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The Quadratic Equation

Where did all these formulas come from anyway? Here’s some interesting information on the Quadratic Equation.

All forms of math and science (including cooking, shopping, etc) are loaded with formulas. Formulas are nothing but a relationship between two different things.

The quadratic formula is one of the most well-known formulas in math – and one you will use again and again.

It is often interesting to see how formulas are derived. After all, it is very likely that you have, or will, have your own formulas you create for your hobbies or work.

Here is a great step-by-step explanation of how the quadratic formula is derived.

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Using Jacobs 2nd Edition with AskDrCallahan Course

Question: Can I use Geometry 2nd Edition by Harold Jacobs  with the AskDrCallahan course?

Answer:

Short Answer – No, not easily.

Longer Answer – Many have asked us if they could use the Second Edition of Geometry with our DVD set. The answer is no, at least not without a lot of grief to the teacher and student.

We initially were telling teachers and students they could use the 2nd edition. Several people told us they had been told the second edition was superior due to a better treatment of proofs. In support of those families, we attempted to develop the syllabus to develop a map between the two editions. We consulted with Harold Jacobs on the map. The resulting dialogue was interesting.

First, the two books cover basically the same material, but in different ways. But, the chapters and problem sets are different enough to cause a significant management issue for the teacher and student – even with a map.

Second, and more importantly, we came to believe that those who felt the 2nd edition was superior were wrong. This was further backed up by Jacobs when he wrote the following in an email back to us.

“There was more emphasis on two-column proofs in the second edition but, as is often the case with such proofs, the things to be proved were rarely surprising and almost always rather obvious. I endeavored in the third edition to build the exercises around more profound material and to give the student more freedom in developing proofs. For really challenging problems, this meant leading the student along in a Polya-like style. Forced into two-column format, some of the proofs in this edition would run 15-20 steps, much longer than the typical 4- or 5-step proofs in the earlier edition. In his foreword on page xii of the book, Andrew Gleason of Harvard University wrote that “This book restores the idea of proof to its rightful place in geometry. Whoever studies this text will know what a proof is, what has been proved, and what has not.” He, together with Dr. Peter Renz, who wrote the supplemental notes in the Teacher’s Guide, looked carefully at the content and structure of all of the exercises and gave his full approval. I feel very honored that he would take so much of his time to do this. Gleason, by the way, is a former president of the American Mathematical Society and one of our country’s most prestigious mathematicians. I hope this helps clarify what has changed between the second and third editions as well as why.”

We hope this clears up any misunderstanding. With the two books sitting side by side, we would clearly choose the 3rd edition for our children.

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Does the geometry book contain proofs? (Is it Euclidean Geometry?)

Yes, the geometry textbook by Harold Jacobs, and our videos that go along with it, is Euclidian Geometry – it does contain proofs. Some parents are under the misconception that is does NOT contain proofs since Harold use less of the formal 2 column proof methodology in his 3rd edition.

Here is an email we received from Harold when we asked him to clarify:

“I endeavored in the third edition to build the exercises around more profound material and to give the student more freedom in developing proofs. For really challenging problems, this meant leading the student along in a Polya-like style. Forced into two-column format, some of the proofs in this edition would run 15-20 steps, much longer than the typical 4- or 5-step proofs in the earlier edition. In his foreword on page xii of the book, Andrew Gleason of Harvard University wrote that ‘This book restores the idea of proof to its rightful place in geometry. Whoever studies this text will know what a proof is, what has been proved, and what has not.’ He, together with Dr. Peter Renz, who wrote the supplemental notes in the Teacher’s Guide, looked carefully at the content and structure of all of the exercises and gave his full approval. I feel very honored that he would take so much of his time to do this. Gleason, by the way, is a former president of the American Mathematical Society and one of our country’s most prestigious mathematicians. I hope this helps clarify what has changed between the second and third editions as well as why.”

 

What does this mean? This geometry course is not like the geometry I had in high school – BORING. Most geometry textbooks (courses) spend so much time in the middle of proofs that the student forgets that they are doing geometry and learn to hate the material. Jacobs has treated proof in a way that is engaging and based on real world geometric systems.

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Teaching Your Kids To Decide What to Do Next

This may sound silly, but your children’s biggest challenge in life is likely to be making a daily decision of what to do next. Really. In the current job market, most people are not ever told what to do next, but instead they are left to their own devices to make constant daily decisions about how they use their time. No matter the job, we tend to have to make a lot of time based decisions. What do we do next? What is a priority?

