We’ve made no secret about the fact that we value the summer months as an opportunity to work with students on all of the things that we didn’t have time for during the school year.

Two of our most popular summer programs are Comprehension through Composition and Math Bridge. Our Comp Comp program gives our fourth through twelfth graders a chance to work on reading comprehension and advanced writing skills away from the classroom, where the bustle of the school year can hamper progress. A Math Bridge helps students fill in any gaps in their math foundation and preview topics for the upcoming school year.

These are only a couple of our summer offerings. Summer is also a great time to develop a love for reading, spend time on creative writing, or get a head start on next year’s science class!

Nurturing Wisdom Academy has developed a unique customized approach to teaching math.  Our math teacher, “Ms. Abby,” explains more about how she customizes to each student’s needs through a variety of classroom activities.

At Nurturing Wisdom Academy, not only am I able to meet the needs of several students in the same math classroom through a variety of activities, but I’m also able to customize my approach to each student. Our students are able to learn at their own pace and truly master the concepts they are taught.

One of my students, “Alex,” is a one of the younger students in our mixed-age classes.  He enjoys math, especially thinking about math concepts and problem solving.  Like many young mathematicians, he doesn’t necessarily love showing his work or working on long computations.

When he started with us last fall, Alex had an amazing conceptual grasp of math, but he didn’t always know how to follow through from his ideas to an answer.  His math skills were rather “average” for his grade because of this.

At Nurturing Wisdom, we love summer! The summer allows students to make a lot of progress without feeling the pressures of homework, quizzes, and tests during the school year, when students can feel like they’re always preparing for “the next big thing.” As such, they never get a chance to take a step back and work on all of the necessary foundational skills that will keep them ahead of the game. Summer is the perfect solution! It gives students the opportunity to make the following school year even stronger, while also incorporating topics that they have a true passion for, like creative writing or reading personally chosen books. Below, Lauren talks about her positive experience with one student she’s worked with for two summers.

Although we have a lot of great summer programs, my personal favorite happens to be our Math Bridge. I have worked with a lot of students on math over the summer, and the difference it makes during the following year’s math class is amazing. One student that comes to mind is Kate. I have been working with Kate for the last two years, including two summers. Each summer, we worked on math and the difference we saw was remarkable. When I first started with Kate, math was not her strongest subject. She also did not really enjoy math as much as she could have because it was so challenging to her. Over the past two years she has gone from being a C math student to a B+ math student. She has gained a great deal of confidence in math and has come to really enjoy it.

When we meet with a student to set up tutoring, we frequently present a tutoring plan, which is customized to that specific student.  This plan is an excellent communication tool to keep the student, tutor, parents, and tutoring director on the same page and guide tutoring throughout the student’s program.

In the beginning, the tutoring plan is a great jumping off point for the student and tutor because it provides basic guidelines for each session. The tutor can then customize the elements in the plan even further to meet the specific needs of that student.  As tutoring progresses, the plan acts as a reminder of what the overall objectives are and helps both the student and the tutor work toward those objectives.

We’re constantly helping students with math. One trend we’re seeing is that some of the “new” math curricula isn’t giving students a strong foundation of basic math facts. Math builds on itself over time. As a student advances in math, tackling increasingly complicated problems and skills, undetected holes in their foundational knowledge can cause huge problems later.

What is “new” math?

Everyday Math is one type of “new math” widely used throughout Chicagoland elementary schools. It has grown in popularity because it’s thought to teach “higher level” problem solving skills. Problem-solving skills are important, and the truth is, many students do quite well with Everyday Math. The consistent problem that we see is that foundational, basic math skills are not taught, which really leaves some kids behind.

In previous posts, Sara introduced the concept of surface structure & deep structure when it comes to problem solving. She then went on to describe the ways the surface structure of problems can help students understand certain aspects of those problems or concepts. Now Sara goes into more detail about how, through knowledge transfer, we can help students move beyond the surface structure of problems to understand their underlying deep structure.

Transfer (applying past knowledge to new situations or problems)is an essential part of how we define learning. We can’t say that we’ve really mastered a concept or skill until we can apply our knowledge in different situations. The question is: how can we promote transfer?

As I explained in my last post, students have an easier time recognizing deep structure if the surface structure is familiar. The key point here is that familiar surface structure is not necessary to solve a problem – but it is helpful. I’ve noticed that when working with ACT students over the years, most of them have an easier time tackling percentage word problems when they have a familiar context. Take these examples:

In her previous post, Sara described the difference between surface and deep structure in math word problems. Here, she talks about how students transfer prior knowledge to new situations.

Applying past knowledge to new situations or problems is called transfer.

As many of us teachers and parents have experienced, getting a child to transfer knowledge isn’t always easy. The ‘laps around the track’ problem that I gave my 7-year-old son was a poignant example for me. Students will often focus so much on the unfamiliar surface structure of a problem that they miss the deep structure, and they don’t realize that they actually have the skills to solve the problem.

Why do students put so much emphasis on surface structure? Because it’s the clearest part of the problem. The surface structure is written out and obvious, whereas the deep structure is hidden and unclear. It seems more efficient to work with obvious and concrete information rather than take haphazard stabs at what the deep structure might be.

It is important to remember, however, that paying attention to surface structure – the content of the words, the meaning of the story – is actually a necessary step when we’re learning new information. We learn new information by connecting it to information we already know.

Even well into adulthood, I used to have the hardest time (embarrassingly enough) remembering which direction I had to turn to loosen or tighten things like screws or knobs. This culminated one day when I was trying to get some screws off the license plate of my car and it took me way too long to finish the task. After I complained to a friend, she taught me “Righty tight-y, lefty loose-y” as a way to remember this which worked like a charm! All the years of struggling to keep this straight in my head boiled down to a couple of simple lines and it’s something I won’t ever forget.

My 7-year-old son and I were watching my older child compete in a track meet. It was a chilly day, and we’d been standing outside, huddled under our coats, for about an hour. As we stood at the fence waiting for the next event to begin, my son sighed, looked up at me and said, “Mom, I’m bored.”

The teacher in me always looks for moments like these to squeeze in some mental activity, so we started talking about the track.

“Do you know how many meters long the track is?” I asked. He shook his head. “It’s 400 meters,” I said. “So when a runner does one lap around the track, he runs 400 meters.”

That seemed to make sense to him, so I figured I’d start off with an easy problem. “All right,” I said, “so if a runner does two laps around the track, how many meters is that?”

I’ll never forget the look of surprise on his expressive face. Shaking his head, his brow knit with genuine confusion, he responded, “What? Mom, I don’t know. We’ve studied meters before in school, but we’ve never studied tracks!”