I'm telling you, sometimes it is like Mark Chubb is reading my poorly constructed blogs and then spitting out eloquent blogs that capture all of my thoughts and beliefs. He says what I think and believe. He just seems to say it in a way that is far more clear.
I've blogged about co-teaching before. Some of the points I've made are:
In his blog, "Co-teaching in Math Class", Mark Chubb distinguishes implications for co-teaching when one partner is a special ed. teacher versus when one partner is a math coach. I wanted to sing out an AMEN as I read specific sections. I'll leave you with these two screen shots from his blog but it is truly worth the time it will take you to read his work. He gets it and has a gift for communicating his thinking.
Visit Mark Chubb's (@markChubb2) blog by clicking HERE.
This is the perfect time of year to consider this question. My own children just received their report cards last week and I'll be completing report cards for my students next week. I was thrilled with my children's report cards. My son is a sophomore in high school who is taking all honors classes. All As and Bs for him...even in geometry and chemistry. My daughter is in eighth grade. She takes all honors classes too. She was recently inducted into the Junior National Honor Society. She received all As on her report card. Good grades are important to me and I've put some pressure on my kids to get good grades. So, my response to Will Richardson's recent tweet about grades might be surprising.
Good grades do NOT necessarily equal a good education. Higher grades do not mean that a student has learned more or knows more. High grades mean that the student has acquired some soft skills, like organization, time management, and perseverance. High grades say that he or she takes school seriously. High grades indicate that a student can use self-control and has developed the ability to make responsible decisions. Good grades, in my mind, actually say little to nothing about learning. Good grades say that a kid has figured out how to "do" school.
However, despite the grade-grubbing culture at my son's high school, I witnessed a beautiful thing happen in his honors English class. It is an ungraded class. This is not to say that he doesn't get a grade at the end of the term, it just means that pieces of his work are not graded throughout the term. Instead, he submits work throughout the term and receives actionable feedback from his teacher. At mid-term, they conferenced and discussed his progress toward his goals. His goals were revised and his work continued. At one point he came home and, in an intense way, said that he had to up his game in English. I asked why. He explained that he had peer-conferenced with a girl from his class and her writing blew him away. She had given him some helpful feedback. However, it was her writing that motivated him. It was refreshing to see my son motivated by the talent of his classmate versus her grades. I hear so many parents, when we talk about the importance of learning versus grades, talk about competition and how motivating and healthy it is. I couldn't agree less. Just knowing that someone is getting better grades than you is not motivational. But for my son, seeing an example of quality writing and receiving some feedback from a peer was helpful, motivational, and inspirational. Inspired learning is what I desire for my kids. I don't want them to be competitive grade grubbers.
So the quick answer: grades have nothing to do with learning. As teachers, we need to concern ourselves deeply with providing rich learning opportunities and then figure out how to measure that learning. I'm fairly certain that the way we measure learning today is actually having a detrimental impact on learning. We certainly have our work cut out for us!
I had a sneaking suspicion that attendance was going to be down today. I have 22 students. I began the day with 17. Then, over the course of the morning, three were dismissed. Still, there was a lot of energy in the room. It was like the 14 students who remained were trying to fill the void the others left. It didn't make sense to introduce new material in math class. I toyed with a Math In Three Acts but I'd hate for so many kids to miss out. We started the day with a number talk. The strategy was to use partial products to solve more difficult multiplication problems. This strategy is truly connected with the math we're teaching in our core lessons right now. The kids are doing a great job of visualizing arrays and then decomposing the arrays into two or more smaller arrays that make solving the larger problem easier.
I knew we'd be trying something new during our main lesson and I was pretty excited. Steve Wyborney is a math educator who shares his work generously on Twitter (@SteveWyborney). My students have really enjoyed his engaging splat and fraction splat routines. I had recently seen a couple of tweets from 5th and 6th grade teachers endorsing Steve's latest creation, "Esti-Mysteries". I couldn't wait to check them out. They couldn't have been more perfect for my students and the day we were having. From the first moment, I had 100% engagement. The students loved how Steve rolled out the clues and the suspense building in the class was tangible. This routine, due to the clues Steve used, addressed quite a few of our fourth grade learning standards. The mysteries welcomed different approaches and demanded higher-level thinking skills. I knew that the learning had been meaningful when my students cheered at the first reveal. We solved mysteries #1, #2, and #3 today and the kids begged for more.
Here is the thing. Math should be challenging. Math should require kids to dig deep and struggle. Math should be fun. It can be all of these things at the same time. Steve Wyborney has certainly figured out how to get it done. I'm thankful for his work and my students are too!
I have a student who is struggling in math. What she is able to do is so interesting. It is even more interesting when I consider her struggles. It seems like the number sense that she should have gained in second grade is NOT intact. For example, she cannot move around the hundreds chart with ease. If asked what 24 plus 30 is she would have two strategies: standard algorithm and counting on by thirty singles! The problem with her standard algorithm use is that she has memorized the procedures with no understanding. Therefore, 26 + 6 is sometimes 86! She cannot count by ten from any number. She has little command of facts that sum to ten so she has a difficult time knowing that n = 6 when 34 + n = 40. She cannot respond accurately when asked, "what would you add to 8 to get a sum of 18?"
Here is where it gets interesting. She knows her multiplication facts COLD. She can play "Big Array/Small Array" covering a larger array with two smaller arrays. She can generate algebraic notation showing her thinking (ex: 18 x 7 = (10x7) + (8x7) 18 x 7 = 70 + 56 and finally, 18 x 7 = 126)
When given a problem to solve like the one shown in the assessment below, she struggled. Even though she works proficiently with the array cards, she is having a difficult time moving from the concrete to a more symbolic representation. Today, she wanted to decompose the 7. I asked her how she would break seven apart. She said she would break it into a 3 + 4. I asked her what her next move would be. She froze. At this point I wish I had her grab the array cards and work to find two array cards that would cover an 18 x 7 array. Instead I showed her the smaller array she was left with. The one we discussed was an 18 x 3. I asked her if she knew her three facts up to 18 or if she knew her 18 facts. There was a long pause. I was even hoping that she might suggest adding 18 three times but that suggestion didn't come. My next move was to ask her if there was another option, other than decomposing the 7. She was able to suggest decomposing the 18. When I asked her how she might break it up, she struggled. I asked what 7 facts she knew by heart. She suggested 7 x 5. I asked if she knew any larger facts. She knew 7 x 10. I asked her to partition the array so that one part was a 7 by 10. She was able to do this. When I asked the length of the remaining side, she couldn't tell me. After many attempts, she counted on from 8 and settled on ten as her answer. Once she was able to decompose the large array and label the array's dimensions, she was on her way and completed the rest of the assessment independently.
I wish I always knew the best path to help students work through problems. I ask a lot of questions. I give think time. Still, I wish I had grabbed the array cards because she may have been able to make the connection between the physical arrays that she has worked with successfully and today's more symbolic representation. I wish I had a math coach or another adult who loves math as much as me, by my side in the classroom, so that we could strategize. I'd love to have more confidence in the math moves I make.
I still have to think about how to fill some of those number sense gaps. I'll begin with an Investigations game called "Capture 5" and go from there. I hope that this game will help her to add ten to any number with ease and to learn facts that sum to ten and make the connection between these facts and figuring out missing addend problems or subtraction problems where knowing those critical facts is helpful. This is what I'm thinking. I just wish I was more certain.