Deciding what to do next
Decisions: What next? (Courtesy Flickr/Creative Commons)

One of the greatest complaints I get from employers who hire recent college grads is “They cannot make decisions. They do a job and then come back to ask what else they need to do.”

What we need to teach our kids, now and not later, is how to set priorities and how to decide what to do next.

Teach Your Kids to Decide “What next?”

1. Show your kids the plan. Get them involved in the planning of your projects and your homeschool year. Allow them to set some deadlines and pick some plans about how they will do school.

2. Avoid the set curriculum. I know as parents we like things all laid out and having a single curriculum for the whole year. But, that is not reality. We have choices to make about everything. Even something as simple as grocery shopping has us picking which stores we buy which products from. We shop price and quality and make decisions as to what is important and why. So, do not skimp on these hard decisions with your kids. Soon they will be in college and will have choices of programs, courses, and even which professor.

3. Pull out the calendar. Now with the courses and the plan, let them decide what to do when. For instance, to read a book with 100 pages could mean 10 pages or 20 minutes per day. Same logic goes for all their courses. Now, let them schedule it on their calendar.

4. Let them find their grove. We all have patterns of when we would rather do certain kinds of work. For me, writing or thinking work comes in the morning. Meetings in the afternoon. In a similar fashion, teach kids to find their own pattern and work habits.

The benefits of this simple method are twofold:

First, you are truly preparing them for what we call “knowledge work” which is the norm in our modern times. Even what we used to think of as blue-collar jobs are loaded with decisions. Teach your kids to make those decisions today.

Second, when you teach your kids this simple task, you have given them ownership and responsibility, which makes your job easier.

After all, a homeschooling parent is not a teacher, but a leader. So quit teaching and start leading.

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ACT and SAT Score are Key to Scholarships

We constantly run into parents asking us questions like

  • Should we count AskDrCallahan math courses as honors?
  • Should we enroll in honors courses in high school?
  • How can we get an athletic scholarship?
  • Do colleges prefer higher grades or harder courses?
SAT and ACT scores are what matters in scholarships
College Move In Day (Courtesy of Flicker/Creative Commons | Matt Runkle)

  What Do Colleges Care About?  These questions from parents make sense, but let us turn it around from the college side. What does the college want? Practically there are only two things colleges care about:

  1. Students who can pay. Forget all the pomp and circumstance, colleges and universities are businesses and they get paid by having students show up. So, as long as you have money and meet their basic requirements, you are in. As one college dean puts it, “We need butts in seats to pay the bills.”
  2. Students who make the school look better. In order to attack more attention to get students who have sources to pay on their own, schools will make great efforts to attract some students who improve their statistics. And, the biggest statistics used is average ACT/SAT scores. So to attract these students, schools provide scholarships.
Now there are other factors we care about in the ivory towers. One of the most notable other factors is attrition. We want to make sure a student that starts also completes. But again, academic ability and financial ability are big factors here.

So, to say more succinctly, colleges do not care much at all about those things parents worry about. They care about money and scores. The only scores most colleges will ever consider are ACT and SAT scores. Will they look at GPA? Sure. But slight differences in high school GPA are of little value. However, a slight difference in SAT and ACT scores are a huge value – to both you and the college.

So What to Do?

So, if you are preparing for college, you need to do these things: 1. Find the college you prefer. Which admissions test do they prefer? (Most schools will accepts either the SAT or the ACT, but you need to check.) 2. Prepare to do well on the test. Test early and often and get help from an SAT/ACT Coach. 3. Go to the actual school and department where you plan to study and talk to the faculty. What else do they want to see? Doing this little bit of work is worth hours, months, and years of all that stuff most parents waste their time doing. It is the basics. Do them well and you succeed.

The Facts about Scholarships

I am sure you have heard of the millions of sources of scholarships out there. It is true. But, let us first look at the money. The bulk of scholarships comes not from the schools themselves, and most are merit based scholarships. Many have a simple metric. For example, see Baylor’s chart showing test scores as they translate to dollars. This kind of chart is common, even when they are not published.

SAT* Score ACT Score Amount divided over 8 undergraduate semesters Amount per academic year
1500 + 36 $153,920 $38,480
1400-1490 33-35 $149,920 $37,480
1300-1390 30-32 $145,920 $36,480
Below 1300 29 and below $137,920

Almost every school has test scores as a major component (dominant component) in their scholarship dollars.

