Thursday, August 25, 2016

Mathematical Mindsets: Chpt. 8

This is one of the chapters I have been waiting to read: Assessment for a Growth Mindset. It seems somewhat contradictory when you think what growth mindset stands for and then the word assessment is associated with it. Let's begin a recap of chapter 8 in Jo Boaler's book, Mathematical Mindsets.

The most important preparation we can give students is a growth mindset, positive beliefs about their own ability, and problem-solving mathematical tools that they are prepared to use in any mathematical situation. ~Jo Boaler (142)

Key Takeaway: Jo Boaler emphasizes the need to transform how we assess students in the math classroom. The goal would be to replace fixed mindset testing with growth mindset assessment that channels mathematics that is broad, creative, and rich in problem solving. In this way, students would be empowered. Rather than students seeing a grade, students should see diagnostic comments/feedback that celebrate their knowledge and guide them to improvement.

Classroom Connections: As teachers, we need to help students become more cognizant of the math they are learning and where they are in the learning process (151).
  • Self-assessment through reflection can help students become more aware of the mathematics they are learning. When asked what are you working on in math, we want students to focus on the content of mathematics and not the chapter, lesson, page, or problem. Students can choose one of the following to respond to at the end of class (158):
    • What was the big idea we worked on today?
    • What did I learn today?
    • In what situations could I use the knowledge I learned today?
    • What questions do I have about today's work?
    • What new ideas do I have that this lesson made me think about? 
  • Exit tickets can be used as a tool to guide instruction. The exit ticket can focus on the key target understanding from the lesson. In the past, I have asked students upon completion to place their exit tickets in a red, yellow, or green basket. In this way, I can get an understanding of student's understanding of content, while allowing students to self-reflect on their ability in completing the skill: green: confident, yellow: getting there, red: help needed. If a student demonstrates understanding yet places his/her exit ticket in the red basket, this may indicate some positive growth mindset messages may be needed. If a student does not demonstrate understanding yet places his/her exit ticket in the green basket, this may indicate a misconception needs to be addressed. 
  • Grading should move beyond checking the accuracy of procedural questions. How might student work be used differently with a shift in focus to whether students ask questions, use multiple representations to show math, build on the thinking of others, and justify their thinking? Math is multidimensional and simply grading if an answer is correct/incorrect does not convey a complete picture of a student's mathematical performance.
Above all else, it is important to view assessment for learning! Assessment should provide information about a student's learning. Rather than focus on grades, the emphasis should be on constructive feedback. Ultimately, the parameters set by a district set the expectations for teachers in terms of grading and assessments, but within those parameters, fostering positive messages and focusing on student learning, and not only achievement, are steps that can be taken.

Thursday, August 18, 2016

Mathematical Mindsets: Chpt. 7

We are winding down with just three more chapters left in Jo Boaler's, Mathematical Mindsets. This week the focus is on tracking to growth mindset grouping. Boaler emphasizes the need to de-track students and group heterogeneously. I know this has been an ongoing debate in some elementary classrooms.

I do not value speed or people racing through math; I value people showing how they think about math, and I like creative representations. ~Jo Boaler (135)

Key Takeaway: The repetitive theme throughout Boaler's book is to move beyond the one-dimensional math class where the practice of executing procedures correctly is valued above others (121). Transforming classrooms into multidimensional classrooms where good questions are asked, ideas are proposed, different methods are explored and connected, multiple representations are encouraged, and reasoning is encouraged through different pathways is a goal to strive for. Dream big!
Classroom Connections:
  • When students are grouped heterogeneously, there are different ways to encourage students to look at a problem. These include asking good questions, rephrasing problems explaining, using logic, justifying methods, using manipulatives, connecting ideas, and helping others (122). In this way, there are multiple entry points to a problem for students of different readiness levels. At the start of the year, it would be interesting to ask students how they can approach/look at a problem and record their responses. Then as the year progresses, we can add to that list. Hm...definitely something to think about.
  • When students are working collaboratively, the role of the teacher is the facilitator. I really liked the idea of how groups were assigned roles such as a reporter. If the teacher needs to share something new to move the task along rather than stop the whole class, the teacher can call the reporters from each group over for a huddle. Love the idea of a "huddle." Once the information is shared with the reporters, they go back to their respective groups and convey the necessary information. Sometimes trying to get everyone's attention when they are immersed in a task to stop can be challenging. I will be adding this idea to my toolbox.
  • Feedback is essential for student learning, especially for those who may not find confidence in the subject. Boaler recommends that feedback to raise status of those who may not feel like they are as "good" as others in their group needs to be public, intellectual, specific, and relevant (135).
    • public dimension: highlights that a specific student contributed the idea
    • intellectual dimension: addresses the aspect of the mathematical work the student offered
    • specific dimension: showcases exactly what the teacher is praising
Math really is a social subject where students can bring their independent understandings to help accomplish a group goal.


