The 10-year-old picked up her pencil, silently read the math problem, circled some numbers, underlined some phrases, paused for thought, and neatly began to work toward her solution. With a grin, she tackled the next problem successfully. She hesitated, looked at me sideways with her dark eyes and deadpanned, “Are you kidding me? These are SO easy!”
This was one of many moments this year that caused me to see the tremendous shift in the mathematical world of our students. As an elementary Academic Intervention Math Specialist, I work with students who struggle academically. This 4th grade student struggled in 3rd grade, and received a score of 2 (out of 4) on the previous year’s New York state Common Core math test. While I was putting together materials one class period, I handed her Book 3 of the 2009 Grade 4 (pre-Common Core) New York State math test. To my amazement, she was able to answer almost all of the questions completely and accurately, using a variety of strategies successfully.
The next was in January, when my principal was observing me teaching one of my small group sessions. The six students sat relaxed on the rug in front of the white board. Since our school had recently adopted a more challenging math program, I asked the students what they thought of 4th grade math year compared to last year. Answers quickly poured out:
“It’s SO hard!”
“Last year, math was much easier.”
“It takes me so long to finish my work!”
After a pause, I asked, “Anything else”?
“I’m a much better math student.”
“I can solve harder problems!”
“I understand so much more. I like when I can teach the class how I did the problem.”
“Even though it’s harder, I like it more.”
“It makes me feel good when I can finally figure it out.”
In late April, a fourth grade teacher implored me to take three of her top math students since they were clamoring for more challenging problems. On a whim, I reached into the cabinet for the 2009 Grade 5 Book 3 (Pre-Common Core), knowing that even if they hadn’t covered a concept in their current grade, they were strong problem solvers and could reason with alacrity. They dove in and solved the problems with almost 100% accuracy. I then reached for a packet of current 4th grade practice questions that were aligned with the Common Core released items. The three students enjoyed the challenge. Although their errors increased, they were motivated to discover and discuss their errors and make sense of the problems.
What has changed in the lives of our 10-year old students?
- Daily Instruction: Shortly after any content is introduced, a problem is presented and students are expected to find viable solutions. They are expected to struggle, and then to learn from their own mistakes and from each other. Teachers use student work to highlight multiple alternate strategies and solutions. Students critique each other’s work with praise and suggestions.
- Assessments: Arithmetic (adding, subtracting, multiplying and dividing) is no longer a focus. Accuracy is expected. “Answer getting” is discouraged. Proof of mathematical thinking is required. Extra paper is provided. Complex word problems are the norm. Failure is frequent, persistence is encouraged, and “try something” is the mantra. Perseverance is celebrated.
- Self-Awareness: Our students view themselves as problem solvers. They expect challenges. They know they must read for understanding, and search their individual reservoir of math strategies to begin. They no longer stare at a problem and say they can’t do it. They know and own their strengths. They take time to think, and then jump in somewhere with confidence.
- Struggling Students: The population has changed. The bar has been raised. The struggling students of 2009 would not have had a chance of being successful with our current program. Conversely, most of our current students who receive extra help would have been awarded 3’s or even 4’s if faced with the 2009 New York State assessments.
So now what does a typical 4th grade student think about herself in this new rigorous math world in which struggle and persistence precede success? The pronouncement of that 10-year-old student as she left my room that day answers with a resounding confidence, “I am a mathematician!”
Karen Marino is an AIS Math Specialist (Grades 3-5) in the Skaneateles Central School District.