A Facebook Emoticon Poll ... favorite online formative assessment tool?

I'm having a bit of fun on my Facebook page ...
Posted this informal poll!

Will you click the picture and participate?  It will take you to my Algebra's Friend Facebook page where you can vote using the emoticons!

While there ... feel free to "like" the page!  I post interest math articles, pictures, and the occasional blog post!

About learning checks #MTBoS30 - 18

After my last post, a couple of colleagues said they wanted to know more about learning checks. I hope this helps ...

About learning checks …

I am using Unit 3: Graphs and Equations of Quadratic Functions to provide a concrete example.  The standards we address in this unit include:

• Write the quadratic function given three specified points in the plane
• Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
• Transform a quadratic function f(x) = ax2+ bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x)
• Formulate quadratic and square root equations using technology given a table of data

We have a separate unit following this one for solving quadratic equations, using the discriminant, and applications.  

We spent four class days on Unit 3.  We tested on the fifth day.

You can see the outline and most activities here.  You’ll see that I borrowed heavily from MTBoS colleagues in this unit and included references for the activities.

Back to learning checks …

On Day 1 there was no learning check which was typical for the start of new units.  On those days I might highlight the most missed question on the previous unit test as a warm-up or I might use the warm-up time for to introduce the new unit.

On Day 2, students took a learning check on basic attributes of a quadratic function.  Here is the Google Form  I used.  Students did well on it - total average being a 91.  The most missed question was #4.  We discussed that question in the next lesson.

On Day 3, students took a learning check on completing the square.  Here is the Google Form I used.  Again, most students did well, the class average was 88.  The most missed questions were #4 and 5 which told me that while they understood some of the steps in completing the square, they had difficulty following through on those steps.  I wasn’t surprised that we needed more practice.

On Day 4, students took a quiz. Because this unit was  short, the quiz was given after a lesson and was short.  (Our district provides a calendar for units, and in our school we are expected to stick very close to the calendar.)  Here is what the quiz looked like on that day.  The results were not as good as I hoped - overall average at a 70.  The test was scheduled for the next class day.  So I sent students email offering a study session before and after school.  (We are on an A/B day so students had time to get their quiz results in email, ask questions before/after school, and attend a study session if they wanted to do so).

On day 5, students took a test over this unit.  The overall average was in the mid 80s.

So about learning checks …

While I said I do them daily, we don't typically take a learning check on the first or last day of a unit. We don't take a learning check on a day when I give a quiz. So in most units of five to seven days, there are 2 to 4 learning checks.

They are most often multiple choice.  Sometimes I require students to show work and turn in that work when they submit their Google Form.  Other times, I only use their a,b,c,d responses to make judgments about their understanding.

Learning checks are short on purpose.  Most days I don’t allow more than 10 minutes, sometimes 15, for completing the learning check.  

I use Google Form because I can use Flubaroo to grade and email feedback instantaneously.  Students know which ones they missed.  They can go back to the Google Form to look at those questions.  With instant feedback on what’s incorrect, they can then determine if/when they want to attend tutorials.

Because of our limited time in class I depend on tutorials heavily. I rarely spend time in class discussing previous assessments except for one or two most missed questions.  Instead, I invite students to meet with me before/after school or at lunch to go over their work.   I offer 5 standard tutorial times each week (administration requires at least four) and more if needed.

My administrator asked me if I spiraled previously learned content in the learning checks.  I didn’t this year.  Currently a learning check is only about the previous lesson.  If I do learning checks again, I might do 3 - 4 questions on current content and 1 - 2 questions on previously learned content.  That would not be difficult and might improve the use of learning checks.

My personal opinion is that learning checks were helpful this year for a couple of reasons.  One they “normalized” assessment.  Once students realized it was an everyday thing, they no longer stressed over the idea of assessment.  Second, the learning checks became a part of our learning … instead of just a way to get a grade.

Learning checks are only a small part of the big picture of assessment.  Learning checks work for me in combination with the informal checks for understanding in the classroom (whiteboards, observation, questioning/discussion) and classwork in which students show/explain their work.

I’m sure there are ways to improve … how do you check for understanding in your classroom?

Assessment - it's more than a test! #MTBoS30 - 7

What is one significant practice in teaching?

