Do you wonder what kinds of things might happen in a first tutoring session, and what kind of a report you might receive from the tutor? Here is an example of an actual report from an initial tutoring session with one of my students, whom I would be helping with math. B was an 8-year-old student, homeschooling through a DL (Distributed Learning) school. He had been struggling with math, and his parents had decided to see if some tutoring could help him. He was nervous at first, but by the end of this first session, both he and his dad were excited about their upcoming math tutoring lessons!
So nice to meet B and family. I had fun! Hope you did, too 🙂 It was good to have B’s dad sitting in for this session, so he can see the methods I’ll be using, and can use them with B whenever they fit with the math in the workbook he is using at home.
Goals of our Tutoring Sessions
As this was B’s first day, my goal was to find out what B already knows in math, and what “gaps” (like missing ladder rungs or missing jigsaw puzzle pieces) he might have that we can fill in, which will make more advanced work much easier.
Getting to Know My Student
B told me he really likes cursive writing and art. He also showed me some work he is doing in his math workbook at home, and he said he likes when there are pictures, but not work without pictures. This suggests that he is a “graphic” learner, and we can take advantage of that to help him with his math. Also, he’s a pretty active, “physical” boy, so we’ll take that into account too, and use methods that include “active” learning.
Exploring My Student’s Skills and Needs
I used a workbook of math skill builders for grades 1-2 math with B, starting out with very simple work and lots of pictures, etc., to make him feel comfortable and confident. Here are some things I found out:
- he is able to count well
- he is able to tell what numbers “come after” but struggles with what numbers “come before”
- he needs help with ordinal numbers (first, second, third, etc.)
- he can “skip count” easily by 5s and 10s, and by 2s up to 10 (but then has trouble with teens and beyond). He really struggles with counting by 3s.
- he knows quite a lot of his basic addition facts, and for facts he doesn’t know automatically, he knows to start with the larger digit and “count up.” His preferred method is “counting up” in his head (rather than finger counting or other similar methods).
- he struggles with basic subtraction facts.
- he is fine with “greater than” and “less than” (aka “more” or “less”)
- he understands “tens” and “ones” for double-digit numbers.
- he is able to measure with inches and centimeters, though he may be a bit confused about which is which.
- he is able to add three numbers (single digits).
- he was nervous about trying to add double digit and triple digit numbers, but once I explained about 1s, 10s, 100s, 1000s columns (place value), he had no trouble to add larger numbers (without carrying). I also introduced very simple single digit + double digit adding with one “carry,” and I think he’s really starting to “get it.”
We did some “word problems.” B was able to read the word problems, more or less (he seems to have a bit of trouble with reading more complex words, but that could have been because of nervousness in today’s first lesson). He also wanted to solve the problems “in his head” and was hesitant to say the equations before giving the answer. It is really important that he expresses the equation, as word problems start to become more complex in grade 3 math, and he needs to be able to work them out “step by step.” I went over a couple of tips with him:
- circle or underline the key numbers in the problem.
- also, circle or underline the “keywords” in the problem, so he knows what kind of problem it is. For example, “in all” is a signal to add; “how many are left?” is a signal to subtract.
Tricks and Games Can Make Learning Math Fun
For the items he was having trouble with, I introduced a variety of “tricks.” I think Dad had even more fun learning the tricks than B did 🙂 He said he wished math was this much fun when he was in school. Now that he knows the tricks, he can use them with B whenever appropriate work comes up in the workbook.
I also mentioned that I have a wide variety of math games, and we will use them during lesson times, when Brett needs a fun break. He is also welcome to borrow games he likes to play at home.
Here are some of the “tricks” I taught today:
- Subtraction is just “backwards adding.” So if B learns his addition facts, the subtraction facts will be easy.
- In fact, B only needs to learn half of the addition facts, because addition is commutative, which means, for example: 3+5 is the same as 5+3.
- Once B has learned one fact such as 5+3=8, he has actually learned 4 facts that are in the number family of (3,5,8): 3+5=8, 5+3=8, 8-3=5, 8-5=3
- I noticed that for addition facts (and subtraction facts) that B has not memorized, he was trying to “count add” them in his head–and it took him a long time. It is good he already knows to start with the larger number. While we ideally want him to be able to do the facts automatically (memorized), it may help him to learn them by using more “hands on” methods for practice. Some people are afraid their children will spend the rest of their life “finger counting,” but actually, using physical methods can be a very helpful way to learn facts, especially if the child is taught to use a variety of methods, so he doesn’t end up just using one and making it a habit. Some methods I will be introducing to him are:
- draw sketches.
