Free Resources for Educators and Students of Mathematics and Statistics
Jim Hogan - firstname.lastname@example.org - 027 461 0702 - based at Central Plateau REAP, 73 Titiraupenga ST, Taupo, NZ
Merry Month of May and National Workshops
The National Workshop Files used and referred to are here for you to download and use.
Session 1 - What's On top, there are comments embedded in the powerpoint but see NZQA moderator news, nzmaths blog.
Session 2 - Raising Student Achievement, is based on two readings from ERO. Really useful documents now on http://www.ero.govt.nz.
Session 3 - Treasure Hunt, is an attempt to train your eyes to find resources on NZMATHS. Here is the hunt and the answers.
Session 4 - PFM Personal Financial Management, are new Standards at L1, L2 and L3 to help stduents become more $-savy. http://www.youngenterprise.org.nz has many supporting resources. Here is one of them called BANKING.
Standard A3 Sheets, see Robyn's Blog Spot http://nzl123.blogspot.co.nz for NCEA A3 Standard Summaries and a lot of other news.
Probability Progressions - Here is the one we used.
Sampling .ppt Y12, this is a demonstration and activity for students to do to empower them with understanding of sample size and 1/√n. I like the implication "Four times the same size halves the variation you can expect"
Nat News Term 2 2016, produced each term and all available for all Learning Areas on TKI here.
From Last Year's Nat Workshop (below), Questions in Statistics , the stats question seems to continue to be an issue. Students must ask a comparative or investigative question and THEN they MUST answer that question. A comparative statement must be made! An inference from the sample to the population must be made. Note in a question it is the "population parameter (median Y12)" to which the reference is made.
My Progression Versions all zipped up. Careful...2mB.
National and Regional Events
LOMAS Numeracy Testing Resources
Readings in Math ED
Lake Taupo Trout
INZight Statistical Analysis Software
Rich Math Activities
Two bookmarks for students
These can be printed backed on card and given to students to help solve math and stats problems. The bookmarks outline robust and trialled strategies for problem solving.
Girth of the Earth
Use your cell phone nav system or a GPS unit and a metre wheel to measure the circumference of our planet. This leads to radius, moon size, distance to sun and very interesting astophysics discussion.
Problem Solving Checklist
A sheet for students to record how they solve problems.
A Key Secret about Learning Mathematics and Statistics is to make learning INTERESTING to the Learner.
Interesting is a Complex Notion. The notes that follow try to explain three important aspects.
- Know the Learner. This means you are aware of strengths, interests and weaknesses. You know about the family background, what has been normalised. You know about previous learning. You can identify the student and you now and use it's name, correctly.
- Normalising behaviour. A young person learns very quickly, from the well before it is born, using all the senses it is blessed with, mainly eyes. As a teacher we MUST model the behaviours we desire and want established. We model solving problems, being on time, being organised, logical reasoning, enjoyment of mathematics, persevering, writing and reading.
- Know the Subject. The specialist teachers in secondary schools have indepth knowledge and experiences in a particular discipline. This is how Western learning has been tradionally organised. Compared to Eastern Philosophies our approach is more siloed and often separated hence we have subjects and a timetable. The more you know about mathematics the more connections you see, make and teach. Having a degree in mathematics is important but not essential, having high level papers is necessary. Reading books about mathematics, enjoying solving problems, pondering new approaches all indicate readiness to teach this complicated, connected, deeply useful and widely applied discipline.
- Ponder with Others. Mathematics is really about ideas, thinking and solving problems. Ideas should be discussed with and explained to others. Working in small groups, making and doing mathematics. Solving problems. Here is a link to the Klein Project (oranges top right) and a paper to read called Lisbon. Challenging thoughts. http://blog.kleinproject.org/ and http://www.projekt.didaktik.mathematik.uni-wuerzburg.de/klein/index.html.
Summer Update Time
National Workshop 2015 Material
The complete ZIP download is here and is about 22Mb. The separate sessions are listed here and can be download individually. Feedback was great thank you. Do you want to see it all? Please ask.
Session 1 CAT, Session 2 ALIM PACT, Session 3 Geo and Measure, Session 4 Data, Session 5 Questions Stats, Session 6 SAMR, Session 7 DEPT. A file full of Starter Ideas for lessons. The National Workshop was informed by a survey at the end of 2014. Another fraction starter, very cool.
Thank you everyone for the participation and contributions to these days. Keep the conversations in local area groups going. The MCAT material we used was a drafty version so please wait until the final version is published by NZQA to see what to expect. The material was to show the "solve a problem" issue, not overall grading. Cheers
KEY CONCEPTS - There are BIG IDEAS in mathematics and I want to see these in classrooms. See SSTLG.
