Recently I have rebooted my professional learning. Following tweets and blogs has inspired me to fill my kindle wish list. I purchased two off the list and read the shorter of the two first. How disappointing. The book described an intervention method for students struggling with multiplication. The author prescribes listing the facts by place value and pointing out the pattern she had found in the ones place. For instance in the nines times table one as the facts are listed the numeral in the ones place decreases by one. She continues through the eight times table and seven. For the seven times table she explains the strategy to list the ones place by following the pattern subtract three unless one cannot subtract three with out regrouping. in that case add seven.
Horrid!!!
I was so disappointed by my $3.99 purchase on Kindle. This offered me nothing to help my students. These lessons did reinforce that multiplication was repeated addition or represents equal groups. She dictated a pattern to the students. Her patterns were legitimate but her teacher led lessons left nothing for the students to discover.
After I dismissed the method, I began top think about how I would do it better. Some time later I designed a template for a number line for students to highlight the multiples as they skip count, a place value chart to list the multiples of a number and write the patterns that they discover for the ones place and tens place and a hundreds chart to color in the multiples of a given number. I then participated in making discoveries using the templates that I created. As I found patterns I asked my self why the patterns worked. I found myself noticing patterns and strategies that I have never thought of before even as though I thought of myself as a proficient fourth grade mathematician.
I now have a intervention tool for my struggling mathematicians, a center activity, possibly some whole class lessons. More importantly I have a stronger number sense and validation that I am a constructivist and facilitator of students discoveries.
So as my budding essayists end their writing with a call to action. I urge you to go read a horrible professional book. May your best teaching grow from the mulch.
This year I have delved into a problem solving centered math workshop. My goal was to use problem solving to introduce big ideas of the unit and come back to the problem to teach the pertinent standards. It is common practice to use a mentor text in a literacy unit. For my math workshop, I centered our units of study around a mentor problem.
With my colleagues on a math team, we focused our work on finding rigorous problems that incorporate the big ideas. Many of the tasks came from Howard County Schools website. This site has been my go to for my mathematical instruction. In exploring the site, I was introduced to Three Act Tasks. Three Act Tasks aligned nicely with my goal to center my math instruction in students unearthing the units concepts. Starting the unit with a Three Act task introduces the concepts but also reveals the misconceptions of the students.
After my class experienced some Three Acts, I decided to create a Three Act of my own.
I worked with one of my students to create the picture to introduce decimal and fraction relationships.
Act 1
The busyness of the end of the year created the necessity to join classes. This was a first in many ways. The students of the class were experiencing a Three Act Task for the first time, I created a Three Act for the first time, AND I facilitated a math experience for 40 something students for the first time.
The students unearthed so many noticings and wonderings. The concepts of value verses coin amount came up for the students. Check. I don't have to do a whole class lesson on that concept.
I learned from the experience how I can foster mathematical practices. Some students feel they only have something to offer if it is a mathematical mindblowing statement. Often it was the simple notings and wonderings that pushed other students to think more deeply. When Anthony then asked, "How many pennies are in each stack?" I asked, "This seemed like an obvious question. When he admitted that it did, I applauded him because no one before him offered that question.The important questions are often the simplest questions and students and teachers need to honor that. More students then felt more comfortable to enter the conversation.
Math is scary but we need to all jump in and try. No as Yoda says, "There is no try. There is do or do not."
I tried creating my first Three Act Task and I fumbled along the way, wondering what is the difference between a wondering and a student question. I found out that my second act picture was not clear enough to lead to estimations and solutions. I debated whether to ask, "Who has more money?" "Who has more value?" or simply "Who has more?" I decided on the ambiguity of "Who has more?" since the students' noticings and wonderings uncovered the difference of value and coin amount.
First Attempt at an Act 2 Photo.
The photo does not lend to estimation or solution.
My second attempt at my second act picture
So as a teacher faced with the the problem solving of problem solving, I have yet to find the solution. I have made discoveries and have I have more questions, yet this is a good thing since this is what we hope for our students.