- use a number line.
- finger counting or counting with objects such as pieces of macaroni.
- “touch math” … which I introduced today. This combines both “physical” (touching) and “graphical” (dots) which appear to be ways that Brett learns more easily. I have given Dad a sheet with the “touch dots” for the digits 1 to 9, and I showed Brett (and had him practice) adding using the dots. To start with, he can put the dots on the smaller number (for example, with 8+5, he can put dots on the 5), and then use his finger, or a pointer such as a pencil, and count: 8…9, 10, 11, 12, 13. After awhile, he’ll be able to stop drawing the dots and just use the finger/pointer … and before long, he’ll know the facts.
Doubles are Handy!
I recommend that you practice the “doubles” facts with B, as once he’s really comfortable with them, he can quickly and easily use them to do all kinds of “tricks” for other facts. The doubles he needs to practice are: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20
Most children don’t have much trouble learning doubles. If B is having difficulty, here are some suggestions:
- have him repeat them as a “chant.” The rhythm makes it easy to remember.
- have him clap or tap his feet or tap a tabletop (or drum) as he chants them.
- make it physical. As he says the facts, have him jump up (or down) stairs; or make a “hopscotch” on the sidewalk with chalk and have him jump from square to square as he says the facts; or bounce a ball (or toss it back and forth) as he says the facts; or call out the facts as he jumps on a trampoline; etc.
Once he’s learned the doubles facts, here are some fun tricks (which I showed B today):
- for numbers that are one apart: example: 6+7 : double the smaller number and add one: 6+7= 6+6+1= 12+1=13 or 7+8=7+7+1= 14+1 = 15
- for numbers that are two apart: example: 6+8 : think of the “inbetween number” and double it: for example: 6+8 = 7+7 = 14 or 7+9 = 8+8 = 16
Learning the 9s Facts Are Easy With These Tricks:
Another set of tricks are the “9s” tricks. There are several fun 9s tricks, for addition, subtraction, multiplication and division. Here are some tricks I showed him today:
- to add 9 to another single digit number, the answer will always be a “teen” and the digit in the 1s column will be one less than the other number: for example: 9+5=___ The answer is a “teen” and the number in the one column will be (5-1) = 4. So the answer is “4 teen” = 14.
- an alternative is to change the 9 to a 10, add the other number, and then subtract 1 … but I find the extra steps can be confusing for some students. If you want to try it, it would work like this: 9+5=____ (9+1)+5= (10+5)-1 = 15-1 = 14.
- to subtract 9 from a “teen” number, the answer is 1 more than the other number in the ones column. So, for example, 17-9=___ The number in the ones column is 7 so the answer is (7+1)=8. Another example: 15-9=___ The answer is (5-1)=4.
Some Recommendations to the Parents
Don’t try to teach all these things at once. Just watch for opportunities to use the different methods as suitable work comes up in his workbook.
Also, it is very helpful indeed to watch for opportunities in “real life” situations, to do addition and subtraction. For example, when you are taking a road trip, get a map that shows distances between towns and have him add up the distance from one town to another. Or if you are baking an apple pie and doubling the recipe, and it calls for 8 apples, ask him what 8+8 is and ask him to count out that many from the apple box. Or if you are having a plate of cookies for supper, and there are 8 cookies to start with, just casually ask him how many will be left after everyone in the family has had one–and if there will be enough for everyone to have a second cookie. These kinds of “real life” experiences come up all the time; just keep an eye out for them, and use them in a casual way. His little sister will also love the game, and it will get her started on math facts without any formal teaching.
Oh! One more thing. If you want to practice “number facts” in some of the ways I’ve suggested, it works much better to just do 10 minutes or so daily, rather than 30 minutes twice a week or 60 minutes once a week. Frequent, short practice sections move short-term memory into long-term more efficiently.
Let Me Know How I Can Help
For future lessons, if you want me to help B with any particular pages in his workbook, just let me know what you want me to cover. Or if you notice he’s having trouble with something, just let me know.
And don’t worry–my first report is always long as it covers all the things I’ve noticed, and lots of explanations. In future, reports generally will be shorter!
Do You Have Any Questions About Initial Tutoring Sessions?
If you do, please feel free to ask them in the comments section, and I’ll do my best to answer them–or you can contact me directly, if you prefer, by email.
You can also find out more by reading the following posts: