This week's article is "Why I stopped putting grades on papers".

My Thoughts

• I like the idea of promoting discussion and conversation but I feel like I'm being dishonest by waiting until later to post the grade. 
• I asked Ashli "For students who do no have access to the online grade book, how did they ever know how they were doing in the class?" Her response "I was fortunate that my school had computer labs that students can use before/after school and during lunch in addition to the laptop cart in my room (it was shared between the math department but kept in my room), so that wasn’t a problem I dealt with. In the past I had posted quiz scores using students ID numbers on the wall and updated them about once a week."
• I never know exactly what kind of feedback/comments to give. According to the archive, we prefer provoking questions rather than comments.
• I've been thinking about using Frank Noschese's quiz idea where students check their work and write their own feedback and then turn it in, so that the teacher assigns a grade later (I'm assuming?). Do these methods align? (lol just reading the archive where Shelli mentions this too...hooray)
• What I've read so far is a list of common errors and making a key where students categorize their errors or we can just mark symbols or numbers to save time. I like the idea of a bookmark. Couldn't this go in our INBs?
• I've been thinking about Bowman's sbg intro using angry birds and I've been thinking, why can't I just grade like that? It seems so simple.
• It's like I have all these assessment ideas in my head floating around and I just somehow need to tie them all together. More on that later, I suppose.
  
  
  

This week's article is Even Geniuses Work Hard by Carol Dweck. In this article, Dweck again works with the ideas of fixed vs growth mindsets, which many of us are familiar with due to her book, Mindset.

Quotes:

• "Research has shown that praising students for the process they have engaged in—the effort they applied, the strategies they used, the choices they made, the persistence they displayed, and so on—yields more long-term benefits than telling them they are "smart" when they succeed."
• "Students who take longer sometimes understand things at a deeper level."
• "It is crucial that no student be able to coast to success time after time; this experience can create the fixed-mindset belief that you are smart only if you can succeed without effort.
• "When presenting learning tasks to students, the teacher should portray challenges as fun and exciting, while portraying easy tasks as boring and less useful for the brain. "
• "When students initially struggle or make mistakes, the teacher should view this as an opportunity to teach students how to try different strategies if the first ones don't work—how to step back and think about what to try next, like a detective solving a mystery."

 

My Thoughts

• It's humbling how much our students' mindset can depend on our choice of words.
• Pointing out the use of the mathematical practices seems like a great way to praise process.
• My mentor emphasized "individual think time" where students try something on their own before any collaboration. I do this by asking kids to "stare at the paper" for 1 minute (using my timer of course) I don't let them talk until the timer goes off. This can help students focus on deeper thinking over time.
• What ways can we show progress/improvement in student work other than pre/post tests?
• I like the phrase "grade for growth". How can I apply that?

 

This week's article is Faster Isn't Smarter.

• What she calls constructive struggle is not something new to us, we know productive struggle
• How do we choose the right level of struggle? How do we differentiate the struggle for different levels of learners?
• How do we challenge students without turning them off to math forever?
• "Constructive struggling can take place when a teacher decides that one demanding, possibly time consuming problem will likely provide more learning value than several shorter but more obvious problems."
• This concept aligns to Common Core ideas: "As students engage in the constructive struggling needed for some of these problems, they learn that perseverance, in-depth analysis, and critical thinking are valued in mathematics as much as quick recall, direct skill application, and instant intuition."
• I feel like a baby teacher....I don't any of the things that seem hard to students because they are hard to me too. Sad face. 
• Can students both succeed and struggle on the same problem?
• How can we extend problems in a natural way that doesn't break students out of their 'flow' or mental focus?
• How can we take away the focus of a 'right' answer and move to a valuable experience?
• Maybe students leave their cups on green longer because it's a visual for their peers as well. It's the reverse of not wanting to try, scared to fail...it's wanting to try harder so peers so don't think your failing.

This week's article is Creating a Differentiated Mathematics Classroom.

• "Student differences in learning mathematics tend to cluster into four mathematical styles."
• Mastery- works step by step, favors repetitive practice, and struggles with abstraction
• Understanding- looks for patterns and reasons, favor concepts and reasoning, struggle with collaboration and routine drill and practice
• Interpersonal- through relationship, conversation, and association, favors cooperative learning and real world applications, struggles with independent seat work
• Self-Expressive- visualize and create images, favors exploration, and struggles with step-by-step computation
  
