Grade 10 Math. Why so tough?

High School Math continues to be a growing struggle for all parties. For some students, it is a maturity piece where they simply need to be an active member of their learning. For others, it becomes a focus on skills. Below are the key reasons for lack of success in Grade 10 math at the present.

FAILURE TO SUCCESS

Students can fail a course and still “succeed” in continuing on to the next level of difficulty (grade). Any gaps in their learning are now compounded with more complex concepts and tricks (like cross-multiplying) which create a dangerous footing to walk. If a student hasn’t mastered a concept in grade 7, how do we expect them to succeed in grade 8 or 9, let alone during high school?

To see students getting 30-40% throughout junior high and then attempt Math 10C, a course hosting the grade’s future valedictorian, seems reaching. They are optimistic, though, because things always worked out before in “succeeding” at that grade and moving on.

There is value is failure.

CALCULATORS

Add ½ + ½ and of course, students will confidently answer with 2/4….CONFIDENTLY!

Ask a student to evaluate (-4)² is of course, -16. Students know that (-#)(-#)= +#, so why are they so confident in the incorrect?

Processes are more straight-forward in junior high and it is “safer” to type basic operations into a calculator, like "8 x 3". The lack of thought going into some processes becomes a risk as concepts/operations become more complex. Even more dangerous is the transition into variable math:

Ask a student to add 2/x + x/3 and they shut down. 

“Where is the ‘x’ button?”, they might say.

If a student cannot tell me all the factors of 24 within 10 seconds, they are likely to struggle at factoring in grade 10. It is convenient that Alberta Education added “recall” back into the K-9 program because, otherwise, a 1 step problem becomes 2.

PACE & PARTICIPATION

I am told by my grade 10 students that they can miss a week of grade 9 math and still catch up without much stress. My students miss a day, and they are behind.  “I wasn't there that day” is a common statement when they don’t know how to complete a task. Students continue to be coached throughout high school that learning takes place, even when they are on a 2-week vacation in early December.

Eventually they learn to take learning into their hands, but it takes time. The sooner they become an active participant in the classroom, the more ready they are to succeed.

I look at my grade twelves, who if I ask to spend 10 hours over their Christmas break on a specific task, would. They trust me and know what is required for success. In grade 10, though, some are simply sitting back and waiting for grade 11 to get here.

Is there room for a Fundamentals of Math Course in High School?

While my Math 10C class has some very less-than-motivated students, I have a number of students truly wanting to improve, but lack many of the core skills that are required for success in high school. If a "Fundamentals of Math" course were created, what would it look like? How long would it be? Who would it be for? Hmmmm..I guess some background first.

In 2010, Alberta Education remodeled its high school math curriculum from a pure & applied set of streams, shown below:

While the intentions where very great, post-secondary didn’t accept Math 30 Applied as Alberta Education had hoped. It became the “non-academic” class from the students’ perspective. Students felt the pressure to take Math 30 Pure to "keep doors open" and stay "academic".

Around 2008, many schools began to feel the competitive edge and from parental pressure, felt they could no longer advertise recommended grades of ~65% to properly stream students, and so student began selected courses above or below their ability. Choice became dangerous! My school, in particular, saw the brightest of 30Applied flounder in 30Pure. Our diploma averages reflected this almost instantly. The Math 30 Pure school average dropped. The percentage of standard of excellence students in Math 30 Applied dropped. 50% became enough for parents and students to validate the next level of math.

Enter 2010. Math 10C and Math 10-3 sets the foundations for most of high-school math. 

Math 10C hosts the grade’s future valedictorian as well as the student who achieved 50% in grade 9. While a similar effect can be seen in science, grade 11 sets a very different stage.

Science offers: Physics 20, Chemistry 20, Biology 20, and Science 20. Students get to choose a discipline of interest or simply take a more general Science 20 class. Below are graphs of every Student that has taken Science 10 and Chemistry 20 at my school. Notice the correlation that suggests many students improve or stay the same from grade 10 to 11. While a number fall below, at least there are "few" that fail:

Considering Math 10C to Math 20-1, though, sees many students with a dangerous drop in grade. According to the graph below, students achieving less than 70% in Math 10C are not doing well. Part of the issue is the large number of students struggling through Math 10C and then “attempting” the most challenging Math course in their K-12 formative years. See below:

Even in Grade 10, students need to understand that missed skills in grade 9 (and earlier) result gaps in learning that WILL catch up with them. Perhaps the most haunting piece of data I have:

(Pulling data from 2 different teachers)
Of all the Math 10C students who got below 65% in grade 9, exactly 5 out of 25 are currently passing Math 10C. That is a scary number.

First, I hear this in other schools, districts, provinces:

“Students are weak”. “They don’t’ practice anymore”. “They don’t want to learn”. While the majority of students are needing much more encouragement than ever before, their lack of fundamentals is causing the root of my concern. There are 3 areas of focus:

1. Number/variable operations: What is the difference between:  (x)(x)  versus “x + x” versus (x²)³ ?
2. Balancing equations:  The heart of “Solving for x” begins in grade 7 and my grade 10s still make fundamental mistakes.
3.  Mental Math: If I ask my class for two numbers that multiply to 24 and add to 11, I would get blank stares from about 30%. If I ask to add fractions without a calculator, I’m not confident that they could.

Regardless, "success" in grade 9 doesn't necessarily indicate success in high school. Motivation and implicit skills can only detail a likelihood for success. We are running out of time in math 10C, and I want to reteach these skills, but there just isn't time to reteach elementary and junior high skills.  Is it time to create “fundamentals of math” course which walks students through their grades and build the skills needed for success in high school?

The motivated students that I have who struggle in Math 10C would do better simply getting a solid base before “half-learning” Grade 10. Whether this is for Math 10-3 or Grade 9 students, give me a class of 20-25 students who were motivated to do better, “High School Math Fundamentals” would be a dream to teach. Confidence builds. Understanding grows. The appreciation for math returns.

Life would be good again.

Be less helpful: Effective Questioning in Math Class

You finish your lesson and your class of 35 students busily gets to work (or so is the dream). Regardless, students are practicing, and Emily's hand goes up. You walk over to her desk and she utters the infamous words you love to here:

"I don't get it."

Whether Emily's "question" is the exact phrase above or some similar form of an ambiguous misunderstanding, it leaves math educators in very dangerous territory. We can take one of two routes:

1. Answer this question only.
2. Help answer this question and potentially many after it.

The second option is really the point of practicing math, right? ...To problem solve and effectively reason through a question so that learning takes place. I think this is where we would all like to be be when we walk over to answer Emily's "question". Due to large class sizes and impatience, though, often the first routes is taken. Observe:

Imagine Emily's Math 10 question was determining a leg of a right triangle using the Pythagorean theorem and you decide the best way to answer her question was the following way:

Emily: "I don't get it."
Teacher: "This is a tricky question. You have to use Pythagoras...like this..."
(*and you finish the question for her, effectively modelling how to answer it*)

Despite the proud moment of demonstrating that YOU know how to determine the leg of a right triangle, you have actually just stolen a great deal of learning from Emily. How could you have used the opportunity to help build her problem solving skills to answer a similar question in the future. (We don't want to keep coming back, right?)

"I don't get it!" implies what? Does she have everything correct but hasn't square-rooted the result? Is she using cosine? Is she incorrectly squaring the legs? Does she even understand the question? This is your opportunity to be less helpful...Start by being unbelievably (painfully) vague. Try something like:

"What don't you get?"
"Do you understand the question?"
"Tell me what you DO know"
"Have you seen a question like this before?"
"Tell me more..."

Only after we have discovered where Emily is struggling can we begin to even start helping. Again, don't give her the answer. Lead her on the journey with ever-more-specific questions. A conversation could look like this:

Emily:    "I don't get it."
(immediately you see that she plugged a leg into the hypotenuse location)
Teacher: "What don't you get?"
Emily:    "I am not getting the right answer."
Teacher: "Can you explain what you've tried?"
Emily:    "I drew a triangle and subbed the sides into Pythagoras. The answer isn't the same as the back of the textbook."
Teacher:  "I'm glad you checked. What do you know about using Pythagorean Theorem?"
Emily:     "You plug the sides into c^2 =a^2 + b^2 for any right triangle."
Teacher:  "Great. What does the a, b, & c represent?"
Emily:     "Sides."
Teacher:  "yes..." (wait...forever if need be)
Emily:     "well, c has to be the hypotenuse and a & b have to be the legs."
Teacher:  "Are you sure?"
Emily (eyes go wide): "I know what I did!"

Emily is less likely to make that mistake again if she is the one that walked through the problem.

If students are continually subjected to a lack of help (careful with that implication), they are going to be better able to reason through what they know and what the might not. As educators, our goal is NOT to answer individual questions, but rather to give students the skills to make them capable of reasoning through their problems and if anything else, at least they won't start their questioning with "I don't get it."

Be less helpful. Determine what they DO know. Answer questions with questions. Ask for more. Get it?