Assessment!

You see it everywhere ... but it's so much more than a "test" marked right or wrong!

Assessment starts with planning ... it's the first step ... not the last!

What do you want students to know AND how will you know they know it?

But it's more than knowing what questions to ask at the end of a unit ... the bigger issue is how do you know students are getting "IT" all along the way!?!

Enter ... FORMATIVE assessment!

So formative assessment is not just a quiz over the lesson marked right or wrong!

It can't stop there ... otherwise the quiz is just so much one more grade ... 

What do you want to know about that lesson?

 ... can students demonstrate the process?

     ... can they explain the thinking that is involved?

          ... can they use the lesson topic in a way not demonstrated in class?

   ... do you want to know if students can just find an answer mimicking the notes given in class?

And now that you have designed the perfect question or task ... that's still not enough!

How will you respond to students?

... a grade at the top of their paper?

    .... a written note or two about their work?

         .... will you discuss it in class?

                 .... what feedback will students get?

                      ... what will they do with that feedback?

And yet there is still more ... yes, this one "formative assessment" amidst many still needs more attention!

What will YOU do with students' results??  You gave a grade, written feedback, or discussed it in class?  But how will the results affect your planning of the next lesson?

And people wonder about the fuss over assessment!  Yes those BIG tests ... there is so much we could write about those ... but really ... it's the day to day FORMATIVE ASSESSMENT that is ... 

... constant

    ... the daily grind or the daily AHA

           ... it's the BRAIN DRAIN - the really hard work!

Assessment ... it's the underpinning of success in the classroom!

Nearpod! Formative assessment in progress!

Today our lesson was about solving absolute value equations and inequalities.  Instead of giving notes, demonstrating solving, and then giving practice, I prepared sets of problems already worked out.  I asked students to study them, to take time to notice was was happening in each problem, to share their noticings, and then work a sample using their ideas.

So our first set looked like this:

Students shared their "noticings" and outlined the steps they saw.  One student wrote: "The distance between the five numbers and -4 can be positive or negative so you create 2 equations.Second once you set up your 2 equations with a positive and negative y, you solve for x.Third you should have two different answers for x." All of their statements are captured on Nearpod - an amazing app!


When they worked out examples, I shared their work with the class and we talked about strengths and misconceptions.

One misconception was "making one" by dividing by 10 on each side of this equation.  Several students throughout the day said that it was not possible to divide 0 by 10.

We talked briefly about fact families.  Can we multiply 10 by any number and get 0?  Can we multiply 0 by any number and get 10?


A second misconception was about absolute value equaling a negative number.

This student said the solution was not possible because 7x can't equal a negative number.

We discussed the solution to the equation 7x = -3.

Then we discussed the difference between |7x| = -3.




Tonight I can look back through all the slides again to see students' thinking and to determine key ideas to reinforce in our next class.

I can see Nearpod being a definite go-to teaching tool!  Nearpod and GoFormative have similar qualities.  Now to determine in which situations one is better than the other!

#70 Days Thinking Through Technology 2: Assessment Tools

Goal 1: Where possible modify and redefine our work using technology. 

I'm looking at three or four tools for assessments:

My number one go-to is Google Forms. There are a couple of things about forms I like.  One is that you can use them as generic forms.  I can still create the paper copy quizzes - project them, or put a class set of quizzes in sleeves.  Students can work out the problems on paper, and enter their answers in the forms.  I can get a quick grade using Flubaroo, sort the papers - reviewing the ones that scored poorly, spending a bit more time on those.

I created several Socrative quizzes last year so I have those handy for use this year.  It will be easy to tweak them, make them fit this year's  classes.  I used Socrative for short learning checks.  You can leave the "classroom" open over night as well - or open it for students who need to work on a quiz from home.  I know there are integrity issues that way, but I ask students to turn in work to support their answers on Socrative.

Kahoot and KnowledgeHook are great for informal assessments that don't affect grades.  I can quickly tell what questions are giving students difficulty, where we need some additional practice.  And they add a definite element of fun to the room!  I rarely create a Kahoot game from scratch.  Most often I search for one already made and make any adjustments needed.  One thing I'd like to do this year is to get students to create Kahoot games for personal review.  

