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Don’t Let Your Child Cheat

Dear homeschool parent,

This is something I feel compelled to share. In my 25+ years teaching in a classroom, and my 3+ years teaching online classes for homeschoolers, I have seen a disproportionately large number of homeschooled students cheating in online classes. I have spoken with several other teachers of online courses for homeschoolers, and some have reported cheating by as many as 25% of their students. Most incidents of cheating involve the student either plagiarizing a paper, or looking at the answer key while taking a test unsupervised at home.

Plagiarizing a paper is harder for parents to catch and prevent. But stopping your child from cheating on tests should be easy.

Believe me, I understand how it can happen. An otherwise good child is taking an online course. He is struggling, the other students seem to be understanding the material better than he does, and unlike most of his previous courses, he is (perhaps for the first time) not allowed to learn at his own pace. He is being required to complete a test over material he knows he has not mastered. He also knows where the answer key is kept, and can look at it because his mom is busy and she trusts him. The temptation becomes too strong, he caves and decides to copy the answers, and does not tell anyone.

Thankfully, he is probably bad at it. When children cheat in this way, they tend to use words and phrases directly from the answer key, even when the answers could have been worded in many different ways. They also aim at 100%, of course, not realizing that a perfect score from a struggling student will set off a warning light to the teacher.

Parents, when the teacher claims that your child has apparently cheated on a test or assignment, listen to him! No good teacher will make such an accusation lightly. It is very uncomfortable to charge a student with cheating, and most teachers will err on the side of giving the student the benefit of the doubt.

When I discover a student has cheated on a test, I first send an email to the parent. I express my concern as a possibility, along with the evidence of the cheating. The child is allowed to make a defense, which is usually pretty flimsy. Almost every time, the child admits to cheating. Some confess everything immediately, some at first confess to cheating to a certain degree (“I only looked at the answers for the first few questions”), and some initially deny it, only to admit it later when they realize that the evidence is overwhelming, or (Lord willing) when their conscience smites them. According to other teachers I have spoken with, the only students who steadfastly refuse to confess in the face of overwhelming evidence are those students whose parents “can’t believe Jimmy would do such a thing.” When they are caught and confess their sin, they should be forgiven, fellowship should be restored on all sides, and they should be given a zero on the test or paper.

Here are three easy rules to follow when your child needs to take a test for their online class:

Keep the answer key inaccessible to your children.

Be in the room with them as they are taking a test, and pay attention to what they are doing.

Have them give you the test to send in.

Getting caught cheating is a hard blessing on both parent and child. The child learns that the truth behind the biblical proverb, “Be sure your sin will find you out.” He also learns that there are consequences to cheating. And the parents learn that their child is a sinner who can fall to temptation, just like the rest of us.

Help Solving Proofs

If you are in Intermediate Logic and learning about proofs for the first time, or struggling through them again for the second or third time, here are some helpful suggestions for justifying steps in proofs, constructing proofs, or just getting better at proofs.

