Prime numbers are the building blocks of maths. Prime numbers cannot be broken down (they have no factors), and so every number can be written as a product of prime numbers (for example, 210 = 2 x 3 x 5 x 7). The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19… They have fascinated mathematicians over the centuries because they do not follow any particular pattern, and thus it is impossible to predict the next one from the previous. They have many practical uses, most notably in cyber-security, but also in nature (for example, locusts only reappear to mate every 11, 13, or 17 years – always a prime number). Try these quick prime number questions, which recently appeared in our newsletter:
1) What is the only even prime number?
2) What is the first prime number with consecutive digits?
3) Apart from 2, prime numbers always end in the same four digits – what are they?
4) A prime quadruplet is four prime numbers as close together as they can be within a decade. The first such example is 11, 13, 17, 19. What is the next example?
5) A palindromic prime reads the same forwards as backwards. The first three digit palindromic prime is 101. What is the next?
Scroll down for the answers!
1) The only even prime number is 2. As you may well have worked out, all other even numbers have 2 as a factor.
2) The first prime number with consecutive digits is 23. This is one reason amongst many that some people believe that 23 is special (in fact, there’s even a group called the 23rdians who believe it has mystical powers). In maths, and particularly prime numbers, it has some unusual properties, for example,
11,111,111,111,111,111,111,111 (there are 23 number 1’s here) is a prime number
10^23 – 23 = 99,999,999,999,999,999,999,977 which is the largest 23 digit prime
And in science, to create human life, each parent has to contribute 23 chromosomes, and the Earth is currently tilted at 23 degrees…
3) Since primes have to be odd (apart from 2) and cannot be a multiple of 5, they must always end in 1, 3, 7 or 9.
4) 101, 103, 107, 109 is the next one. Incidentally, if you cross decades, prime quintuplets and sextuplets also exist. Incredibly, 43777, 43781, 43783, 43787, 43789, 43793 are all prime.
5) The next is 131. Their search can rapidly be narrowed by a process of elimination. For example, we can immediately discount palindromic numbers in the 200’s since they will also end in 2 and thus be even. And we can discount 4-digit, 6-digit, 8-digit palindromes (etc.) because these can all be shown to be multiples of 11. So the next few are: 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, for example.
“If what you’re explaining takes more than 30 seconds, either you’re not explaining it clearly, or the concept is currently too difficult for the child..”
But what exactly does that mean? We mentioned the 30-second rule a few weeks back in our “Dealing with study tantrums” post* but we didn’t really delve into the reasoning behind the rule and why it’s so important to consider the way in which we present ideas and concepts to children.
Before we continue, though, it’s worth noting that the 30-second rule applies best to short-answer questions on fundamental concepts (fractions, decimals, areas or metric units.) There are teaching strategies for problem-solving and mathematical reasoning, which require constructing a more lengthy argument, but that’s a topic for another day.
Our attention spans vary, not only from age to age, but also depending on the time of day, the type of activity we engage in, and our own disposition towards the subject at hand. It’s widely agreed that children’s attention spans are much shorter than those of adults, so it’s very important to keep explanations concise and to the point.
But how do we do that? Here are some suggestions if you find yourself past the 30 second mark:
#1. Ask yourself: Do I understand what I’m trying to explain?
Sometimes we need to check with ourselves whether this concept is clear to us or not. If it isn’t, it’s worth looking for a way to explain it to yourself, so that you can then explain it to your child.
#2. Consider your presentation – are you going overboard with the explanations? Or are you getting lost in an example?
Some people understand things better when the concept is contextualized (ex. linking fractions to baking a cake.) Some would rather have the concept presented to them straightforwardly. The best explanations are a combination of both, but it’s easy to go overboard on either side. If you rely on one, why not try out the other for a while?
#3. Break it down.
Consider what you are explaining. Can it be simplified into two or more steps? Or perhaps you need to go back to basics and build from there. If you have a problem with fractions, go back to illustrating basic ones using a pie chart, then build up from there.
#4. Take a break.
Studies would suggest that focusing too much on a single task diminishes our capacity for understanding. If you and your children are finding it hard to focus, why not take 3 minutes for a cup of tea and a biscuit before you review your explanation? The solution might well present itself.
What is the teaching rule you swear by?
We’re almost three weeks into the school year – does anybody else feel like time is flying? We sure do! Hopefully by now the children have eased into learning mode, new knowledge is being effectively built up, and all is well in the world.
Until the time comes for a parents’ evening.
On paper, it should be easy – after all, both you and your child’s teacher have the same goal in mind, which is helping your child to succeed. But sometimes misunderstandings happen, and it can sometimes be the case that the teacher has a different plan on getting to that goal than you might. (And if your action plans happen to coincide, GREAT! You’re in for an amazing year.)
