This blog will take the load off the Mathemafix message board by hosting important information about 2021 OC preparation.
Parents talk about how their kids struggle with logical questions. I start to realise that people need to be familiar with conditional thinking to become good in dealing with logical thinking. One vital still is to set up conditional statements.
Factual statement: A rocket has one or more jet engines.
A conditional statement: If a machine is called a rocket, it has to have one or more jet engines.
This conditional statement has two parts. The order of the parts is important.
1 - If a machine is called a rocket, it has to have one or more jet engines.
2 - If a machine has one or more jet engines, it is called a rocket.
The clause with "if" is the conditional clause (also dependent clause). It is also called the antecedent. The main clause at the end is the consequent.
Now, you are ready to reason!
If a machine is called a rocket (P), it has to have one or more jet engines (Q).
The logic rule is : A => B
Now one can use Modus Ponens or Modus Tollens to reason. Often, they set up statements going the wrong way (B => A) to trick students. The only correct way to reason is to follow the direction of the arrow.
Parents should work with kids to train them to think conditionally.
As I mull over the topic of reasoning, I realise that people generally use 3 types of logical reasoning (even if they are not aware of the names and most have not been formally trained in any of them). These are inductive logic, propositional logic and mathematical logic.
Inductive: The volcano is due to erupt some time in this century because historical records show that it had an eruption approximately every 600 years.
Propositional: If weather is hot and sunny, the beach will be full of people. As the weather prediction for this weekend is warm and sunny, I won't go to the beach as I hate crowds.
Mathematical: There is a chance above 80% that the baby turtles will be females when the nest temperature rises to 31C or higher.
In general verbal reasoning, we may encounter all three types of logical reasoning in a single conversation. This would be very confusing for students and this is similar to the trouble of mixed maths problem solving using several types of skills.
Covid-19 is a disease with severe flu-like symptoms.
If the above information is true, who has the best argument?
Joe: My uncle has severe flu-like symptoms, he could have covid-19.
Anna: No, severe flu-like symptoms do not necessarily mean that a person has covid-19.
Sue: You are both right, but Anna misunderstood what Joe said.
In the above example, Joe seems to be incorrect if you apply propositional logic. Joe reasons backward and this is invalid. However, he uses the word "could" which introduce a possibility. In a sense, this is mathematical reasoning based on probability (even though it is very hard to recognise that it is actually mathematical reasoning). So, Joe is actually correct. He does not insist on absolute truth.
Anna, on the other hand, uses propositional logic and she states that you cannot reason backward. She is correct.
Sue can see that Joe is correct and she also see that Anna is correct. But Anna misunderstood what Joe said. Anna missed the word "could" and thought that Joe thought the person surely had covid-19.
In this case, Sue has the best argument.
So, the TS questions with a conversational format are the ones to fear. One has to be very careful in judging what style of reasoning each character uses and also look at the modality of the wording (strength of words) to decide if the character makes good sense or not. Frankly, it's too much to ask kids at year 4-6 to know the differences between different reasoning styles and spot them and apply correctly. They may have to rely on experience of doing the questions to cope.
I find that some students have problems with the strength of statements and commonsense vs logic. This is part of English comprehension. When this is mixed with logical thinking skills questions, it can be a real probem. Students must pay attention to "will" vs "would". I had a poor example before. Now I have tracked down a a decent example.
Cornstarch dissolves in water immediately, leaving no lumps after stirring.
Barry: “So if I mix the powder and water together and no lumps appear then it must be cornstarch.”
Mike: “No, it is when you mix the powder and water, with no lumps appearing it would be cornstarch.”
If the information in the box is true, whose reasoning is correct?
A. Barry only.
B. Mike only.
C. Both Barry and Mike.
D. Neither Barry and Mike.
Barry looks guilty of backward reasoning. The powder is not necessarily cornstarch when it dissolves without lumps. One student pointed out that Mike could be wrong too. But the problem here is the use of the word "would". Mike is only talking about a possibility so he is making sense. If Mike said "... it will be cornstarch", then he is wrong and the answer for the question will be D.
In English reasoning/argument, often all choices that have weak statements with "possibly", "could", "would", "perhaps", ... are wrong as they carry opinions (rather than facts). In TS, we have to be very careful! Is this question a logical question or it's an English comprehension trap? Many TS questions are not easy to classify because they look like logical questions but they are in fact verbal reasoning.
I find that some students are trapped by the sort of TS verbal reasoning questions that looks like logical questions but in fact, they can be treated as a normal English comprehension questions.
The light on the door is green and that means you can enter the room.