  1. Think about what a proof does. Recognize that the conclusion of a previous step becomes a proposition to use as a premise for a new step. Proofs are a series of connected arguments, conclusion of previous arguments becoming premises for new ones.
  2. If you are learning how to justify steps in proofs (that is, you are working on Exercise 14a:10-16, or 15a:1-6, or 16:11-18) and you are in the middle of a proof, ask yourself which steps you have not yet used. If you are trying to justify step 6, and the previous lines already used steps 1, 3 and 4, then you will probably use steps 2 and 5. Try reading them aloud, and listen for familiar patterns from the premises of the rules of inference.
  3. Rewrite the argument that you are trying to prove. This will help you more clearly see the premises you have and the conclusion you are aiming at. You also might recognize patterns for rules of inference and replacement that you need to use. Often, a proof is built around a single rule of inference or replacement, and the other steps are just needed to set the premises up. For example, if you read Exercise 17a problem 7 aloud, you might recognize the modus tollens. But it takes a couple of steps to set up the second premise of the modus tollens, and one step afterward to fix the double negation.
  4. In general, find the premises you have available to you (e.g. if you’re on step 5, the available premises are from steps 1-4), read them aloud, and listen for rule patterns. In fact, get used to the patterns of the rules by reading them aloud, using something other than p’s and q’s (e.g. for Disjunctive Syllogism say to yourself, “This or that, not this, therefore that.”
  5. See if later proofs use procedures from earlier proofs. Exercise 17a problem 9 is built around a hypothetical syllogism, but you need to modify the proposition is line 1 to turn the conjunction into a disjunction so that the middles match for the H. S. To do that, you follow the procedures you used in problems 3 and 4.
  6. If you’re stuck, consider whether the next step might use the rules of Addition or Absorption. These are the rules that are often difficult to see when you need to use them. This is why in Exercise 14a:10-16, five of the seven proofs use one of these two rules, and in Exercise 15a, half of them use one of these rules. You need the practice.
  7. Another hint for if you are stuck constructing a proof is to try writing down every possible conclusion you can make from the available premises, and see if any of them help.
  8. You may have struggling through the assignment, succeeded writing some proofs but needed to look at the answer key for others. That’s okay. But I would suggest that you then go back and do the assignment again without looking. Practice makes habit.
  9. If it is still hard for you, if you are still not quite getting it, don’t sweat it. Take your time. Go drink some coffee and come back. Don’t say to yourself, “Well, I don’t get this, but I’ll just go on to the next lesson.” No. The lessons build on each other. If you are worried about getting through the entire text, stop worrying about it. You don’t need to cover it all. Better to learn a small amount of material well then a large amount of material poorly.
  10. If you need specific help (you’re stuck on a proof and you don’t know what to do), ask me. I would love to help. Message me on Facebook, or post a question on my Logic Facebook page.

Think about proofs like solving a puzzle, rather than thinking of it like homework. Make it a fun challenge.

Enjoy!

Logic with James B Nance

Conditional Proof and Reductio ad Absurdum

With the nine rules of inference and the ten rules of replacement taught in Lessons 13-17 of Intermediate Logic, we can construct a formal proof for any valid propositional argument. But for the benefit of the logic student, I introduce two additional rules in Lessons 18 and 19: the conditional proof, and the reductio ad absurdum. The conditional proof will often simplify a proof, especially one that has a conditional in the conclusion, making the proof shorter or easier to solve. The reductio ad absurdum method usually does not shorten a proof or make it that much easier to solve, but understanding the concept of reductio is beneficial for purposes outside of formal logic, such as understanding proofs in mathematics and apologetics.

Both conditional proof and reductio ad absurdum start with making assumptions. I want to clarify what happens with those assumptions. Continue reading Conditional Proof and Reductio ad Absurdum

Quick negation rules

Here are some quick rules to help you symbolize propositions that use negation:

Not both p and q  =  ~(p ⋅ q)
Either not p or not q  =  ~p v ~q
Both not p and not q  =  ~p ⋅ ~q
Neither p nor q  =  ~(p v q)

Truth tables can be used to show that the first two proposition forms are equivalent, and the last two forms are equivalent. The meaning of the sentences also help to show this.

In which I take issue with Isaac Watts

watts[1]In his excellent Logic: The Right Use of Reason in the Inquiry After Truth, Isaac Watts identifies 14 forms of syllogism that he considers valid and useful:

Figure 1:  AAA, EAE, AII, EIO
Figure 2: EAE, AEE, EIO, AOO
Figure 3: AAI, EAO, IAI, AII, OAO, EIO

From the list that I consider valid, he omits these ten as either invalid or “useless” Continue reading In which I take issue with Isaac Watts

Adorable Fallacies

In The Amazing Dr. Ransom’s Bestiary of Adorable Fallacies, Doug Wilson and son N.D. have given us a comprehensive book that makes learning about informal fallacies a hoot! To the familiar fallacies of ad hominem, circular reasoning, equivocation and their ilk, they have added a section on millennial fallacies with which we sorely need to be familiar: cool-shame, milquetoastery, ad imperium, pomo relativism, sensitivity shamming, and more!

In our day of muddled thinking, this guide to fifty popular ways to reason poorly is must read for anyone who recognizes the need for a field guide to thinking clearly!

Another helpful book for our times from Canon Press.