Change and Variation
Data can be calculated and decisions made despite looking like a school of fish. Variation is always present, no more so than in my golf! We live with change and variation daily in this dynamic world. The more we understand about data, likelihood, sample size, population, estimates and relative risk in this data driven world the better. Fantastic software like iNZIGHT running on fast modern computers make learning about statistics fun.
Structure and Generalisation
Models, abstractions, and representations. These big ideas are more about the exact nature of mathematics where number can generalised with algebra. Algebra is the international language of the sciences and a working knowledge of patterning and abstraction is worth learning. The critical step in my experience is to become multiplicative first. Without this confidence algebra becomes a very cryptic and meaningless exercise.
Argumentation and Proof
Logical argument based on facts leading to a reasoned proof is owned by mathematics. In no other discipline can something be proved. Learning how to formally prove something is a beautiful skill to experience. Try it yourself now and "Prove that the angles in a triangle add to 180".
This ability can be learned. I have added this here beacuse it is vital to mathematical success. Persevere, learn from mistakes, create new paths of investiagtion and become a problem solver. Everyday in every classroom.
Invitation for teachers to form an online Learning Cluster ---> see "Let's form a Cluster".
I am planning an online cluster network this year rather than running an all day workshop. I am planning this to be responsive to teacher need and pretty much anyone can join. If you are interested please email to email@example.com. You will need SKYPE.
Secondary Student Achievement Contract (MY JOB) is again operating in schools and primarily working INDEPTH with middle leaders to lift student engagement and achievement. This is excellent work to be involved in as it is all need driven PLD, rich in inquiry into practice, curriculum development, research based and supported by some very informed people at Team Solutions in Auckland University. Check out the website for Team Solutions.
I have been a fan of the work Prof Jo Boaler is doing at Stanford University. She is the Professor of Math Education there and ran the successful "How to Learn Maths" at Stanford Online - website. The work connects with Mindset by Carol Dweck who just happens to be in NZ in March 2015. The Mistakes Grow Your Brain is one of the 7 key messages Jo promotes for teachers. See her work and download all for free from http://youcubed.stanford.edu/.
Just for Fun and to Niggle at Sociologists.
SPAN - Society for the Prevention of Abuse of Numbers.
1=1, 2=2, 1+2=3 and I am very glad it does.
I get a bit annoyed at 1.10 being referred to as "one point ten". Names using numbers are not numbers. Like telephone "numbers" they are just names. Convenient names, I must add, but all the same, just names. One does not do arithmetic on telephone numbers or titles. Words could suffice.
The overs in cricket are represented as 4.2 meaning 4 overs and 2 balls out of the next 6 completed. I don't hear commentators saying "4 point 2" overs but it would be nice if they used another symbol like 4~2 or 4*2. There are plenty to choose from afterall. How about a cricket ball 4ø2?
Another annoyance is the abuse of the linear 1,2,3,4 and 5 when attached to a very non-linear questionaire or Likert Scale such as "Strongly Dislike, Dislike, Neutral, Like and Strongly Like" or some other discrete continuum. The social scientists add and then interpret the average, 3.23 say, as if there is meaning to the last decimal point. My feelings are logarithmic on some days and certainly never linear. Attaching meaning to these inventions is an illusion.
Ludicous to say the least and both instances are, to me, clearly ABUSE. Say so at every opportunity please point out the abuse, raise the validity question and join the voice of SPAN! Popint out the use of a,b,c,d,e instead of 1,2,3,4,5 would make just as much sense.
If you read this you are automatically a member.
The Klein Project, http://blog.kleinproject.org/ is about "a sense of connectedness between the mathematics of the teachers’ world and contemporary research and applications in the mathematical sciences." It is refreshing to be thinking mathematics instead of assessment, pathways, organising students and managing management. Take a look at this sight and freshen your classroom with some interesting problems in mathematics. I took an immediate affinity to the oranges problem having written a resource about the patterns that the balls form when stacked in this way a few years back. These are still on www.nzmaths.co.nz under SNP activities but here is the resource [Math Investigations]. The Klein Problem is about finding how to stack spheres in the most densely packed way.
Just For Fun
I keep discovering new Englisgh language words as my fingers type and work in strnage ways. Some, with the meaning are listed below:-
- plerase … this is a new form of asking nicely
- teh …another spelling of the common word for the particoular articel.
- releaiving… this is another attempt at getting out of school.
- claculator…this is a new device that resolves transposition errors in calculation
- lagebar … a state of generalised stupidity
- learnign …what happens just before you know something
- fo ... a reflective form of "of".
I maight make up a webapge of typos and thiungs for all to enhjoy. Plerase send new discoveirs to firstname.lastname@example.org
The image of the cryptic xword can be copied and printed full size. Try it!
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