Whatever the case, it’s important to establish a good dialogue with teachers, so, as parents as well as educators, here are our Dos and Don’ts for those first face-to-face meetings:
DO ask the teacher questions. Sometimes (especially for new teachers) it can be difficult to articulate everything they wanted to say. In cases such as these, having a few concrete queries can help the conversation flow.
DO talk about things that concern you. If you read an article in the Daily Mail about how the curriculum is getting more demanding and you worry about your children being overloaded, tell the teacher. It’s likely that they’ve considered this already in depth with their colleagues and will be able to allay your concerns.
DON’T make assumptions that last year’s action plan is still on. Teachers change schools. Budgets get revised. The Ofsted report said the school was a couple of points short of being “Outstanding” so now everyone must Work Harder! and restore honour. None of this means that your kids will get worse tutoring, or that the teachers won’t try to make that very neat idea from last year happen in some shape or form. Keep an open mind to change – after all, the end goal remains the same.
DO ask about the best way to help your kids from home. We all want what’s best for our children, and the teachers come only second to you in knowing their individual strengths and weaknesses. Maybe your daughter needs to work more on her spelling. Maybe she’s on top of her class and doesn’t need to do anything in that area. It’s always a question work asking.
DON’T ask the same question again and again. If the teacher already gave an answer you didn’t like, repeating the enquiry won’t change it. If they don’t have an answer immediately, assume it’s because they’re working on a solution and they want to be sure on it on their end before they bring it up with you. Again, keep the end goal in mind.
DO arrange for a follow-up, if there is no time to discuss everything. In business, a major factor contributing to goal-keeping is having regular check-ins between team members. The same logic applies to school. If the teacher can’t discuss everything with you at the moment, exchange numbers and arrange for a good time to call. (And call exactly when agreed upon. And set up an agenda beforehand. If you say you need five minutes to discuss your son’s latest test, then make sure the conversation lasts four and a half. This allows you to cut the frills and see the point of the matter.)
DON’T demand a point-by-point discussion of the school budget. Even if you’re on the governing committee and the teacher in question is in charge of finance, a parent-teacher conference is not the place to have this talk. If the teacher brings up the plans for buying iPads, then by all means, ask them about details – they have likely anticipated the questions and prepared in advance. (Or, alternatively, if you think it’s a neat idea to buy the children iPads, and if there’s time, you may bring it up on the condition you and the teacher agree on a follow-up conversation. They would likely need to do their research first.) But don’t put anyone on the spot – it hardly sets the grounds for a happy relationship.
DO celebrate the children’s (all of the children’s) successes. While we’re all anxious to solve any issues that may arise, focusing on the negative can take away from the joy of the positives. Take the time to congratulate the teacher on a school project they supervised, or to say how much your kids enjoyed their summer learning project. If the teacher brings up plans to innovate at the school which you like, say so, and if you can spare it, volunteer to help out. (Even if they don’t need extra hands. The gesture counts.)
What are your dos and don’ts about communicating? Are there any tips you’d like to share?
Early in August, we took part in a #BETTchat on Twitter which posed a fascinating question: Is Education Technology too expensive to work?
Given our upcoming appearance on the ICT for Education conference in Newcastle, we thought it might be worth revisiting the topic.
As the chat quickly revealed, the cost of buying a bunch of apps for students to use in the classroom is the smallest item on the ICT budget of a school. (Indeed, the apps themselves range in price, but it’s rarely enough to break bank.) Nor is the cost of acquiring hardware necessarily the biggest barrier to implementing #EdTech, although not all schools can necessarily take part in volume purchase programmes like those on offer by Apple. Aside from capital expenditure, the two biggest items on the ICT budget of a school are maintenance and training costs.
While we agree that EdTech can be financially demanding, though, we strongly believe it’s a profitable long-term investment, for schools and teachers alike. These are our top reasons why:
- Technology, especially interactive apps, can cater to a variety of learning styles.
- Big data (like the performance of a student over time) can be harnessed to create individualised work programmes at minimum cost for the teacher, as it saves them time and effort.
- Interactive apps increase student engagement and encourage them to take ownership of their learning.
- Technology is an integral part of students’ lives – it makes sense to bring it into the classroom as well.
- Teachers get the most out of their face-to-face interactions with students when the software helps them target and address the most important areas of weakness.
- Teachers become more confident in the classroom.
- Teachers also become more tech-savvy the more they use EdTech, so they are able to identify the kinds of apps that would be most effective in the classroom.
- Student performance improves.
None of these changes can happen overnight – both students and teachers need time to learn how to use a piece of technology and integrate it in lessons. All of it requires time and patience, which can be difficult if a school needs to meet criteria or is preparing for nation-wide exams. But as educators we need to consider the long-term effects of our policies. Learning more about EdTech and giving teachers time to get comfortable with using it can well prove to be the winning factor for a school.
Where did the holidays go? It felt like just yesterday that schools broke up and we were coming up with action plans to not let learning slip over summer. Now, all of a sudden, we’re back at school.
