lesson to his year 8 class he suggested that I use the socrative resource he had used and set up for his class.

Now, at this point I hadn't used or heard of socrative before and so he explained what it was and how it worked to me in the 10 mins before the bell was due to ring. The website www.socrative.com is a site where teachers can set up quizzes for their students to answer in class using their mobile devices. The resource by HoF had set up was the S2 Standards Unit lesson. There were 11 questions all exactly the same as those in the resource and all required students to answer true or false to the statements (there was also 1 question asking for their name). How socrative works is once you have an account (free to sign up) you get a 'room number'. When students access the site on their mobiles, by going to m.socrative.com they are asked to type in the 'room number'. This then goes to the teachers live quizzes once set from the teacher account. At this point the teacher is able to see all results live as they are completed by the students. So, after my brief tutorial, my HoF very kindly allowed me access to his quiz by sharing it to my account and my lesson was ready to go.

In the lesson, the socrative quiz worked really well. I had the website up on the board where I was logged in and the live results were appearing on screen as the students were doing the quiz and entering their true or false answers to the statements they were given. The added bonus of this is that I was able to see who was getting them right/wrong and the 'room number' was displayed clearly for students to see. As I hadn't prepared students for the task they were excited about being able to use their mobile devices and were highly engaged in the task. However, as they weren't told about the task prior to the lesson not every student had access to a mobile device that could access the Internet. This, would probably be the case anyway even had I told the students they would be using their devices next lesson so, how I got around it was by asking students to, once they had completed the quiz themselves to share their devices with their partners or other students that didn't have one with them. Most of the students obliged and it wasn't long before all students had completed the task.
We had a few problems with some devices not being able to connect to the Internet or not being able to load up the socrative page, but all students managed to complete the quiz eventually.
Once all students had completed the task the results were there to see on the board, with all the students names and their scores out of 10 on the board. This created a healthy bit of competition across the class as they attempted to get the highest score in the class, or higher than their friends' scores.

After all students had entered their results I then fed back to the class the answers by entering my results on the IWB just as they had done on their mobile devices. I went through each statement and discussed with the students any misconceptions that they may have had on the questions before choosing the correct answer and going to the next question. It was interesting to see which questions caused the most misconceptions with the class and those that caused little confusion.

What I liked about socrative is that when I closed the quiz it then gave me an option to receive an e-mailed report of the class' results - this for future reference was great to have to hand.

I will definitely use the socrative website in the future with students as I feel the kids really bought into it, they were excited about using their mobiles, they were using their mobiles in a productive learning environment, we were able to get instant feedback of their results and analyse these together addressing misconceptions the students may have had and it was really easy to use given that it only took me and my HoF 10 mins to set up an account with me and 'train' me how to use it!

Too Puzzling

The content objective: adding and subtracting fractions with unlike denominators, for 5th grade students.

What game? On short notice... I have a couple race games and Mr. Schiller has pattern blocks - but those use the fraction cards which I like, but were also at my office.I was thinking about a game where students start at one, and one team tries to race to 2, while the other team takes away and races to zero.  That would be good for building intuition, and learning to record fraction number sentences, but this is their last day with fraction operations before moving on to something else. What could serve as a review?

I thought about a game you could play with a small number of cards (one sheet), or a game where they would be doing review problems and checking each other as they play. Somehow I was reminded of a tarsia puzzle. (Here's a bunch at tes, among other places. Not sure who tes is, really.) Mostly those are triangular, but I decided on a square pattern, more familiar to the students. Here's what I wound up with. Made the grid in GeoGebra, of course.


A lot of thought went into the puzzle. I repeated a couple values to make it so that a match did not conclusively mean that two pieces went together (harder). I made all of them doable with 24ths (easier).  I decided on a 3x3 vs a 4x4 (easier). I made almost patterns on borders (harder and easier). Made sure some of those were nonmatches (easier). Related problems, like 1/4+1/2 and 3/4-1/2 (easier). Some operations where the common denominator is one of the present denominators, 2/3-1/6. And one mistake. (Crazy harder. Fixed version above.) I tried to put in some common characteristics on adjacent tiles. (Hmmm?) If they've been doing these problems in general, I thought that this would be enough support for everybody, especially working in teams.

To differentiate, then, I was mostly thinking upward. On the original puzzle they could make 3 more squares to make it a 12 piece puzzle. I made one with some triangles blank for the students to work out sums, differences or make up a problem, and then an entirely blank one for them to make up their own Tarsia.

I launched the puzle by showing cut out pieces, telling them it was a puzzle and asking how it might go together. Through whole group discussion they figured out that the sums and differences matched some of the fractions. I compared it to the puzzles that are all squares that divide up pictures, which are pretty tough. After finding a few of the matches together, they formed pairs and came up to pick up their choice of puzzle. Only one group took an option on the partially filled in puzzle.

They did not like it. Found it too hard, or didn't know how to start. Mr. Schiller and I circulated and helped people get started. They found lots of matches, but before our time was up were moving on to other pursuits. Not interested in making their own.

