#EduRead: Creating a Differentiated Mathematics Classroom

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.

#EduRead: The Case For and Against Homework

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

#EduRead: Teaching Students to Ask Their Own Questions

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?

#EduRead: Homework: A Math Dilemma

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

#EduRead: Mental Mathematics Beyond Middle School

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