If the above information is true, who is correct?
Fred: "The light is red right now, so I cannot enter the room."
Anna: "Yes, and the light has been red all day, so no one could enter the room."
A. Only Fred is correct.
B. Only Anna is correct.
C. Both Fred and Anna are correct.
D. Both Fred and Anna are not correct.
Students often use their "outside" knowledge to answer this question. A red right means the room is locked or occupied, so you cannot enter. But that's not true in formal reasoning. The provided text does NOT state the meaning of a red light. It only states the meaning of green light. Therefore, there is not enough information. And that means Fred can be right or he can be wrong. This cannot be determined. Therefore, Fred is wrong because there is no choice saying "The truth cannot be determined".
Anna is wrong too as the truth cannot be determined due to lack of information.
There is not enough information to support any of the above speakers. So, choice D is the answer.
If you want to use formal logic, it still works the same way.
P => Q does NOT lead to not P => not Q
If you eat rotten food (P), you will get sick (Q).
does NOT lead to
If you do NOT eat rotten food (not P), you will NOT get sick (not Q).
They do not expect year 4 kids or year 6 kids to understand formal logic. They expect kids to use common sense and experience to work this out. The nasty bit is that they do not include a choice E, "There is not enough information to decide." What this means is that kids have to pick the choice that the statement is wrong when it is neither right nor wrong. It is simply a guess/opinion that could be right or wrong. This is a confusion between causual conversational English and formal logical argument.
Kids are now up to OC trial 4. It is tough for the kids but the strong ones are doing much as I have expected.
Here is a tip about logical reasoning that can help kids to get extra points. Parents should get to understand the stuff here to help the kids.
The trap of reasoning direction
Good boys eats fruits
1/ Joe is a good boy => Joe eats fruits (TRUE)
2/ Joe eats fruits => Joe is a good boy (FALSE)
Going the wrong way is always FALSE.
Modus Ponens and Modus Tollens
The understanding of Modus Ponens and Modus Tollens is of enormous help as they are formulas that one can learn and apply in so many cases of logical reasoning. Parents should learn from the video lessons I provided for OC level and guide kids to recognise and apply them consistently. This is better than just rely on experience.
Modus Ponens (to confirm)
Assume that this statement is true.
X is a good boy => X eats fruits
If Joe is a good boy, Joe eats fruits
Modus Tollens (to deny)
Assume that this statement is true.
X is a good boy => X eats fruits
If Joe does NOT eat fruits => Joe is NOT a good boy.
The 1st OC trial set will be open this weekend. Parents should arrange for kids to find a block of 2.5 hours to work continuously on the trial tests. This will give a realistic performance. It's a very bad idea to do the OC trial set over several days as this will not give any idea of real performance in an exam. Students get tired as they do a test and they score tend to fall depending on how tired they become. This is a chance to observe their mental endurance and help them improve strategy to best use their "fuel tank" to last the entire exam.
As the trial is set at year 5-6 level, students who are still doing year 4 work are not ready for it. There is no need to do it right away. It's better to work on year 5 work and OC boosters for a bit longer.
Suggested plan for the day
- Do OC English trial #1
- Rest for 5 minutes
- Do OC Mathematics trial #1
- Rest for 15 minutes
- Do OC Thinking Skills trial #1
Students can get very tired if they do not manage their time and effort during the first two tests very well. The risk is highest in the maths test as it burns up mental energy like crazy. If they put too much effort into solving the hard questions, they may burn themselves out and by the time of the Thinking Skills test, their minds no longer work. The key strategy to managing energy is the skipping of hard questions. When students see a hard (or very time consuming) question, just skip it. Do these at the end if there is still time left over.
To prepare for this OC trial, students should do the following
- Go to More ... and practise the new English question type called Sentence Cloze
- Do some English comprehension tests at grade 5 level
- Do some OC maths Boosters and review failed questions for this series
- Use the module Thinking Skills in More ... to watch video lessons and do the boosters and review failed questions for this series
- Do the OC General Ability Trial #1 to warm up to the Thinking Skills trial. This GA trial (for past OC test) is still very useful.
According the the SSU,
The weighting of the different component of the OC applictation will be out of 120 points as follows:
The OC test will provide 100 points shared equally between English, maths and TS papers. Schools will provide 10 points for English and 10 points for maths.The total weighting for each area including school marks will be roughly: Eng 36%, maths 36% and TS 27.7%
This means the impact of school marks will be a lot less and this is good as school marks are very unreliable. The TS component is now only 27.7% (vs 33.3% in the old OC application). So, it is now the weakest area of the whole OC application. So, TS is now NOT a big deal like GA used to be.