I didn't use Edmodo last year, but I want to revisit again this year.  The "snapshot" feature intrigues me.  They've added the Texas TEKS for both Algebra 1 and 2.  I can see assigning the Algebra 1 snapshot questions to preview a unit, to determine what students retained from previous courses, to get a read on what they know.  Until I get the hang of them, I don't envision assigning a grade to the snapshots.  I'm curious about the questions and if they are worthwhile.  Has anyone used the Edmodo Snapshot feature??

Other informal assessment tools that I have used briefly are IXL and MangaHigh - both without subscriptions - no money for those.  I keep wanting to use Quia because I hear so many teachers suggesting it but writing the math in laTeX is challenging for me.  Does anyone else use Quia ... and if so, what's the key?

Are there other online quiz programs that are suitable for math?  Share in the comments!

Addendum ... just read an article on 10 formative assessment tools for 2015.  I need to check out Go Formative.

Electrifying and Intriguing!

Yesterday was one of those rare days in our classroom ... an odd day out ... a day where I could choose to explore topics outside of our typical planned curriculum.

First up, I wanted to learn about Kahoot.  So I found a public game that had questions suitable for review for our upcoming benchmark test.  I told the students I wanted them to teach me how to play.  And teach me they did!

1. As soon as I said we were going to play Kahoot, the atmosphere was electrified!  Students were beyond eager to get started!
2. I set up teams of 4 but after a few questions, students began suggesting that it would be more fun to play in pairs ... more students engaged in the problem solving!
3. The game we used was created by a generous teacher unknown to us who made his or her work public.  For that we are thankful.  But we learned 30 questions is a bit long!
4. Students pointed out that some questions had too long of a time limit ... 120 seconds were just too many.  They suggested keeping most questions at 30 seconds.
5. I learned that we will need an answer document to hold all students accountable. 
6. Kahoot definitely will be a game of choice for future formative assessment and review sessions!  I can envision starting class with a 10 question Kahoot reviewing the previous day's work.

In the second half of class I wanted to explore one of the new Desmos class activities ... PolyGraph.  Kahoot was such a big hit that I thought maybe Polygraph would be a let down ... but it was NOT!  Students said, "This is too much fun!"  They were not eager to quit and in fact, kept playing even when I offered other choices.  We played the parabola version of PolyGraph this time.  But very soon we will be working with Rational Functions ... and I envision PolyGraph as a great classroom activity for reinforcing vocabulary and attributes of the functions.

Our curriculum is mapped out fairly tightly, so a "free" day doesn't happen very often.  The day provided the perfect opportunity to test new technologies to determine how best to use them!

Island Study

So today's activity went very well.  The noise level was high ... but all due to constant math talk!  The very talk you want in your classrooms!  (I didn't post a picture with students - no faces allowed but here is a picture of our empty space ... waiting for students to arrive on the islands!)

This idea comes from Cheesemonkey's post ... read it here!  Thank you for sharing.

I am drowning in grading.  Giving feedback is a must!  This process is great for simplifying peer to peer feedback as well as teacher feedback.

To break up the monotony of working in desks, I brought in beach towels - 10 of them ... to create "islands" ... oases of math learning!  On each island there is a group whiteboard, 3 markers, 3 calculators, and necessary handouts (could be done without any but I'll explain why they were helpful).

As students entered they set their bags aside, brought only their math notebooks with them, selected an island and had a seat.  I required no more than 3 people to an island.  I had a few islands with just 2 people.

I gave each team an index card ... students put their names on it.

Then I gave instructions ... our topic of the day is solving systems using matrices.  The first half of class was practicing solving 2 x 2 matrices by hand, the second half of the day was practicing solving 3 x 3 matrices by calculator.  (We have 90 minutes ... every other day ... rotating schedule).

I projected 3 systems on the board.  In groups students solved each system using matrices ... clearly outlining the determinant, inverse matrix, and matrix multiplication.  As groups finished a problem I checked it and hole-punched their index card.  When punched, students immediately moved on to the next problem.  Groups had to rotate who did the writing and who coached.

As students finished the 3 systems that were projected, they moved to a handout with word problems - practicing the same skill but first finding the equations.  So having the handout served as a differentiation tool ... students who worked quickly through the projected problems could move forward.