Coaching Matters

I am often shocked that parents will think nothing of paying for a batting coach for their kids or paying for piano training in hopes of a scholarship, but think paying for ACT/SAT test prep coaching is too costly. But many parents get it, and for years have been asking us to coach their students as they prep for these tests. We have always had to say no because we did not have the capacity. There are many national companies doing coaching and test prep, but we really never felt they were offering a good enough service to recommend them. But, a few months ago we finally found a partner who we really trust. It is Higher Test Scores Prep run by Lauren Gaggioli. Lauren is passionate about helping kids prepare. To here her story, listen to this podcast: Online Coaching Business Startup | Lauren Gaggioli of Higher Scores Test Prep.   If you are interested in a college SAT/ACT coach, Lauren provides a 10% discount to AskDrCallahan customers. Just go to her website and enter discount code “ASK10”.

Website: Higher Scores Test Prep

Discount Code: ASK10

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Why College is NOT the Goal of Homeschooling

As homeschooling parents we want our children to succeed, and there is a part of us that is unsure we are doing it right. Even if we have had older kids go to college and get jobs, something creates doubt. Recognizing that our children are all different, we wonder if what worked for one will work for others.

Courtesy Flickr/Creative Commons | Queen's College
Courtesy Flickr/Creative Commons | Queen’s College

So as we talk to homeschool parents who are struggling with high school subjects, especially math, we hear worry about college. Will they get accepted? Can they get any financial help? What college is the best?

Leaves me wondering, since when did college become the goal?

Education is not Owned by Universities

I am a firm believer in higher education. My primary university faculty role is working with professionals who are looking to make the next step and need education to make it happen. But, what is confusing is how the university system has become the de facto standard of higher education. It is not. Consider these other ways to get an education:

  • Internships
  • Reading books
  • Searching the web
  • Taking courses on specific subjects (such as how to earn a living blogging)
  • Watching educational videos
  • Talking to experts in the field

Education is everywhere and with easy access.

What is the goal? Take the Long View

Instead of working to help our kids get into college, we should instead be helping them to find their calling and prosper. Consider the normal path to college these days. Johnny is a high school student who is good in math and science and enjoys doing math and science. So he enters college as a chemistry major. But, has Johnny ever talked to a chemist? Has he ever seen what they do? or, did all of his interest in chemistry come from watching CSI? Does he have any idea what he is getting into?

Or the other approach where Sally enters college with no real idea of what to do. She just knows she needs an education. But why? To what end? To make the college wealthier and her and her parents poorer?

If your child is interested in a field, bypass the college and make sure they are talking to people who are making a living doing what they want to do. Get the real story.

For example, our oldest daughter wanted to be in the FBI. Her attraction was largely based on movies and television shows. So for clarity, we got her to meet a local FBI agent. The agent was a woman. She drove up in the same exact kind of car my daughter was driving. The agent was a mom, a wife, and an agent. When our daughter came back she explained how neat it was to meet a real FBI agent and talk to her. She was thrilled. But, our daughter no longer wanted to be in the FBI. While she still admired them and thought it was a neat job, the fantasy allure was removed. This agent was a normal person with a normal life, not some larger than life character as seen on TV.

The Decision is Not Permanent

I see a ton of high school and college kids stuck on indecision. The reason they cannot decide is that they are worried about how the decision will impact the next 30 years of their life. They listen to well meaning parents and other adults and they see how many of us have made decisions and stuck with them – with many hating their jobs. A recent Gallup Poll shows over 70% of American workers disengaged with their work. In other words, they are bored and do not like their job. So, no wonder kids are undecided and worried. They are not worried about the work they will do, they are worried that they too will find work they do not enjoy.

While some decisions are permanent, education is not. I work with people of all ages who have had a wonderful career so far, but now are looking to make a change. Some changes are radical, others are minor shifts of focus or industry. I myself have made a few of these career changes along the way.

We need to help communicate to our kids that today we can do almost anything at almost any time. People have left corporate jobs to become missionaries. A missionary friend of mine is now working as a high paid industry consultant. I have seen engineers become medical doctors and lawyers. And, I have seen many people become professional bloggers and podcasters! (If you really want to get way out there!)