I have solved all the questions in the sample OC test to see what they are like. My assessment is that the OC sample test is brutal for year 4 students. If we take the writing task out, the OC test is nearly the same size as the selective test (90 questions vs 105)! I find the English level is almost the same as that of the selective test. Maths is very challenging and not much easier than the maths in the selective test. The TS paper is significantly easier only in the verbal reasoning and the logic which accounts for about 45% of the paper. The maths and spatial reasoning in the TS paper is almost as hard as that of the selective sample.
The huge problem with the sample OC test is that students will run out of time. The questions of maths type are very heavy in working out. English is brutally hard. It turns out the TS questions in the area of verbal reasoning and logic turn out to be the easiest. This means there is very little need to prepare for the TS verbal reasoning and the TS logic questions.
The English reading paper has extremely long texts and difficult texts. It's so demanding on short term memory as students must read carefully and remember a lot to be able to answer the questions. Forgetful students with poor short-term memory will struggle badly and will run out of time as they have to go back into the texts to re-read.
The maths paper is so long and the questions are big. The students who do not have great mental maths to do the calculation will waste time and run out of time.
The TS paper is not very hard but the time is too limited. So, students will run out of time due to the hard maths reasoning.
It was clear that they made the real selective maths component easier to the sample (according to feedback from year 6 students). They also made the maths reasoning in the selective TS paper easier than what seen in the selective TS sample. If they do not make the real OC paper simpler, a lot of students will score very poorly. The effect of this will be all students who are not really good will crash. Only the smart students who also work very hard will do well. The hard-working ones who are not smart will not do well. The smart but lazy ones will not do well.
THEY MIGHT MAKE THE MATHS QUESTIONS A LOT EASIER LIKE THEY DID FOR THE SELECTIVE TEST. BUT WE CANNOT BET ON THIS!
So, students should
- Practise the new English question type "Sentence Cloze" using the Sentence Cloze module in More ...
- I will complete the TS module in More ... with prep tests and a TS trial series will be provided.
- Complete ALL year 5 school maths with Maths Online and work hard on Maths Problem Solving Strategies Year 4-5 and do the Maths Challenge series and all the OC Maths Boosters.
- Do all the GA series as well. Do not give up on GA as the GA on my website covers just over 50% of the TS paper.
They will replace the GA questions by thinking skills questions. If we look at the selective sample TS paper, they have about 50% of mathematical+spatial reasoning questions and 50% verbal reasoning questions. The big question in the mind of parents would be whether GA tests are still relevant. My opinion is that the GA questions are still relevant as they boost skills in maths reasoning, spatial reasoning and vocab which is useful for understanding verbal reasoning questions. This is why I think students should still do GA tests. There is nothing to worry about about the 50% of mathematical+spatial reasoning as I expect students onthis website have all what they need to do well.
Then the next question is "What is the TS verbal reasoning?" It's a new style of questions based on verbal arguments. It is grouped into 2 groups. One is of argument and the other one is of logical deduction (only a few questions). The argument group uses the basic skills students learn in English reading with a focus on Main Idea, Supporting Details, Conclusion and Argument. An argument can be defined as a process where the writer/speaker presents the main idea and supporting details on the way to reach a conclusion. So, one can consider "argument" as a presentation method (writing method). Students already work these basic skills when they do the Reading Skills series from year 3-5. What Cambridge does with TS questions is that they set them at a very hard level where all the basic skills must be good enough before students can deal with Cambridge's questions.
There are a few things, parents need to know.
1/ Mathematical reasoning is not a problem. Students who are good in maths here are fine as I have all what they need. Students need to reach to the end of year 5 school maths and practise maths problem solving and do the maths challenge series.
2/ Students really need English reading skills to year 5 level before they are ready to deal with verbal reasoning. So, it's not realistic to get them to deal with TS questions when they are still working at year 3-4 level. Most students won't be ready until they are 2 months away from the OC test.
The strategy I have for TS is to ask students to work hard in English reading skills and general comprehension to year 5 level. I am working on a module called Thinking Skills. The section for Year 4-5 level (OC) is being developed. Students will focus on Main Idea, Supporting Details, Conclusion and Argument as the basic level. This will help them understand the verbal TS questions and then learn to deal with them. After the selective test in Mar, I will focus on OC level and create TS questions that are easier for the OC level. By around 3 months before the OC test, the SSU should have released a sample test for OC. And that will give a better idea of how difficult the questions are. This is the time students will start practising TS questions and get ready for the exam.