Students clamored for their hole punches!  Amazing. Free.  Simple!

About half way through we switched gears so that students could learn how to solve systems of equations using their calculators.  To get a hole punch every member of the team had to have the answer on his/her calculator.

Teams earned about 12 - 16 hole punches in the class period.  BUT much more than that ... every student was coached in how to solve the problems of the day.  Every student got feedback.  Every student had support for the parts they found difficult.

And the energy was high.  The conversations totally about math.  And they clamored for their hole punches!  Amazing. Free. Simple!

Central Park via Desmos

Today was a rare day where one set of classes had an "extra" day before the test.  We had reviewed and I felt good about student understanding so I decided to spend part of the class period on "enrichment."

Our enrichment activity today was Desmos' Central Park.  Our next unit is on systems of equations in which our focus is on problem solving.  Students need to be able to write equations for problem situations.  I thought Central Park would be an interesting formative assessment to see how well my students can interpret a problem creating the necessary equation.

When I worked through Central Park on my own, I enjoyed the process.  I also thought the activity might be a bit easy for my students.  I guessed that only the last question might give students pause.

In class students were engaged totally in the activity.  Many finished it in 15 - 20 minutes.  That's what I expected for the majority since they are advanced algebra 2 students (many of them are only in grade 9).  What was more interesting to me were the few students who struggled over the last equation and their response to the struggle.

• Students would delete their whole equation instead of making adjustments.
• Students struggled with multiplying the number of dividers with the width of the dividers.
• The part they gave students the most difficulty was recognizing that they needed to divide by the number of dividers plus 1.
• Whey I suggested they go back to problems with numbers and write those down to analyze the process they were hesitant.

Before I do this activity again next year, I want to create some follow-up problems - especially for the students who struggled.  One activity that I think might help are problem situations without numbers.  I used to have those for my  middle school students ... I need to find some for my algebra kids!

#70Days Will you stop putting grades on papers?

Whoa!  I just watched "Why I stopped putting grades on papers" and was blown away at the possibilities.

First thought at the title ... that won't work in my community!  Second thought ... write a comment on every paper every time?  No way!  Third thought ... but imagine the possibilities in awesome conversations!

On Wednesday night we are discussing this blog post on #EduRead.  We meet online at 8 central time and if you have even a few minutes I hope you will join us for the discussion.

Maybe you already grade differently than the norm.  I read a LOT about SBG (standards based grading) online.  Our school doesn't participate and in fact a few years ago, when the math department tried it, there was a district wide uproar.  I know I can't go down that road.

But there is no reason I could not withhold the grade until after the conversations around the feedback occurred.  The idea that students might actually examine their papers, read the feedback, and talk with classmates about their work is powerful!

I have these questions ...

• In recent reading I realize that students need quizzing often, even daily!  Would you write comments on 150+ papers daily?  Or is this routine saved for the more developed quizzes or tests?
• And over time would you develop a set of typical questions to put on papers to help automate feedback at least to some degree?  I realize it couldn't be canned feedback and be helpful.

After listening to the video and re-reading the blog post, I went to the article that Ashli noted - Working Inside the Black Box: Assessment for Learning in the Classroom.   Two key ideas from this article that I plan to put into action include:  better questioning and student reflection using the red, yellow, green ideas.

IDEA 1: One simple and effective idea is for students to use “traffic light” icons, labeling their work green, yellow, or red according to whether they think they have good, partial, or little understanding. These labels serve as a simple means of communicating students’ self-assessments. Students may then be asked to justify their judgments in a peer group, thus linking peer assessment and self-assessment.

IDEA 2: Another approach is to ask students first to use their “traffic light” icons on a piece of work and then to indicate by hands-up whether they put a green, yellow, or red icon on it. The teacher can then pair up the greens and the yellows to help one another deal with their problems, while the red students meet with the teacher as a group to deal with their deeper problems.  This would create a student self-assessed opportunity for differentiation.

IDEA 3:  A useful guide is to ask students to “traffic light” an end of unit test at the beginning of the unit: the yellow and red items can be used to adjust priorities within the teaching plan.  This could be especially helpful in Algebra 2 - first semester - when much of our content reviews Algebra 1 topics.  You could also then review the traffic light pattern towards the end of the unit to help students determine an efficient review plan.

