May 11, 2021

Apex-Math Videos

I hope to keep my videos:

  1. personal
  2. short
  3. organized
  4. study-ready

Personal:  I want to reach of you as a person, like it is a conversation between just you and me.  I am a veteran teacher and tutor.  I am going to try videos from both angles, on a large white board in front of a class and on a small white board, like we were tutoring one on one.

Short:  Each topic that I want to present, doesn’t need to be long and involved.  I want to get to the point quickly and do many videos.  Each one will allow the topics to be broken down into smaller pieces and some videos will need to be grouped as a cluster to grasp the entire “unit.”  For example, I will teach all the pieces that go along with graphing a quadratic and have one or more videos where I pull all of that together, those videos will assume mastery of the previous videos, but this will allow me to keep each video reasonably short.  No one wants to sit for an hour at a math video!  Let’s learn what to do and move on.

Organized:  Staying organized in mathematics is very important.  I encourage each of you to take notes and stay organized with me!

Study-ready:  Teachers don’t teach students how to study for math tests.  I want to provide individual videos on this topic as it is so important but also provide study notes for the student in each video.  Write down the steps, you will need them.  Very few teachers break down the information, they do an example but all those steps run together, we will always break it down and make notes about what to do.

Topics:  I have so many ideas of topics to do but eventually will start taking requests so that I can help each of you as the school year goes on.  You can always suggest a topic in the comments section of You-tube or emailing directly.  Be sure to like my videos when you leave comments and requests.  There is so much math to get to… Kindergarten through Algebra 2 is my goal but my first videos will start with middle and high school mathematics, especially some of the harder topics that don’t need to be so hard!


Changing Math – One Video at a time

Everyone is born with gifts.  Some people are talented at art, some are great “people” people, some are helpers who give to the needy and feed at the soup kitchen.  We all have gifts and we should use our gifts to help make the world a better place.  My gift, from the time I was a little girl, was to teach.  I can teach anything.  I can learn something one minute and teach it the next.  I have the ability to analyze something and break it down into smaller pieces that make it more understandable for people.

I like to learn, I am good at learning, and I know how to take in information, process it, then I can change it to make it easier for other people  to learn.  There are many things in this world that people learn, some are easy and some are more difficult.  One, however, that seems to come naturally for some and not for others is mathematics.  Often those who are born with the ability to understand mathematics are not also born with the ability to understand that it is not as easy for everyone else.  In fact, this very idea creates one of the biggest problems in today’s education.  Just because you understand something, very well and it makes perfect sense to you, doesn’t mean you are also able to explain that information to other people.  It is likely that you can explain the information to like minded people.  Those that grasp math easily, learn math from math teachers who are “okay” at their jobs.  They may even learn math from those that are “terrible” at their job.

However, we have many people in this world who just don’t understand math as easily as others.  It falls on a spectrum, some might be very lost when it comes to grasping math concepts while others can get there if they have strong teachers.  However, all that fall in the category of the “less mathematically minded” struggle without strong math teachers.

So why do we have math teachers that are great and amazing, some that good, some that are okay, others that are not so great, and some that are down right terrible?  Well, all the math teachers are most likely mathematically minded people.  Who would choose to teach math unless it naturally made sense to them?  However, some of those are just people who can do it easily but don’t have the gift of being able to break it down to easy to understand pieces.  Many don’t even understand that some of their student’s brains don’t work like their’s does.  Some are just in a job to get paid because it is easy for them but they have no passion or natural gift for education.  Hence, we get the large variety of math teachers in our schools.  The real problems happen when you get the not so good or worse, the terrible math teacher lined up with the student who really struggles to understand mathematics.  Math builds on itself, one bad step along the way and you can be turned off from math or left in the dust.  And remember, how many different  math teachers does a student get over their lifetime?  For those mathematically minded, what is the probability that a student will get a great/amazing or good teacher each year, year after year?

One misstep, that is all it takes to send a child off the math track.  Does our country do anything once a child shows that first sign of falling behind?  Not really and certainly not to the extent it is needed if we all had the goal to help all students succeed in mathematics.

So, I have been given that gift of being both mathematically minded and having the ability to see things from the perspective of the learning student.  I am also passionate about education, specifically math education.  I spend a lot of time watching how it all falls apart and wondering if one person can somehow scale to reach millions.  I look at what Khan Academy tried to do and it gives me hope but Khan Academy still falls in the “teaching okay,” category and if the world of mathematics education is going to get changed, it must be changed with exceptional explanations, by people who are truly extraordinary in their gift of mathematics education.  This is not to say anyone (myself included) is perfect but part of doing what is right is listening to feedback and making adjustments when your goal is not being achieved.