• The big idea with differentiated instruction is that you have the same learning goal and expectation for all students and they can take different paths to achieve them.
• Resource: Differentiated Instruction Learner Profile
• Resource: Me at a Glance
• Resource: Learning Styles Discussion
• Resource: The Four Types of Mathematical Students
• Resource: Math tools and Strategies for Differentiating Instruction and Increasing Student Engagement
• Resource: Styles and Strategies for Helping Struggling Learners Overcome Common Learning Difficulties
• Resource: The How-To's of Planning Lessons Differentiated by Learning Profile
• Resource: Task Rotation
• Resource: Assessing Middle and High School Mathematics and Science Supplemental Downloads

My Thoughts:

• I'm still envisioning some kind of template whether for class work or homework split into the four different types. Maybe two problems per type and they have to complete 5? That way they can choose their strongest two styles and then attempt one they aren't very comfortable with.
• If the template was simple and versatile enough, it could work for quizzes, tests, homework, and class work.
•  When I think about choice boards, I think I would have to develop one choice board of options that could last the whole school year. Each option would have to be hard enough that I would feel okay about a student picking the same option all year long. That seems tough. 
• If students are taking multiple paths to achieve the same goal, that sounds like a lot of work to assess all of the paths.

This week's article is The Case For and Against Homework by Robert Marzano. This week's article explores some of the research behind the ever-popular issue of homework. For most of us, homework can be a hot topic, so I'm really eager to hear your thoughts as we chat about the article.

• Students that make below a certain grade must complete homework
• Homework packet due on test day
• Working for a specified amount of time, then reflecting on problems that were easiest, hardest
• Ranking problems from easiest to hardest
• How can we create closure on homework assignments? Reflection?
• If homework doesn't improve learning, then eliminate it.
• How can we be purposeful about the homework we assign?
• We want students to think about the work we do...what other ways can we make them think rather than assigning a bunch of problems?
• I'm thinking about error analysis, contrasting cases, sort problems into categories, reflecting on differences in problem types, explaining steps in a problem in writing, creating different versions of problems, giving a problem with the answer and they show steps, etc.
• Resource: Adult Input Page

This week's article is Teaching Students to Ask their Own Questions. This week's submission is by the authors of Make Just One Change and as we all know, very small changes in our teaching practice can have huge impacts in student achievement. With the increased emphasis in education on "inquiry learning", I think this week's article will really push me as an educator to make small, but significant changes in my classroom.

Quotes:

• Love this: "When you ask the question, you feel like it’s your job to get the answer, and you want to figure it out."
• "When students know how to ask their own questions, they take greater ownership of their learning, deepen comprehension, and make new connections and discoveries on their own."
• "The Question Formulation Technique (QLT) helps students learn how to produce their own questions, improve them, and strategize on how to use them."
• "In the classroom, teachers have seen how the same process manages to develop students’ divergent (brainstorming), convergent (categorizing and prioritizing), and metacognitive (reflective) thinking abilities in a very short period of time." 
• "Teachers can use the QFT at different points: to introduce students to a new unit, to assess students’ knowledge to see what they need to understand better, and even to conclude a unit to see how students can, with new knowledge, set a fresh learning agenda for themselves." 
• "Teachers tell us that using the QFT consistently increases participation in group and peer learning processes, improves classroom management, and enhances their efforts to address inequities in education."

QFT Steps:

1. Teachers Design a Question Focus (Not a question. A statement or visual/aural aid)
2. Students Produce Questions (The four rules are: ask as many questions as you can; do not stop to discuss, judge, or answer any of the questions; write down every question exactly as it was stated; and change any statements into questions. ) 
3. Students Improve Their Questions (Categorize questions in open-ended and close-ended and practice converting between, realizing that phrasing affects depth. and quality.)
4. Students Prioritize Their Questions (Teacher offers guidelines, students zero in and plan concrete action steps for getting information.)
5. Students and Teacher Decide on Next Steps (Work together.)
6. Students Reflect on What They've Learned (Making the QFT completely transparent helps students see what they have done and how it contributed to their thinking and learning. They can internalize the process and then apply it in many other settings.)

I love questioning so I really enjoyed this article. I can't really think of how this would apply to math. The article mentioned analyzing word problems, maybe they could guess what the question will ask before seeing it? Although that doesn't seem like a good use of the technique.

It seems like it would work well for projects and possibly the beginning of a unit. You would have to make sure to give enough guidelines that they would pick the questions your unit actually answers.

What do you think?

This week's article is "Homework: A Math Dilemma and What to do About It". The homework issue is typically a topic that comes up about this time every year as teachers starting reflecting on the 13-14 school year and brainstorming how to improve for the upcoming year.

My Thoughts:

• It all sounds nice.
• I'm not going to do it.
• I did not assign homework this year and I did not miss it.
• I always feel guilty about this.
  