I look forward to hearing what others already do, and how they will respond to this article!

#70Days Systems of Inequalities Lesson Planning

A bit of lesson planning tonight ... still thinking about systems.

This year I want to organize our notes using the Cornell formatting.  In the first unit the notes are scripted with fill in the blank.  In this second unit, I've included the focus questions and will guide students in taking notes in the main section.

Students will start in small groups.  They will discuss the guiding questions and make notes on whiteboards.  Then we will reconvene as a whole class to discuss together, compile their thoughts, and make notes.  Whole class discussion is described here.

After discussing the notes, students will meet again in their groups to work through the given problem. Students will create posters of their work to display.  As students are working, I want to try a formative assessment strategy entitled, "What are you doing and why?"  It's #73 in the book, Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning.  After students have had time to get well into the problem, I will ask them to "press pause" and respond to the question, "What are you doing right now? and "Why?"  Students will have just a minute or so to explain what processes they are doing and why.  I hope that in using this particular strategy students will become more aware of their thinking and have the opportunity to hear the thinking from other table groups.

We'll hang the posters and share the outcomes.  At this time we will discuss how the polygon formed by intersecting inequalities informs decision making in a linear programming problem.

Here is a copy of our notes:

Solving Systems of Inequalities

Read Chat Reflect Week 2: Feedback

Call me weird or what ... I feel excited about this week's "Read Chat Reflect!"  So excited I'm already reading the article for the week and thinking about how it applies in my class.

The first sentence that caught my eye in "How Am I Doing?" is "Her paper did not tell her what she was good at or what she needed to keep working on—the marks did not function as effective feedback."  I know students get nothing from the papers I return to them other than a grade.  In my mind, feedback has to happen way before I take up a paper ... and when I do take one up, it's usually a summative activity.  If students want to make corrections or work on that same assignment I invite them to tutorials, and we talk through their errors.

The next thought that I've been pondering this afternoon is this, "Absent a learning target, students will believe that the goal is to complete the activity."  Learning targets are huge in our school.  In fact we not only have targets but also criteria for success! When I joined this school I was familiar with learning targets - I was ready to roll.  And then I heard all the talk about criteria for success and I felt like I was starting over.  Once I got the hang of it, it made sense to me.  So ... the learning target on Monday is, "I can solve equations with rational expressions."  The criteria for success include:

1. Find a common denominator for every fraction in the equation.
2. Multiply every term in the equation by the common denominator.
3. Simplify the equation (distribute and combine like terms where necessary)
4. Solve the simplified equation.
5. Check the solution to determine if it works or if it is extraneous.

One way to look at criteria for success is as steps.  As I teach I need to assess each step to determine which students have the individual steps and to remediate immediately those that do not.  This is tricky.  Sometimes we use individual whiteboards and check step by step.  Other times students work through problems, and then I ask them to self-report ... on which step are they struggling.  I go to the list as in my example ... how are you doing with step 1?  Step 2?  Etc.  I try to modify examples based on that feedback that students give to me.

Two other thoughts caught my attention in this article ... Effective feedback occurs during the learning, while there is still time to act on it. And, Effective feedback does not do the thinking for the student.

I can't wait until test day to give feedback.  Students need feedback while they are learning the math skills.  And when I give feedback, I can't do the work for them.  I have a bad habit of taking a student's pencil in my hand and writing the next step or two.  I know this is not good.  It's better if I have an EXPO marker in my hand, write something on their desk - that will help them figure out the next step on their own if my questions are enough to lead them there.

I wish there was a good article or book on feedback specifically in math class. Suggestions???

My new Fave ... Edmodo!

I used Edmodo for the first time this week to give a quiz.

It's a win-win situation.

• Students receive instant feedback.  
• They can review the quiz questions they missed - right then or later.  
• The program randomizes the questions and answers in case you have wandering eyes in your classroom.  
• The program provides me with graphs of how well students did on each question so I know which ones I might need to spiral back in our conversations.
• I can easily create a 'retake' quiz because when you ask to edit a previously created quiz, the program automatically opens a copy for you.  That copy can be renamed, questions tweaked ... and the retake is ready to go.
• I don't take home 150 papers daily ... fight to grade them all ... so I can return them in a timely manner!