Explore

So while looking at colleges and educational paths, take care to look beyond the university and ask “But what do I want to do to serve others and who is doing it now?”

For help in this explore, check out the free ebook How to find Your Calling on my site dalecallahan.com.

 

 

 

 

 

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Preparing for the Professor | Homeschool to College Transition

Do you have a homeschool to college transition plan? As we homeschool our children, we are often highly focused on getting them accepted into college. But what about preparing them to actually succeed in college? They are different issues. What those of us teaching at the college level demand and care about are wildly different from what the high school of homeschool teachers care about.  We need to prepare our kids for the professor.

homeschool to college transition
Courtesy Flickr Creative Commons

Key Aspects in Preparing to Transition from Homeschool College

1. Seek truth. While not everything that goes on in college is evil or a lie, much of what your kids will hear will be with great authority and from new sources – professors and other students who suddenly have tons of freedom and think they also have great wisdom. Teach your kids to find the truth and sort it out from the lies. Rarely are the lies alone – usually they are mixed with enough truth so that confusion results.

And I am not only talking about a religious view here. I also mean more everyday truth and lies. Things like “to get a job in this field you must….”. These kinds of statements spoken with authority from faculty are most often innocent views from the limited persecutive of a faculty member.

2. Prepare your children to be self motivated. Empower them today to take control. At the university, the faculty member will not hold their hand. It will be up to your child (now a college student) to take the initiative of their studies, the college, and their career. If they show up waiting on someone to help them, they are already behind.

3. Time management. You kids need to know how to manage a calendar and multiple priorities coming at them. Unlike the homeschool parent, who is aware of other demands and will make adjustments, the college professor neither is aware of the other demands nor will they care. Your child needs to be able to learn the skills of managing time and commitments.

4. Teach them how to study. Study skills are not meant to be hard. In fact, my first few years in engineering school were wasted on a lot of procrastination called study. When I learned how to study, I got better grades, studied MUCH less, and had more fun. Some real skills in how to consume information fast are in order here.

5. Teach them how to skim. With a massive amount of reading that will be required, the art of skimming is a true life saver. Teach them now.

6. Teach them to understand what others expect. This is the most important skill they will ever get from college. Understanding what each professor wants and cares about and how to deliver. This skill has little to do with college, but everything to do with reality. The rest of their lives they will be working for and with other people – customers, bosses, coworkers,etc  – and working to quickly determine what others expect and how to deliver will yield them success in many levels in life. And, this skill alone allows you to focus on others as yourself.

Coming Soon – Preparing for the Professor

We will soon be releasing our new teaching plan that helps college bound kids get prepared to meet the world in which the professor rules. Whether a homeschooler or a student in public or private school, this course will give you those things you will wish you had – but did not know to ask. It is a course in succeeding in college.

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Contact Us

Thanks for visiting AskDrCallahan! 

We have people contact us for various reasons – so we decided to place all information here. 

 

Help doing the math!

Here is where you would ask about

  • how to work a problem,
  • a possible error in the textbook or teachers guides
  • how to implement the math in your situation (questions moms ask!)

Who can ask Questions

Any student or parent using the AskDrCallahan DVDs

Whether you purchased them directly from us, one of our vendors, or you borrowed them from Sally down the street. Whatever the case, if you have them and are using them now, we want to help make that course experience the best it can be. oh, and did we mention it’s free? Yep. FREE for your student today, and any siblings down the road. That’s just our way of saying thanks for helping prepare your students for college and for life.

Common Questions

Many of the common questions have been placed on our new support site at AskDrCallahan support page. Simply go to the page and search for your problem. This is the fastest way to get help!


Ask a Question

You can ask a question in a few ways. Remember to give us the COURSE NAME and the problem NUMBER!

Email us to ask a question to support@askdrcallahan.com. If we can’t answer you over email, we have phones and video tutorials on standby.

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Speaking

Dr. Callahan does a significant amount of speaking. If you are interested in having him speak to your group, please contact him at  support@askdrcallahan.com putting SPEAKING REQUEST in the subject line. 

 

Questions about Applications

If you have questions about product selection or application, please contact us at products@askdrcallahan.com or by phone at 205.578.2320.

Please note that we answer every call or return those we cannot answer. We have a small staff and cannot always get to the phone – but if you leave a message we will promptly return the call. Please remember that if you leave a message, leave your phone number and email.