Thursday, August 11, 2016

Mathematical Mindsets: Chpt. 6

Well, hello, again! Here we are in Chapter 6 of Jo Boaler's book, Mathematical Mindsets. The focus of this week's chapter was mathematics and the path to equity.

Mathematics is a broad subject that goes beyond computation and procedural speed and involves understanding of ideas. ~Cathy Williams (101)

Key Takeaway: Mathematics needs to be a balance between computational/procedural skills, conceptual understanding, and problem solving.  It is really important that we take steps to move beyond procedural based math classrooms and transform math into a connected, inquiry-based subject (104). As Jo Boaler would say, "Viva la Revolution!"

Classroom Connections:
  •  "Mathematics is not more difficult than other subjects--I would challenge people who think so to produce a powerful poem or work of art. All subjects extend to difficult levels; the reason so many people think math is the most difficult is the inaccessible way it is often taught (Boaler, 96)." This is such a powerful statement that I will need to keep nearby as I continue this journey and support others in helping our students develop a mathematical mindset.
  • Creating hands-on experiences, offering project-based curriculum, providing real-life applications, and fostering collaborative work are ways to help strengthen engagement for students, especially girls (103). 
  • The issue of homework was discussed. Boaler's recommendation is that homework should be given only if the homework task is worthwhile and draws upon the opportunity for reflection or active investigations around the house (109). In her beliefs, homework should be eliminated, reduced, or changed. The idea of procedural practice with repetitive problems for homework needs to be re-evaluated in our quest to foster equity for all students. 
As a teacher, intentional decisions need to be made to ensure equitable opportunities are provided for all students to thrive in mathematics. Mathematics is a gateway to their future!
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Monday, August 8, 2016

$75 Monthly TpT Gift Card Giveaway - 2 Winners!

I am so excited to be participating in this month's TpT Gift Card Giveaway hosted by An Apple for the Teacher! This month there will be TWO winners! With school in full swing or just around the corner for you, this would be a welcomed treat!

Giveaway Details: $75 Teachers Pay Teachers Gift Card

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Thursday, August 4, 2016

Mathematical Mindsets: Chpt. 5

August is here! Thank you for stopping by. This week we are talking about rich mathematical tasks from Jo Boaler's, Mathematical Mindsets.

Teachers are the ones who can create exciting mathematics environments, give students the positive message they need, and take any math task and make it one that piques students' curiosity and interest. ~Jo Boaler (57)

Key Takeaway: Mathematical tasks should be challenging but accessible to students. The tasks should be engaging and require students to think about math visually and numerically.

Classroom Connections:
  • When giving students problems to solve, pique curiosity and prime their brains for learning by giving students the opportunity to explore problems even before the methods to solve the problem have been explained to them. Yes, you heard that right, even before they know the methods to solve. Through exploration, students may come to a point when a method needs to be explained for them to progress further in solving the problem. At this time, the method can be introduced in response to students discovering the need.
  • These are six questions that can help guide in creating and offering rich mathematical tasks (90) to students. These are great questions to have nearby when planning.
    • Can you open the task to encourage multiple methods, pathways, and representations?
    • Can you make it an inquiry task?
    • Can you ask the problem before teaching the method?
      • This is a definite one to try out! Pose the problem first. See where students take the problem. Be sure to ask them to be able to justify their thinking!
    • Can you add a visual component?
      • Drawings can put a new lens on a math problem for students!
    • Can you make it low floor and high ceiling?
      • Tasks can be created so that they are accessible to students of various readiness levels while offering extension to those you are ready.
    • Can you add the requirement to convince and reason?
  • Flipping questions found right in textbooks is a starting point for creating rich mathematical tasks. Starting slow is key. In this way, you can begin to build a bank of rich tasks that parallel the standards you need to teach.
    • Here are some websites to peruse for additional ideas. It is important to consider your students when choosing problems. Raise the ceiling and see how high your students can soar!
As the new school year is upon us, let's consider ways to transform the types of math problems/tasks students see in the math classroom.