Solving the Problem

Do you remember that feeling you had as a child or teen when you got to the problem solving part of a lesson or unit in your textbook? Perhaps you felt joy in finally getting to do something somewhat more challenging than completing the 50 number sentences you just solved. Or maybe you felt fear that someone might actually notice that you really have no idea what you are doing. Worse yet, indifference may have become your bland taste for math and none of it mattered to you anyway. For me, the word problems always seemed like an enigma. Often it was just for extra credit – a nonessential part of mathematics. Other times it was assigned and I prayed for the magical key words to guide my way to a solution. I always felt uncertain. Having just practiced a set of rules for a page of tedious equations, the word problems didn’t fall into the same category as the rote memorization of the lessons practiced. It was disjointed and out of sync. Even those memorized key words didn’t help most of the time. They didn’t match multi-step problems or ones not involving algorithms at all. We all know the joke about the train –  If a speeding train is heading towards Los Angeles at 84 mph….Who cares? I’m not on that train.

I often find students in the same quandry. Upon entering 2nd or 3rd grade, students mistakenly believe that to solve a word problem you take the numbers, throw in an addition or subtraction sign, and then find the answer. The answer doesn’t need to make sense since the problem may not have to begin with.

My feelings about problem solving changed drastically when I went through training and implemented Cognitively Guided Instruction (CGI). Problem solving became the basis for my lessons rather than the afterthought. It became both my tool for teaching and the students’ access for understanding. I could finally really see what my students understood, and determine precise next steps for instruction. It took time to cultivate a classroom (and a teacher) that values problem solving. Through conversation and strategic share outs, students had real access to the underlying complexities within math that had evaded them. I came to understand mathematics with much greater clarity than before. And you know what? My students don’t need 50 problems to develop that understanding too. As it turns out, problems solving is the key to understanding, not the afterthought.

This is a sample format for differentiating word problems for your students. The sample on the left is a subtraction problem (SRU: Separate Result Unknown). There are multiple number choices for students to choose from depending on their comfort with the problem. The box is for the plan. I expect students to try at least two plans before trying a new number set to solve. I don’t always use a formal paper, as students have math journals to work in. However, it is nice to have a sample to send home or collect to collaborate and examine with colleagues. I have a rubric attached to my Snowmen Subtraction Word Problems that can be used to grade word problems. Again, I don’t grade all of the student’s word problems, but I do keep anecdotal records that tell me how they thought about a problem and how I need to push them to the next level.

Unpacking Common Core

I have spent countless hours unpacking the old standards, and in beginning to unpack the literature standards for common core, I am finding it a bit challenging. Of course, I think I could have started with a simpler standard, but as it is, I decided to kickstart my differentiated task cards for common core with reading literature standard 6, which is essentially examining point of view. To get a better understanding, I examined the standard from Kindergarten through Grade 3. I looked at what ideas kids need to know, skills kids need to be able to do, and bigger ideas they need to understand. In my research, I came across a book by Lucy Calkins, Pathway to the Common Core, Accelerating Acheivement. Her first two chapters are posted online, and one of the major changes she defines between the common core standards and old standards is the focus on textual analysis. There is much depth in the area of comprehension in common core, however, there is little in relation to personal response. That “ah-ha” for me really helped illustrate why it was so challenging to unpack and differentiate this standard. This focus on text structure is very different than what I am accustomed to. I searched a variety of places to get better acquainted with the essence of point of view. Most of what I found was the goal for upper grade and beyond, which really helped me examine how the primary grades build to that point. Therefore, point of view in the primary grades is pieces of point of view, which build towards a larger meaning. For a quick tutorial on what point of view really is, check out this video on youtube.

 You can find the results of my efforts in unpacking this standard for grades K-3, lesson ideas for grades K-3, an overview of point of view, and 8 differentiated task cards on point of view for 2nd grade by clicking on the button to the left and downloading the free packet on teacherspayteachers.com. Also , please visit my literacy tab to see examples of how this standard would look across the grade levels K-5. Please give me feedback on what you think. I would love to hear from you.

To learn more about how the differentiated task cards were developed, check out the differentiated literacy centers tab underneath the  literacy tab above.

Your skills are so fine

My mom would like to take the credit for my son’s exemplary fine motor skills, and if truth be told, she is probably right. As an occupational therapist, my mother looked at play time very differently than the average person. Sure, she let my son have free play, but she also crafted games and activities that would help promote his dexterity. When my son was a baby, he spent a lot of time on the mat laying down. To entertain him, my mom would slowly tear paper towels and blow on them so they danced above my son’s head. He would shriek with delight, and it wasn’t long before he began taking the paper towels and shredding them to pieces too. Everyday, he would become engulfed in bits of this snow. Sure, it was entertainment, but you know what? He was able to hold a tripod grip on any writing utensil by the age of 2, and to be honest, I never showed him how.

Developing Fine Motor Skills: Pumpkin Pegs

So here is a fun activity for working on fine motor  that I am ripping off of a few preschools that I looked at. You can use a pumpkin of any size. Kids can draw on the pumpkins with washable markers and hammer in pegs. For younger kids, it is helpful to make some holes as starters. You can have some fun with it and make the pegs hair and draw a face on your pumpkin, or just doodle and write “words” like my three year old did!

Check out the preschool tab to get a FREE download of activities you can do with your child or students to promote fine motor skills and tool control! 

What does understanding look like?

In education, determining what understanding looks like is one of our biggest quandaries.  We examine learning goals from multiple perspectives, and with our given resources, often fall short. Learning is complex, and therefore, understanding is too. It is much easier to determine proficiency in skills and rote tasks. Often we accept mastery of skills to be synonymous with understanding, and this is where I would contest is one of our greatest shortfalls in education. It is far easier to see if a child gets the answers right or wrong, than if the child understands the how and why. When I first began my journey into the teaching profession, I was asked to take a proficiency test in math to determine if I was current enough in my skills to bypass a more current math methods course. It was the first time anyone ever asked me to explain why and how an algorithm for regrouping worked. I thought it was really strange at the time. My whole life, I never questioned the “whys” of math. Of course, I am a rule follower, so I did very well. I did not need to understand, I just had to keep to the rules. My husband is my opposite. The rules never made sense and he had his own way of thinking about numbers that did not fit into the rules. Therefore, he did not do well in his mathematics courses. Guess who is the better mathematician? It wasn’t until I stopped “teaching” my students and started listening to how they thought that I truly began to understand mathematics. And, learning to teach in a way where I was the real learner has proven to be a far more complex and rewarding methodology than any textbook I have seen.