Here is a great article from EdSource, a California group dedicated to improving teaching and learning. Although CA could not be further from NH in every way, this whole story about how the Common Core math standards are affecting K-3 teaching in CA sounds as if it could have come from Sanborn, Whitefield, Portsmouth or many other NH school districts.
A particularly good story comes at the end of the piece:
Juh’Ziyah Atchinson, 5, was one the students who couldn’t seem to get it right. Dawson, who has been trained in a method of teaching mathematics called cognitively guided instruction, was more interested in understanding why Juh’Ziyah kept counting bears twice than he was in correcting her. The idea behind this method is for teachers to build on a child’s existing knowledge about math to guide them to the correct answer, rather than quickly correcting them. Instead of simply telling Juh’Ziyah to only count each bear once, Dawson started a conversation with the little girl to determine if she even understood that basic counting rule.
Path of discovery
“I’m not an imparter of information,” Dawson said later. “I want my children to discover.”
Getting them to discover often means conversations where Dawson simply says out loud what he’s seen a child do – “I noticed you counted a few (bears) twice.” Observations like this are meant to make a child reflect on what she has just done and hopefully learn something new by being directed to focus on the actions called out by the teacher.
In Juh’Ziyah’s case, Dawson concludes that she does know objects can only be counted once but is having trouble keeping track of which bears she’s already counted. He shows her a tool to help with that: Organize the 20 bears into several short rows, rather than trying to count a messy jumble.
Megan Franke, an education professor and teacher trainer focused on math education at the University of California, Los Angeles, said research shows that teaching math like Dawson does is more successful than teaching methods focused on memorizing right answers. The Common Core elementary school math standards, Franke said, are based on that research.
“The math practices (in Common Core) are asking kids to explain their mathematical thinking, to represent their ideas and to make sense of other people’s ideas,” Franke said. She hopes these principles encourage a shift in how math is taught that will ultimately change what children know about math.
Dawson is confident that teaching math based on these principles will help Juh’Ziyah and his other students meet the Common Core Standards. In previous years his students have exceeded the old state standards, he said.
By the week before Thanksgiving, his confidence proved warranted: Juh’Ziyah was not only counting to 100 by ones (i.e. 1, 2, 3…) and 10s (i.e. 10, 20, 30…), she was solving three-part word problems using subtraction.
“If Juh’Ziyah had 15 cookies and wanted to give three to one friend, three to another friend and two to a third friend, would she have enough?” Dawson said he asked the girl in November. “And if she had enough, how many would she have left?”
Juh’Ziyah, who hadn’t been able to count to 20 three months ago, was undaunted. Using small objects to represent the cookies, she nailed it: Yes, she’d have enough cookies to share, she told Dawson, and she’d have seven left.
Notice, in particular, the table at the end of the article comparing the Common Core math standards for grades K-3. You can easily see, on the one hand, how closely parallel they are and, on the other, just what the differences are and how the Common Core standards bring depth and focus.