After reading the archived conversation:

• If assigning differentiated hw, or allowing students to pick a certain amount to complete, you would have built in reviews for tests: go back and complete the problems you didn't do before.
• Would students complete homework based on past concepts that they should have mastered which also builds fluency and retention?
• What if you created 1-2 problems per learning style and asked them to complete problems from two styles? You could create a template of sorts.
• Resource: Homework Rubric
• Resource: Do you have a boring worksheet that you want to make more interesting?
• Resource: Conceptualizing Drills
• Grade using peer feedback or self assessment?
• Students discuss answers together and collaborate to create the answer key, verified later by teacher- prompts discussion of who was right and why

This week's article is "Mental Mathematics Beyond Middle School". I'm really excited to chat about this article because this is a topic that has come up in twitter chats in the past, especially when discussing multiplication facts, etc. We've all had frustrations with our students not recalling their elementary arithmetic skills or putting things like 10x35 in their calculators. How can we develop these mental math skills in our secondary (and post-secondary) math students?

Quotes:

• "Number sense matures with experience." Thank God!
• "Mental math makes easier the understanding of inverse operations.
• " If students have never been asked to solve problems without calculators and if they have not learned calculator- free strategies, then mental math will never be an option that they choose." 
• " Having specific objectives that are clearly known to students is part of building a successful program." 

My Thoughts

• I really like the idea of "Think Twice Mentally"- an authentic way to integrate writing into math.
• I am also a huge proponent of mental math. I found that doing it as a bell ringer every Monday made a significant difference. Throughout the week students would ask if they were allowed to use the calculators. Just my emphasis on one day a week made them more aware of their dependency.
• Quite a few students took it as a personal challenge to use the calculator less throughout the year.
• Throughout lessons and activities I would say "Does anyone know the answer in their head?" similar to the way they author said "Here's a good chance to use our mental math." 
• I like the idea of a two part assessment. How often can I incorporate this?
• Does mental math mean not using a calculator or doing everything in your head?
• I'm a fan of the included example problem sets. I need to think of concepts that I hear adults complain about teenagers not knowing and cover those as well- although I like the problem sets I used last year. I thought they were well thought out and developed nicely over the course of the year.
• Resource: http://www.estimation180.com/blog

This week's article, Raising a Moral Child was submitted by @jrykse for this week's chat. While the article is aimed at parents, quite a bit of it would apply to our classrooms as well.

Quotable Quotes:

• Praise is more effective than rewards
• When parents praise effort rather than ability, children develop a stronger work ethic and become more motivated.
• Praising their character (rather than behavior) helped them internalize it as part of their identities. The children learned who they were from observing their own actions: I am a helpful person. 
• When our actions become a reflection of our character, we lean more heavily toward the moral and generous choices. Over time it can become part of us.
• If we want our children to care about others, we need to teach them to feel guilt rather than shame when they misbehave.
• The most effective response to bad behavior is to express disappointment. 
• parents raise caring children by expressing disappointment and explaining why the behavior was wrong, how it affected others, and how they can rectify the situation.
• The beauty of expressing disappointment is that it communicates disapproval of the bad behavior, coupled with high expectations and the potential for improvement: “You’re a good person, even if you did a bad thing, and I know you can do better.”
• Children learn generosity not by listening to what their role models say, but by observing what they do.
• People often believe that character causes action, but when it comes to producing moral children, we need to remember that action also shapes character.

• At the end of the year, I like to give an award to every student in my class. I try to pick something that shows I really noticed them but at the same time I try not to be negative because I don't want that to become a self-fulfilling prophecy
• The most loved teacher at my school is the one who is always giving students guilt trips vs strict discipline. They understand that she knows they are good students who sometimes do bad things but are intelligent enough to fix them.
• How much more can we as teachers turn to modeling rather than preaching and repeating ourselves? What behaviors we want to see in our students should be what we begin to model without speaking.
• For example, I preach to my students about reading directions but how can I model myself doing that visibly?
• Can I model my mathematical thinking through modeling or writing rather than verbally?
• What does this look like in the classroom? "You're a quick thinker" vs "You finished your work quickly"?
• Can our praise of effort and character as high school teachers make a dent in the terrible experiences and feelings about math that students have had in the past?
• What behaviors have I modeled without knowing it?

• A often believe that character causes action, but when it comes to producing moral children, we need to remember that action also shapes character.Photo

This week's article, "What does Multiplying Two Candy Bars Really Mean?" is about writing in math class from the April 2014 issue of Educational Leadership. 


Quotes:

• "By having students write word problems that encompass a variety of contextual situations, teachers gain insight into how students have interpreted a mathematical idea as well as their preferences for problem-solving strategies"
• "By having ELLs write their own word problems using situations familiar to them, as well as language they can manage, teachers can more easily assess their mathematical abilities."
• "As students share their word problems with the class and invite their peers to solve those problems, they're led into discussions, both in small groups and as part of a whole-class discussion, about the meaning of their problems and how best to solve them."
• "A problem-posing activity can bring in many forms of communication, such as writing, speaking, reading, and listening, which benefit not just ELLs but all students."