To wrap up, we came back together and did some together to get a firmer idea of how to do it. They confirmed that it was beyond them. When I asked for words of wisdom, one student volunteered: "You might want to try it yourself, first. If it's too easy, add stuff to make it tougher. If it's too hard, make it easier."

Wise words, indeed.

To use this in fifth grade again, I think I might concentrate on first getting a square of four made, and then try to grow it. Mr. Schiller recommended either a fraction equivalence puzzle or a fraction-decimal equivalence puzzle to get it launched. I still love these kinds of puzzles, but fee like I learned something about introducing and using them with younger learners.

Post Script:
Jeff says: The equivalent fraction version of that worked a lot better.  I sort of sneakily encouraged them to also incorporate equivalent decimals too.  In the version we played in the afternoon,  they created their game board in pairs and then they matched up with another team and exchanged puzzles and it became a race to finish the puzzle first.  I sort of mentioned in an offhanded way - oh yeah, and if you wanted to make it a little more challenging for your opponent, you might include some equivalent decimals, too.  (That did the trick)

National Story : Arithmetic skills in a decline in India as per Survey

ASER 2012 Findings

 

 The HRD Minister Sri Pallam Raju speaks at the release of the survey.

Maths Skills decline in India

മാത്സ് ബ്ലോഗ് ഒരുക്കം - ഐ.ടി - 2

വിവരവിനിമയശാസ്ത്രം പുതിയ കാഴ്ചപ്പാടിലൂടെ കുട്ടികളിലെത്തിച്ച് മൂല്യനിര്‍ണ്ണയം ചെയ്യുന്ന ആദ്യ വര്‍ഷമാണ്.എട്ട്,ഒന്‍പത് ക്ലാസുകളില്‍ ഇത് നടത്തിയിരുന്നെങ്കിലും ഒരു പൊതുപരീക്ഷയുടെ എല്ലാ ഗൗരവത്തോടെയും സമീപിക്കുന്നത് ഇതാദ്യം.പാഠപുസ്തകത്തിന്റെ സൂഷ്മതലങ്ങളിലേയ്ക്ക് ഇറങ്ങിച്ചെന്ന് തയ്യാറാക്കിയ തിയറി ചോദ്യങ്ങളും പ്രാക്ടിക്കല്‍ ചോദ്യങ്ങളും ഇതിനകം കുട്ടികള്‍ പരിശീലിച്ചിരിക്കും . എന്നാല്‍ എല്ലാ കുട്ടികള്‍ക്കും ഒരു പോലെ ആയാസരഹിതമായിരിക്കുമോ വരുന്നICT പരീക്ഷ?
കുട്ടികളുടെയും അവരെ പഠിപ്പിക്കുന്നവരുടെയും മനസില്‍ സംശയങ്ങള്‍ ബാക്കിനില്‍ക്കുന്നു.നമ്മുടെ വിദ്യാലയങ്ങളില്‍ പഠിക്കുന്ന വളരെ കുറച്ചു കുട്ടികള്‍ക്കുമാത്രമാണ് സ്വന്തമായി വീട്ടില്‍ സിസ്റ്റം ഉള്ളത്. ബാക്കിയുള്ള മഹാഭൂരിപക്ഷവും ആശ്രയിക്കുന്നത് സ്ക്കൂളിലെ പഠനം മാത്രമാണ് .എല്ലാ പാഠങ്ങളില്‍ നിന്നും ചോദ്യങ്ങള്‍ തയ്യാറാക്കി വേണ്ടത്ര സമയമെടുത്ത് പരിശീലിക്കാന്‍ സത്യത്തില്‍ സാധിക്കുന്നുണ്ടോ? നമ്മുടെ പ്രധാനവിഷയത്തിന്റെ പ്രാധാന്യം ചോര്‍ന്നുപോകാതെ ചെയ്യുന്ന അഡീഷണല്‍ വര്‍ക്കായിരിക്കും ICT അധ്യാപനം.
പ്രാക്ടിക്കല്‍ പരീക്ഷയ്ക്കുള്ള കുറേ ചോദ്യങ്ങളും അവയുടെ പ്രവര്‍ത്തനഘട്ടങ്ങഴും ഇന്ന് പ്രസിദ്ധീകരിക്കുകയാണ് . പരീക്ഷാസമയത്ത് സമര്‍പ്പിക്കേണ്ട വര്‍ക്ക് ഷീറ്റ് മാതൃകയില്‍ തന്നെയാണ് ഇവ തയ്യാറാക്കിയിരിക്കുന്നത് .കഴിഞ്ഞ രണ്ട് പരീക്ഷകള്‍ക്കായി തന്ന CD യിലെ ചോദ്യമാതൃക തുടരാന്‍ പരമാവധി ശ്രമിച്ചിട്ടുമുണ്ട് .ഈ വിഭവങ്ങള്‍ പരമാവധി പ്രയോജനപ്പെടുത്തി പ്രാക്ടിക്കല്‍ പരീക്ഷ വിജയകരമാക്കുമെന്ന് പ്രതീക്ഷിക്കുന്നു.
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