It is time, therefore, to start one video at a time with content that teaches mathematics in easy to follow steps that a student can not only learn math from but learn how to study math.  In my next post, I will address the goals of my videos and I always welcome comments and suggestions!

FREE WORKSHEET: Multi-Step Word Problems

After searching for some multi-step word problems on the internet, I could not find any that were hard enough to match the North Carolina homework questions that my third graders were getting and struggling with. If this is going to be a goal for 3rd graders (and it is a high goal as this is a challenge for third grade math students that struggle) then the teachers need to provide a lot more practice in class and outside of class on these types of problems. Instead, I continue to get frustrated as they just advise parents that their child can’t do these, that it is a problem, and yet push on forward. So, in an attempt to provide more practice – I hope these problems can be copied and used by others!

1. Red buckets can hold 3 apples and blue buckets can hold 5 apples. If Joy has 4 red buckets of apples and 5 blue buckets of apples, how many apples does she have altogether?

2. A string is 7 yards long. Jeff needs 2 feet of string and Lori needs 15 feet of string. If they both cut their string, how much string will be left over?

3. A toy box can hold 9 toys. A toy carton can hold 6 toys. Jen brings 2 toy boxes and 5 toy cartons of toys to donate to an orphanage. How many toys did she bring?

4. A ribbon is 5 yards long. Carol uses 5 feet of ribbon for her craft. April uses 6 feet of ribbon for her craft. How much ribbon is left over?

5. A van can hold 4 adults and 2 children. A car can hold 2 adults and 2 children. If 5 vans and 2 cars go on a camping trip, how many people are able to go on the trip?

6. Wendy has 5 packages of macaroni and cheese to donate to a day care center. Each package contains 10 boxes of macaroni and cheese. If she hands out 45 boxes to the center, how are left over?

7. Kimi has an album with pokemon cards in it. Each page holds 36 cards. She has 6 pages total. If she chooses to give 10 cards to her brother, how many cards does Kimi have now?

8. Tommy has candy bags prepared for his party. There are 8 bags of candy. Each bag contains 4 pieces of candy. If little brother Harry sneaks two bags for himself. How many pieces of candy does Tommy need to buy to replace what Harry stole?

9. Keelie has 42 pieces of paper for her friends for an art project at her party. If 7 friends come over, how many pieces of paper will each person get?

10. There are 3 red baskets, 5 blue baskets, and 2 orange baskets. Each red basket has 2 gifts in it. Each blue basket has 3 gifts in it. Orange baskets can hold 10 gifts. How many gifts are there in all?

Grades in school – are they meaningful?

I run a tutoring center and tutor students in Wake county, North Carolina.  I get students from many different schools, although they are all in the same county.  However, their courses, although identical in name and in “theory” content, vary greatly.  If the level of a course can range from easy to extremely difficult and yet we award a grade based on test scores to both classes, how is this fair to the student and how is this truly a measure of anything?  Here is an example.  I am currently working with a student taking Honors Geometry through Wake County Virtual Public Schools.  This is an online class given when the school is not able to provide instruction within the school.  In this case, the student is in a middle school that does not offer this course so he has to take this online version of the course.  There is only a virtual teacher who responds to questions that the students (currently 3) ask and it takes about 10-20 minutes before they get a response to each of their questions.  There are no in person lessons, just self teaching from online materials.  The students turn in assignments and their assessments are never looked at by a person, they are always multiple choice so that a computer can grade all their work.  In a typical “in house” Honors Geometry class, students are expected to do 2 column proofs on exams, however, since this is not possible in an online class (it can’t be graded by a computer) these types of problems aren’t given.  Proof type questions might be asked but in a multiple choice format, which is hardly the same as generating a proof from scratch.  The students still have to do some exercises with proofs but aren’t tested on these proofs and their exercises, I am told, count about 10%.  It seems the multiple choice questions are quite easy and a student who in a “in house” Honors Geometry class who might not be passing with the same level of knowledge, can score a B in this multiple choice testing format.