Formative assessment just got easier by a long shot!  I can give a quick check, look at the scores, determine who needs help, create small teaching groups or set up tutoring sessions.

I like to take baby steps when using new platforms.  After we have taken a couple of quizzes and we have that process under control, I want to use the front page ... "notes" very much like the "status" page on Facebook, for class discussion.  I plan to use the Math Munch site as our source of discussion topics.  Hopefully I can report on that in a week or two!

Fraction Stations - Understanding Concepts

Students need to have a deep understanding of fraction concepts.  Our textbooks often focus on the basic skills.  It’s important to provide opportunities for mathematical discourse, reason abstractly, and construct viable arguments.  I adapted problems from various sources to create five stations providing opportunities for elementary students to explain their thinking about the concept of a fraction, the meaning of fractions, and reason about equivalence and addition.

The stations address these Common Core State Standards:

•       CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

•       CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

•       CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

•       CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

You can use the stations as journal entries, group work, formative assessment and purposeful practice.

Check out the stations here in my Google docs or here at my TpT store!

Let me know if the stations work well for you!

How do you challenge students to think deeply about fractions?

Using Card Sorts in Math Class

I like to use card sorts in my math classroom. I've been working on various sets. Recently I created a card sort for identifying the difference between linear and nonlinear functions. The card sort has 20 cards - 12 equations and 8 tables. Get the link below to the set of cards!


When I use card sorts, I don't always tell students the categories I'm looking for. I might tell them how many categories I want them to create. Keeping the categories open allows for a rich discussion about what they see on the cards, and how they choose to sort them. It allows students to show off their understanding of math vocabulary and to make connections that I might not have thought of.

A card sort can be used at several different levels. It can be used as a discovery activity, a pre-test, and a post-test. The sort can be used as both a formative and a summative activity. The card sort works well if you use math stations. Students can work on the card sorts individually or in pairs. Sorts can be glued into notebooks, or checked as they are completed on the desk.


After sorting the cards, I like to ask students to create another set of cards - for each category. In creating their own set, they demonstrate understanding of the concepts. You can use student create cards for additional practice during the unit!


Check out the card sort ... it's free ... try it and let me know how it works for you!
On my Google Drive
In my TpT Store

PS ... How would you use this card sort?  What cards would you add?  What concepts work well as a sorting activity?

eliciting student responses

Chapter 4, "Eliciting Evidence of Learner's Achievement" in Wiliam's Embedded Formative Assessment is all about ways to figure out if students have learned what has been taught.

The chapter includes very practical discussions of how to elicit responses.  I have been guilty of calling on the students who raise their hands knowing full well that the others are quite willing to let those few answer all the questions!  One suggestion in the book is that students should only raise their hands if they have a question.  The teacher should have a plan for calling on students randomly in discussion.  I used a random name generator and the students loved it.  But because it was online, it tied up my computer/projector ... made it difficult to flip back and forth if I was displaying questions electronically.  I purchased Popsicle sticks last year but never wrote students' names on them.  I think that I need to put them in place for the coming year.  But I might try this "card-o-matic" idea ... names on index cards, same name on more than one card, cards on a ring ... looks easy!

To gather input from all students, I plan to make a simple A, B, C, D card for students to keep in their binders.  To add variety, I'll use technology as well.  Clickers are great if they are available.  We can use Socrative since our 9th graders are being issued laptops.

Students love to use their phones.  I saw the Spanish teacher's students talking on phones near the end of school.  I asked her what they were doing.  She uses Google Voice to capture student dialogue.  Students dial her Google Voice number and "leave a message!"   I want to explore this tool for sure ... would love for students to verbally explain their work to me.

Besides the practice "how-to" capture students' responses, the author discussed the kinds of questions to ask and how the right question can tell us so much about a student's thinking.  One example had two equations:  3a = 24 and a + b = 16.  Students were asked to solve them.  Students were puzzled, said it couldn't be done.  It confused them that in this set of equations a and b both equal eight.  It's so true that so many of our examples are carefully contrived, that it is difficult for students to overcome the hidden patterns that we teach.

