Friday, April 24, 2015

On Task - Guided Notes Work Time Update


On Task Update:

Since the end of February, I have been using the on task tracker described in my Back to the Future post.

Students have interacted with the tracker in four ways:

1. Students and I co-created the “on task” criteria for work time:

2. Daily public tracking of the whole class:
Students earn a 4 (green) if they are meeting all the criteria and a 1 (red) if they are not meeting all of the criteria. I project this on the board during work time.

3. Weekly data overview:
I project this at the end of the week and we talk about the class goal for the week and progress towards it.

4. Individual reflections:
Students are  reflecting and setting goals for themselves.

My Analysis/Reflection:

Pros:
- (mostly) nonverbal redirection
- group goals and accountability: students have been reminding each other to be on task
- in general, work time has been more productive
- students have been motivated by my linking the class’s on task score to a related reward: the class earns the privilege of choosing seats if they meet the goal for the week

Cons:
- some students check out after they earn one red
- I can’t project anything else while I am tracking
- some students are only on task when then know that I am doing a check (which is better than nothing, but could be even better)

Moving forward:
When I started this, it was never my intention that this was something I wanted to do forever, or even for a long period of time. I wanted students go get into some good habits and then take the scaffolds away. So therefore, here is my plan for taking away the scaffold:
  • Week 1: During work time, students do their own on-task check when I ask them. At the same time, I will be doing a check for them on my computer. At the end of the period, they should compare their perceptions with mine as well as calculate how on task they were. They will use this organizer to do that:
On Task Check
Are you on task?
Did Ms. Hansen agree with you? (Circle One)
YES
NO
#1


YES              NO
#2


YES              NO
#3


YES              NO
#4


YES              NO
#5


YES              NO
#6


YES              NO
#7


YES              NO
Analysis
What percent of the time where you on task?



What percent of the time did you and Ms. Hansen agree?


  •  Week 2: Students will self-assess in the same way as week 1, but I will not officially assess them. At the end of the week, students will reflect on the week and say whether or not they think they still need the checks to keep them on task.
  •  Weeks 3 & 4: Check list only for students who need it.

Monday, April 20, 2015

NCTM Days 2 & 3


Three(ish) things I want to remember from the sessions I went to on Friday and Saturday

Building Student Understanding of the Mathematical Practices through IN-formative Assessment
Matt McLeod, Mary Wedon (EDC) 
 - Assessing students’ use of structure (MP7) through computation problems. In directions, write “avoid unnecessary computation”
- "Hidden Meaning" questions
- ex: 36(65) is equivalent to 67. Explain or show why this is true.
- "Chunking" questions
- ex: Simplify the following: 8(992-4)+3(992-4)-11(992-4)

Fake-World Math: When Mathematical Modeling Goes Wrong
Dan Meyer
- There are 5 steps of modeling. Students do a lot of steps 3 and 4 in textbooks. We should be doing a lot more of 1, 2, and 5. Students don’t need to do all 5 steps every time you do modeling. Celebrate what students are contributing at each level through praise, one clap, etc.
            1. Identify the variables
            2. Formulate models
            3. Perform operations
            4. Interpret results
            5. Validate conclusions
- When modeling, we need to be honest about whether the math “works.” Have a discussion why the predicted height in cups with all accurate computation isn't the actual height in cups.
- Set up situations that require knowledge that students don’t have yet. This creates a need for a “bigger boat” (Jaws reference) before we give it to them.

Investigating the Pythagorean Theorem and Its Proofs
Robyn Carlin
- What is the definition of “proof” in the common core? Is it enough for students to be looking at examples and then making generalizations?

Reasoning Revisions Revolution
Patrick Callahan and Jessica Murk
- In having students work on problems you don’t know the answer to, you authentically cede authority and model reasoning and revision
- After having students/groups write and revise their own rules, having all students write the same rule down at the end defeats the purpose
- With peer feedback, the authority shifts from teacher to student. Feedback expectations:
            - it takes practice
            - giving feedback is not the same as being mean
            - think about what you would find helpful
            - avoid opinions
            - be specific












What do my students know? How do they know it?
Barbara Dougherty and Jeanette Olson
- Encourage students to show their thinking rather than show their work. In doing so you open the door for valuing logical reasoning over structured algorithms.
- Challenges of open response questions in progress monitoring:
            - students couldn’t explain
            - hard to score
            - students often skipped
- In multiple choice, options have different point values based on complexity of thinking required for the (wrong) option

