Assessment Tools

After reading the article about assessment types to use in the classroom, I realized how crucial it is to choose the right form of assessment for our lessons. We all as teachers know the importance of assessing and probably do it every day in the classroom. However, this article shines light on the language we are using during our assessments, and what kind of questions we are asking. The authors explain "show-me" and "hinge questions" as successful forms of assessment to really show what is going on in the students brain. Show-me assessments can be simply asking the student, "can you show me how you found your answer?" The words "show me" implies that we know the student can demonstrate what they are learning. This provides the teacher with a glimpse into the students thinking and allows the student to show off their work. The article also mentions that the show-me method may seem only perfect for number relations; however, it can be used in every subject and almost every lesson.
The hinge questions method includes asking students questions at a "hinge-point" in the lesson. This informs teachers how where they have gone with the lesson and where they still need to go. I rarely stop lessons to assess student learning, but this method seems like it could be very successful with determining what the next steps for learning are. Do any other teachers already use this method or is this somewhat new to you too?

On Composing Meaning

In the journal article, Constructing Meaning: Standards for Mathematical Practice, the writers discuss the differences between modeling with mathematics versus modeling mathematics.

Modeling mathematics "is using concrete materials or other visual representations to clarify or give meaning to mathematics" and modeling with mathematics is using mathematics to describe and/or explain a real-world context.

The teachers that were involved in the summer institute that the research was based on did certain standards for mathematical practice and reflected on their day's experience.

This distinction makes sense, because one term discusses using manipulatives to explain a mathematical problem and the other is to use math to describe a situation.

The teachers worked through a problem and then reflected on what they did. It is important to provide teachers with this distinctions because it provides insight in the language of teaching.

Open Curriculum. . . Open Mind

Open curriculum is an idea I am certainly implementing in my own classroom. I love the idea of having a teachers manual and resources as a back bone of what and how to teach certain subject matter. However, often I venture out and use outside teaching strategies and resources to complement my approach. The article really does a nice job encouraging teachers to venture out as not all set of students learn the same way as perhaps the book anticipates.

Do any of you feel the same way? Is your school supportive of an open curriculum approach?

Scripted math programs don't know our students

Scripted math programs don't know our students.

So how can we have any lesson plan script in the math classroom?

Here are the many ways scripted lessons are failing our students:

They're not leveled. Every classroom in America has students of all different levels. A scripted math lesson plan cannot possibly be teaching ALL the students in the classroom. If you believe in student-centered learning -- which I do -- you can't possible use a teacher-centered/scripted lesson. You must meet the individual student where they're at in their learning.

Scripted lesson plans are on a strict time constraints for each section, so you miss all the exploratory elements of true math inquiry -- whole group, talk it out, think it out lesson.

Scripted lesson plans typically offer only one preferred method or style of answering a math question. There isn't any variation in problem solving, and if there is it's limited.

What's the point of the teacher if the lessons are scripted? Why not just have a robot in front of the classroom, reading each portion of the lesson, no skill, no training, just a great facilitator of scripted lessons? A scripted lesson misses the human element -- the teachable moments -- that are always more important when the lesson is taking place than the nuts and bolts of the lesson.

So its great to "open spaces" in curriculum but why not toss these scripts all together and just jump in.

Opening Curriculum

I found this article to be quite insightful into the way teachers are supposed to teach math versus how teachers want to teach math. I’ve said before that I struggle with using our math curriculum and would much rather supplement my own lessons. This article follows the idea that students need to develop more skills and knowledge than current math curriculum allows. The article discusses different strategies to help build students’ MMKB (multiple mathematics knowledge base). The first strategy aims to manipulate the sequence of the lesson, or even cut out parts altogether. Rather than always following the same pattern of instruction (opening, lesson, practice problems, word problem), change the order and allow students to problem-solve first. The second strategy invites teachers to differentiate and adapt practice problems so each student can be successful. Teachers should encourage students to complete practice problems at their individual level using their own strategies and methods. The final strategy discussed is to make math relevant to the students. Build connections between math and real-world problems.  Using these strategies may not solve the problems that we are having with teaching math, but they definitely may help students stay more engaged and motivated to learn. 

Dig Deep for More Effective Lessons!

Amazing Rainforests, Jesse's Train, and The Geometry of Scoliosis are three new lessons to add to my stock that explore elementary mathematics.  The lessons are inquiry-based, allowing students to explore the manipulatives and/or information and use questioning to get to their answers.  They work in pairs or groups, documenting their progress throughout.  Then, they share out their findings whole group and discuss the strategies each group used, critiquing their findings.

I really love these lessons especially since they are cross-curricular, integrating science, social science, and language arts.  I’m  always looking for ways to make math time more exciting; special.  I’m going to try Amazing Rainforests soon!  Which one of the three lessons did you find most applicable to your math instruction?

Number Sense Intervention

After reading the article about a Kindergarten student named Kyle and his struggle with number sense, it became clear to me that there are so many students struggling with the exact same problem in schools today. The NSI system made so much sense to be and seemed like it would be very successful for students. I really liked how it emphasized beginning to work with numbers 0-3 and establish a firm understanding of those numbers before moving on. I also thought the chart was great that showed each number being one more than the last and one less than the next. This is a simple, yet so important concept that students must achieve in order to be successful in math. I agree with the language they used as well, such as, "one and one more is two, two and one more is three, three and one more is four, etc." This really shows and explains to students that each number is one more while also introducing addition. They understand the larger the number the larger the quantity. This concept may seem simple and quick to teach, however it must be thoroughly taught and looked at through different ways. Understanding a strong sense of numbers is crucial to further number calculations, word problems, real life problems, mental math, the list goes on and on.
NSI is a great system for struggling students and should really be further understood by all teachers teaching in the primary grades!