On the other hand, I also see a huge variation from one school to another.  For example, School A’s Honors Geometry program is so challenging that even I can get stumped on some of their questions from time to time and I have a Ph.D. in Mathematics Education, Masters in Mathematics, etc.  The level of proofs required in School A are truly much harder than I feel is appropriate, especially considering it isn’t in line with other schools and way off from the virtual school.  I tutored a student from School A who is extremely bright, knew so much about Geometry that most high school math teachers (outside of School A) who might sit down and work with this student would be very impressed with this student’s knowledge of Geometry but since he attended School A, his grade for the year was a C!  If he had been in School B, he would have gotten an A, if he had taken it online, he could have slept through the course!  School B is right now the road from School A but the same math classes – and I am not just talking about Honors Geometry but all other high school math classes  – are so much easier at School B than School A.  School B requires a much more reasonable amount of homework as well.  School A requires way too much from kids and somehow thinks that if they assign 60 problems of the same type that will make the kids smarter.  My son is 11 now and smart enough to take Honors Geometry but if he has to take it at School A, I won’t let him.  In fact, I am not sure I will sign him up for any honors math classes at School A because their math program is so out of line with what is reasonable – and if you happen to get a less than stellar teacher in the mix, then just forget it!

These grades students make determine many things for students in high school – they make up their GPA – this makes them competitive to get into colleges.  How does that C in Honors Geometry look to a school like Stanford?  They perceive the student as a poor student, when in fact, this student had he been down the road in School B, would have straight A’s in Honors and AP math classes!  What a difference in perception and yet it is the same student, the same knowledge.  All School A did was make the student get frustrated and feel like he can’t be successful in math and now this student will choose not to continue on with Honors and AP math classes that he is capable of.   I have to tell the student that it ISN’T him – I hate to put blame on outside forces with teens because it is important for teens to learn to take responsibility for their actions, however – when I work with a very bright student and watch him achieve a C (and it wasn’t for not doing assignments, etc.) – there is nothing else I can do but try and help salvage the student’s math self-esteem that School A has taken away from him.

Another example; a parent calls me – her son is failing – well almost, he barely has a D, in Algebra 2.  He is generally a B student in math.  She begins to relay the story.  The teacher, who gives math credit for whether a student uses the bathroom during class, is telling her that her son has only completed 47% of his homework.  Well, one would argue, if a student isn’t completing their homework, that is a reason for a poor grade.  However, despite the fact that she said those exact words, the truth is that he did 100% of his homework but she graded his homework and he only got 47% of his homework correct so he has a 47 homework GRADE, not that he only did 47% of his homework.  However, isn’t homework supposed to be for learning, not an assessment?  Why are we teaching a new topic, assigning homework, then grading it the NEXT day, and weighing it so heavily that it takes a student that has a B average on tests and lowers his grade to a D (almost an F) in the class?  Shouldn’t you be able to come to class the next day and say, “Ms. Teacher, I didn’t understand homework problems # and #, please go over these.”  This is how it always worked for me.  This is how I always taught.  This teacher scores the homework and weighs it so much it fails him even though his understanding on true assessments is a B.  Now when colleges see his transcript, yet again -they think this child is a D student when his knowledge of Algebra 2 clearly indicates a B level of understanding?

What are these GRADES supposed to measure?  Whether we use the bathroom?  If we could do homework the first night it was assigned?  If we can do super hard proofs when other students can get A’s in the same class for basic multiple choice questions?  How is this an accurate measure of anything?  And yet, it has an impact on what college a child gets into, if they get scholarships for college?  I remember one college professor I had, he got it right.  He gave us tests, we took them and got grades (this was in math).  Our final exam was cummulative – it tested everything for the whole class.  If we knew everything on the final, then we had proven we had mastered everything we were supposed to learn in class.  So, he said to us – IF you take the final and your final exam grade is higher than your grade would be if I factor it in at 20% (or whatever the assigned weight was), I will just give you the grade you scored on the final.  So, if our grade going into the final was a D but we got an A on the final, we got an A in the class.  Why?  It made sense … What is the purpose of a grade?  To measure your knowledge of the class content?  He didn’t care WHEN you managed to “get it” – if it took you longer but you got there by the end and could demonstrate it on the final – you proved you mastered the material in the class so your grade should REFLECT your ACTUAL knowledge at the end of the course.  It was BRILLIANT!  Dr. Kenton, you are a brilliant man and teacher!