Bringing the Standards for Mathematical Practice to Life In Classrooms
Ruth Parker
- Daily objectives are too fragmented of a way to learn math. Instead, there should be 6 to 8 units of study a year where you are looking at the same math on the first and last day of the unit (see Phil Daro on grain size). Then, students should be able to answer “what are you trying to figure out right now?” instead of “what math are you learning today?”
- Big mathematical ideas are never fully mastered. They deepen in complexity over time. Therefore, learners should encounter:
  • fragile understandings
  • periods of cognitive dissonance
  • mistakes as sites of learning
  • states of not knowing… yet
- Can You See? (Teacher starts by asking questions, then turns it over to the student)





            - 2/5?
            - 2/3?
            -1 divided by 2/3 ?
- a way for students to gain addition fluency
- after doing an example or two, ask students to come up with their questions and explore them

Thursday, April 16, 2015

NCTM Day 1


The sessions I attended and three things I want to remember from each one.

Incredible Math Tasks! Supporting the Productive Struggle in Learning Mathematics
Bill Barnes and Jenny Novak
- Five Practices for Orchestrating Productive Math Discussions by Stein and Smith
- Choose a learning target and find a task that matches it, then:
- anticipating, monitoring, selecting, sequencing and connecting

Building Middle Grades Ratio, Proportions, and Proportional Reasoning Essential Understandings
Travis Olson, Hannah Slovin, Melfried Olson
- Keala makes pizza at a rate of 3 pizzas in 5 minutes. Casey makes pizza at a rate of 4 pizzas in 9 minutes. Who is faster?
- You cut 2/5 of a piece of a board. The piece is ¾ of a foot long. How long is the whole board?
- Two solving methods I hadn’t thought about:
(2/5)x = 3/4
Scale up both sides by 2 ½
(2/5)x = (3/4)(5/2)
(2/5)x = 3/4
(1/5)x=(1/2)(3/4)
1x = (5)(1/2)(3/4)=(5/2)(3/4)

Developing Fractional Reasoning through Number Talks
Ann Dominick and Sherry Parrish
- Fractional Reasoning: Distinct numbers, parts of a whole, denominator, numerator, equivalence
- Comparing Fractions: benchmarks, unit fractions, distance from whole, compare numerators, compare denominators
- Whole # Multiplication: Partial products, doubling and halving, repeated addition, breaking factors into factors

Getting Students to Pose Powerful Questions
Jane M. Wilburne
- When you ask a question, you are more interested in finding an answer
- People don’t ask questions when they are angry/upset/troubled/victimized, other people around them have more knowledge/power --> intimidation, can’t formulate a question, haven’t felt supported in the past, lack of time
- Promoting classroom questioning: model questions, multiple platforms for students to ask and answer questions, invite questions, safe environment, plan for questioning (prompts)

Getting Students to Argue in Class with Number Sense Activities
Andrew Stadel
- Is the circumference of a Nalgene bottle greater than its height? Students improve their justification each time in first explaining to someone who agrees with them, second explaining to someone who agrees with them, and third convincing someone who disagrees with them, all while using the sentence frame: “I believe the circumference is {less than/equal to/greater than} the height of the bottle because _______”
- Each answer faces in a different direction, once they are done justifying, get the option to choose direction change
- Sentence frame for justifying prediction “I noticed ____, so I _____”

Tasks That Build the Essential Understandings in Middle Grades Algebra
Zandra de Araujo, Barbra Dougherty, Fay Zenigami
- Tasks:
  • g - 227 = 543. g - 230 equals what?
  • Write an equivalent expression for 5 - 7m
  • d + 1 is less than d + 3. Is this always, sometimes, or never true?
- Flexibility, Reversibility, and Generalization problems
- Essential Understandings in Practice book coming out in the fall

Teachers as Designers: Mindset and Multidimensional mathematics in Classrooms
Jo Boaler
- even if you are not aware of making a mistake, your synapses will still fire because you are making a mistake (or possible because you are thinking hard?)
- pose the problem before teaching the method

Michael Pershan
(I sadly came in at the end of this, so he was the only speaker out of six that I saw)
- Problems with our hints: too vague, kill thinking, don’t have reasons, we improvise too much
- For better hints: add context, add reasons, be just specific enough. Example: If you’re dealing with lots of data it can help to make a table to help us notice patterns.