For some, coming back to school is a surreal experience after 6 weeks of holidays – and not just because you have to sit still and learn for hours at a time! Remembering all you learnt the previous year, adjusting to a school-year schedule, and dealing with constant reminders that “SATs are just X weeks away!” can all take a toll on a child.
So how can parents help with the adjustment period? We offer three tips, all variations of the old adage that “Fast is slow and slow is fast.”
#1 Don’t set high expectations from the get-go. Your children have just finished their holidays – an adjustment period is not only expected, it’s necessary. Start them off with just making sure homework is done, and don’t bring up too many extra learning activities until the second or third week. This would allow your child time to adjust to the new schedule.
#2 Encourage some revising. For knowledge to build up, it needs a solid foundation, and the way to do that is to revise, revise, and revise some more. This is especially necessary if your child is struggling with understanding new concepts – it could well be that they need to reinforce old knowledge before they make the connection. Be patient, and remember the 30 second rule.
#3 Remember to leave time to play. We said it once, but it’s worth repeating: We need to recharge our batteries often in order to learn more effectively. This is especially true nowadays, when physical exercise and play are becoming more tightly regulated. (It’s something a lot of people discuss: An article in the Washington Post, for example, attributes the increase of children diagnosed with ADHD to a lack of physical exercise.*) Let your kids be kids – the homework sheet will be there in the morning.
What are your top tips for easing back into a school schedule?
*For more information, find the article here: http://www.washingtonpost.com/blogs/answer-sheet/wp/2014/07/08/why-so-many-kids-cant-sit-still-in-school-today/
[Gail, our Sales Manager, writes her first blog on why giving students choice does not make them autonomous learners.]
It’s a long held belief that giving students choices makes them autonomous learners. Having talked to a school today about the needs of their learners, I’d like to clarify this.
This school teacher had been using the market-leader for ICT-based maths resources for a number of years. He had come to the conclusion that, far from creating autonomous learners, too much choice was doing the opposite.
The software he was using (and 24% of schools in the UK use it) either gives children a choice of games and activities to do, else the teacher can set them work directly. In the first instance, they either do not know what to choose, or default to the easiest choice. In the second instance they are reliant on the teacher.
In using DoodleMaths, children are restricted to two choices: reinforce what has recently been learnt, or learn something new (which is relevant to their individual needs). Children are autonomous because they can choose to do their maths at any time, as much as they like, and see visible improvements in their DoodleMaths Age. The can work independently on content that is exactly matched to their needs. To expect a 7 to 11 year-old to be autonomous to the extent that they know their own learning needs is to expect too much – to the detriment of their progress.
So in future, when challenged that the prescriptive nature of DoodleMaths restricts student autonomy, my answer is simple: autonomy means independence, but independence does not necessarily imply choice – as any parent will know!
P.S. If you’d like to create a classroom of autonomous, independent learners, email me direct on email@example.com or the rest of the team at firstname.lastname@example.org and we will set you up with a school trial.
(Katya on the importance of fostering a sense of community in the classroom.)
I don’t know about you, but my school experience was a fairly individualistic one. Grades were always a reflection on your ability and your knowledge, and there is a lot of value in giving children a sense of responsibility about their own success. However, I am supremely glad to have gone to a University that encourages teamwork. It’s a skill I needed to develop, and I feel like it has been crucial to my development in the last few years.
Steve Wheeler talks about the ways online groups work together, and why a social aspect is key in getting children to participate in online learning exercises. It’s a very interesting read, as well as the articles he links, because they underline a truth which is one of the foundations of DoodleMaths (and indeed, many of the recent posts on this blog.)
Namely, that play supports and enhances learning.
Playing with friends and teamwork have quite a bit in common. In fact, the only difference is the context in which the words are being used – “play” implies a seemingly pointless activity, while “teamwork” is something that you usually do in the office, if that. However, both activities involve more than one person engaging in an activity to achieve a common goal, and in both cases, there are certain group dynamics at hand.
As we grow older, we start hearing words like “leader” and “mediator”, and businesses spend thousands of pounds on getting their employees trained to work better together; when we’re kids, though, we’re bossy, or meek, or come up with ideas that work for everyone, and those things come about more or less organically.
So why don’t we take advantage of naturally arising group dynamics and have kids work together more in class projects? Why not nurture good practices about working together as a team? Perhaps you can find students that are more advanced in your subject and have them help out their friends? Or maybe have students work on exercises in small groups to encourage knowledge sharing? Not only does this take away the edge of competition (and have some feel bad about not ‘getting it’ straight off the bat,) you are creating an opportunity to help your students build effective relationships beyond simple friendship. And if you need any more proof, check out this article about where the value of a school lies.
Try it out – who knows, 15 years from now, you might be saving your students’ employers a lot of money on training.