Speaking of grades – tell me if this makes sense – Wake County schools offer higher quality points towards the weighted GPA based on Honors and AP classes.  If you take a regular class and get an A, you get 4 QP, if you take an Honors Class, you get 5 QP, but if you take an AP class, you get 6 QP.  So, why do you get 6 QP for an AP class?  Well, it makes sense because AP classes are supposed to be college level classes offered in the high school.  So, college level work should be awarded more QP than an Honors level high school class, right?  That makes sense.  However, if the student actually goes TO a college and takes a college course AT a college, the county’s policy is to award only 5 QP for an A.  So they equate an ACTUAL college class the same as an Honors level high school class – giving more weight to an AP class than an actual college class taken in college.  So I could take AP Calculus BC, get an A and get 6 QP but if I take Calculus III as a dual enrolled student the following semester while still in high school and get an A, the school will only give me 5 QP for it.  So it would LOWER my GPA and make me LESS competitive for colleges looking at my GPA and class rank.  Again, pointing out these grades are meaningless.

My final comparison is the grading scale used.  Most schools use a 10 point scale.  90-100 A, 80-89 B, and so on.  So if you are in states with this scale, and you get an 84, you would have a nice solid B.  However, Wake County decided that they wanted to make things more challenging for their students and now use a 7 point scale, so that same 84% would equate to C in Wake County schools.  Do colleges take this grading scale into consideration when looking at applicants?  These inconsistencies make the meaning behind grades useless.  When I taught college and graded, I preferred to think of grades this way – to me, an A meant Excellent Understanding, a B was Good Understanding, a C was Fair Understanding, a D was Poor Understanding, and an F was Little to No understanding.  After I computed a numerical grade for a student, I was looked at the student and said if I didn’t have any true grades and just looked at their “understanding” and had to attach a word to their understanding – how would I define it – excellent, good, fair, poor, or little to no – I wanted to make sure their numerical score matched their TRUE understanding – luckily, it did because I was very careful with each individual assessment but this was especially helpful when students were borderline and I had to choose between two letter grades.

I chose to homeschool my son for one year of high school.  It was so liberating to not worry about grades and just have him learn for the sake of learning!  Of course, we had to “make up grades” for his transcript to send off to college.  I tried to think about what he would have gotten if had taken the class in a public school.  He always got B’s in English in traditional classes, so I gave him a B in English.  Things he was passionate about and worked hard on because he just really wanted to learn and master (which he did) – those were clearly A’s.  None of that really mattered to me though, he learned what he needed to and worked really hard at what was important to him.

In closing, I think back to my undergraduate years when I was minoring in Philosophy and one thing that interested me was the concept of a grade-less school.  In the book, Zen and the Art of Motorcycle Maintenance, the author wrote about a professor he had who chose not to grade his college class and instead let the students choose their grades.  It was a great read and I would encourage everyone to check it out.    I would welcome any comments on this topics.

Progressive Math Now Available

Progressive Math Level One is now available in a hard copy. Our digital copy has been finalized and is also for sale.

This is the first book is a series of mathematical books designed to provide a fresh approach to mathematics that approaches math in small progressive steps. The goal of the course is to build a student’s new knowledge of concepts from their existing knowledge. The book provides teachers and parents with lessons on how to work with the child on these concepts and includes sample dialog. It provides many pages of practice that gradually increases in difficulty and provides constant review. The topics are carefully chosen so that they all link to topics that the student has already had exposure to.

Topics that are focused on in this book include:

  • Patterns (and applying patterns to applications such as counting money and adding without using fingers)
  • Addition Facts – we stress teaching students overall number sense and ways to learn their facts without having to count on their fingers.
  • Subtraction Facts – we use methods that allow students easier and less frustrating ways to find solutions to subtractions facts, especially harder facts such as 16-7.
  • Telling time to 5 minutes – we use the student’s previous knowledge of counting by 5’s and link this together to build the concept of telling time.
  • Counting Money – student’s use their pattern abilities and apply this with concrete visuals to learn how to easily count money.
  • Word Problems – we help students learn to look for key words to help them decide if the problem is asking them to add or subtract.
  • Getting prepared for Multiplication and Division – there are times when teaching early material lends itself to introducing concepts that prepare students for later concepts, we don’t ignore these situations, we embrace them and we introduce students to the idea that doubling a number is the same thing as multiplying times 2.
  • Place Value – In order to move forward, students need to understand place value – we have units in the book that address this issue and give students practice in locating the place value of numbers to the hundreds.

We feel our series is very different and advantageous over many of the traditional books available. We give students tools that other books do not. Other books just give practice. We teach students “tricks” and new ways to think. If they just can’t memorize that 9 + 8 = 17, what other options do they have but counting on their fingers every time? We provide them other options!