Another example, Simplify (if possible):  2a + 5b, at first glance seemed unusual.  The author purports that this example is fair and worthy.  If a student can be tempted to simplify that expression, then the teacher needs to know that before moving on.

This chapter challenges me to consider the questions I'm asking in class and the methods I use to collect student responses.

How do you engage all learners in responding to discussion?
What are your best questions?

School's Out ... PD on the horizon ...

School has ended!  YaHOOO!

Now I am thinking about professional development ... the kind I structure for myself as well as the work that my school wants me to participate in.

I want to read at least two books ...

The first one is Embedded Formative Assessment by Wiliam.  Formative assessment is and continues to be the primary initiative in our school.  Our principal and all others who visit our room, comment on lessons, evaluate our work, expect to see standards broken down in chunks and assessment of each of those chunks.

I chose this particular book on formative assessment because of druin's compelling thoughts as she read the book recently.  I look forward to sharing what I learn as she did!

The other book I want to read is Mindset by C. Dweck.  I work with students who lack motivation in math.  I want them to believe that they can grow in their math ability ... that ability is NOT fixed!  This blog post attracted my attention!

I also noticed this book/author when signing up for a MOOC this summer!  The MOOC is from Stanford University, EDUC115N How to Learn Math.  The following concepts are discussed:
CONCEPTS
1. Knocking down the myths about math.
2. Math and Mindset.
3. Teaching Math for a Growth Mindset.
4. Mistakes, Challenges & Persistence.
5. Conceptual Learning. Part I. Number Sense.
6. Conceptual Learning. Part II. Connections, Representations, Questions.
7. Appreciating Algebra.
8. Going From This Course to a New Mathematical Future.

I'm hoping that through the reading and the participation in the Stanford course, that I'll be better prepared to lead students to a growth mindset and ultimately success in Algebra.  

This past year all my students passed the course, and 95% passed the state end of course exam.  I'm celebrating that success but I want a deeper understanding and more tools for making this next year even more successful!

What professional reading or activities do you have planned for this year?

Made4Math Technology Baby Steps

Our school was chosen for a laptop initiative.  Laptops were distributed last week to 9th graders who returned permission slips and had their student IDs. In our first class day with laptops about 50 - 75% of the students had picked theirs up.

Knowing that we have limited amount of math time, but wanting to integrate the new tool right away, I planned just a few short activities with the laptops.  For the next several lessons, the computer activities will not be heavy duty; instead they will be a way for me to observe my students use of the tool, gauge what might work, and give me a foundation for future planning.

The first tool I implemented was Google forms.  I love Google forms ... they are quick, simple, and easy to manage ... awesome for collecting data.  Tomorrow students will check their homework and check the problems they missed on the Google form.  That way I will know which problems were the most difficult for the class.  I can work those problems into our warm-ups and homework.

Great for Ticket Out of the Door

A second tool I am using is Today's Meet.  Today's Meet requires no set up.  I simple go to the site, enter a name for our meeting, and post the link for students to access.  Then at the end of class I can collect qualitative data about the lesson. I ask a question aloud in class, and students respond on the Today's Meet site.  I can keep that record of responses if I need them for future planning.  Last week I asked which step was difficult in solving systems of equations by substitution.

Another tool I'll use tomorrow is Super Teacher Tools: Speed Match.  I plan for students to match words to equations as a warm-up since our lesson is on solving systems in context.  If students don't have their computers, I have a paper copy.  If they do have their computers, they will play the "game" online.

Our school has adopted "Evernote" as its online note-taking system.  A few students have asked if they can take their class notes online ... and so far I've said yes.  Typing math notes is much more difficult than typing notes for other classes but I want students to try it if they think they can take good notes that way.  I do hope to help students build an Evernote notebook ... possibly on vocabulary.  I think it would be a great way to keep track of the math vocabulary they learn in high school ... since Evernote will be an ongoing tool.

The IT folks just pushed out the virtual graphing calculator over the weekend.  We use TI 83+ in class ... now everyone will have one on their laptops as well.  This is a bonus in working problems at home!  Before I couldn't count on students having access to a graphing calculator at home.  Yes, there are online ones, but not everyone has Internet access.  Now the virtual calculator is installed on their laptops ... no Internet required to access it.

If you use an online tool to support formative assessment in particular, or to present math lessons, please share!