My Thoughts:

• 'Problem-posing activities' would be a great tool for the beginning of the year or as a preview at the beginning of a unit; also could be a alternative way to assess.
• This could go along with My Favorite No or error analysis
• Writing their own problems could be an example of application problems for students who are using INBs or formula sheets as a resource; takes the depth past just a procedure

This week's article: How Good is Good Enough? is from the December 2013/January 2014 issue of Educational Leadership magazine and the article is about what "mastery" really is.

My thoughts:

• This article was depressing.
• I don't even consider myself a master; don't know how to teach mastery or create these type of tasks
• If my assessments and grading are of low standards now and I have kids doing poorly, then raising my standards would mean the whole class doing poorly!
• Just a reminder of how unprepared me and my students are for any Common Core aligned exams.

This week's article: The Many Uses of Exit Slips. It is from the October 2012 issue of Educational Leadership magazine and the article definitely touches on so many useful topics, from classroom closure to formative assessment.

 My thoughts:

• While the last three types of exit slips are interesting, I definitely would use the first type most.
• The easiest way for me to do this would be to create a question or two ahead of time and pass out index cards at the end for them to respond.
• What happens if you don't get through the lesson and your exit slip question doesn't apply (yet)? I guess that's where the other three types come in.
• I want to mostly give students problems for the exit slip. Could I them group them by common errors the next day and see if they can find their error as a group without me telling them? Could this be a way to receive immediate feedback in a social setting? Does that mean I need to give them another problem to use that feedback effectively?
• Would it be acceptable/effective to have the problem fully worked out and projected and ask students to identify their error and write it down on the index card? This incorporates writing and feedback. Would there be a more useful way to organize this so students can refer to their common errors moving forward?
• Refer to druin's post; make a powerpoint ahead of time?
• Laminate exit slip cards that can be written on with dry erase marker and reused?
• Is this sustainable on a daily basis?
• When my class spends most of the time practicing problems, what can I ask instead of a problem of the day that will give me feedback?
• I really like the idea of error analysis; if they can see the error and correct it, I know they know it; if they can see the error but not correct it, I know they are halfway there; if they can't see the error at all, they're probably lost. For the last two groups, I could start class the next day with a correctly worked example and the original incorrect one so that they can compare. The top group could...work out a new problem or a harder version (enrichment)?
• I like the idea of sorting kids by exit slip resposes; could keep groups different on a daily basis.

This week we will be reading the article 'How Am I Doing?' from the September 2012 edition of Educational Leadership. The theme of the magazine was Feedback for Learning and this article is about how to provide effective feedback to our students.

My thoughts:

• How in the world is there time to regularly give such in-depth feedback to students? 
• I need to work on starting class with "here is your goal of the day" and ending it with "did you accomplish our goal?"
• Do we give a lot of this feedback verbally without realizing it? Students have no 'hard copy' to refer back to.
• Could we use gallery walks as a way for students to give and get immediate feedback but take some of the toll off of us?
• For those that have a lot of board space, sending as many students to the board to practice helps us as teachers see more at once and give verbal feedback with the immediate opportunity for students to use the feedback.
• I read in the archive about asking advanced student for suggestions; we just read in the article that those students have no problem doing this. We need to ask the struggling students what feedback would help them if those are the ones that need this the most.
• How can we make feedback social? Read Michael Pershan's "Immediate Feedback Is Too Soon For Feedback"

This week we will be reading the article'Advanced Math? Write!' from the November 2002 edition of Educational Leadership. The theme of the magazine was Reading and Writing in the Content Areas and this article presents an easy to implement way to encourage writing in the math classroom.

My thoughts:

In an effort to integrate writing into our classrooms naturally and in a way that is easy to assess, could we:

• Ask students to pick one problem from every quiz/test and explain the process in words.
• As a review (or when a substitute is there), give them a random page number from their INB and ask them to summarize the concept/process in writing.
• Ask students to write a monthly reflection of something pertaining to class: a test, a quiz, a review game, an activity, a worksheet, seating arrangement, etc. This would also double as interesting feedback to the teacher.
• As an exit slip, write a summary of the lesson in text/slang or every day language and have them rewrite technically with correct vocabulary.
• On a test or quiz, give them a graph, diagram, chart, or table (pertaining to current classwork) and ask them to write everything they know about it, using as much vocab as possible.
• For those that use word walls, have them randomly pick two words and compare and contrast.
• Give a problem that is worked out incorrectly and have them to explain and correct the error in words only.