Signed Numbers

Confession...I'm planning to use Khan Academy this year

2011-08-26T20:21:00.000-05:00

It seems Khan Academy (henceforth referenced as KA) has a pretty bad rap in some math teacher circles. I understand that the videos are somewhat lacking in the engagement factor, and motivating students with points and badges can seem somewhat elementary. I also see that KA tends to focus more on a procedure/pattern than actual problem solving.

All that said, I will be using KA this year in my resource classroom. I have a group of students that are in my class for numeracy skill building/strategies instruction. I'm supposed to be teaching them 25 mins/day and allowing them 25 mins/day to work on their homework or classwork. I have students of all grade and ability levels in one resource class, so lesson planning becomes difficult. Twenty-five minutes is not a long time when you think about it, seemingly less when you think about real problem solving tasks.

Enter KA. Each student can be working on exercises related to what their individual math course is or will be addressing. I can monitor their progress as a "coach" and assign them individual tasks. My district uses Google Apps for Education, so all the students have email addresses that they use to log in. I can, in theory, email them instructions for which exercises or videos I would like them to do during their 25 minute instruction period. Two days in, some students are more engaged than others. That is to be expected. When assigned topics directly related to material they were working on in their math class, the students were more engaged.

I'm sure that things will change throughout the year as we continue to develop this strategies portion of the resource class, but for now, KA is a useful tool. Just sayin'.

p.s. I (obviously) made it through week one at the new school. Yay!

Transitioning...

2011-08-09T10:06:00.000-05:00

For those of you that don't know, I'm about to start teaching at a new school in a new state. I will be still be teaching high school math to students with special needs, but those special needs are not necessarily deafness or blindness. I am very excited to work with a math department as opposed to one other colleague (even though she was fabulous). All in all, though, it's a lot of transition.

Here are some things I have learned in the process:
- I'm not as good at transitioning as I like to think I am
- I have a difficult time making any kinds of decisions when there are so many unanswered questions and uncertainties ahead
- It's really difficult to transfer certifications between states
- I'm not sure I entirely know what I'm getting into, but I'm still excited
- I am *not* a detail person

I went to a workshop hosted by the district I'll be working in. It was great to collaborate with teachers from the different schools and create materials. I should get back to working on my post-workshop assignment, but I hope to start up blogging again this year.

Help!

2010-07-21T12:04:00.001-05:00

Here's the deal: I'm working on curriculum for my school and Algebra 2 is making my eyes cross. I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones. This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too. Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time. To give you context, our school teaches it as a semester-long block course. There's only so much a brain can handle in one day, though!

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note: Gray items are not included in old or new SOLs but might be necessary for student understanding
Blue items are being taken out of the SOLs starting next year
Red items are new to the SOLs starting this year

Unit 1 Algebra 1 Review/Solving Equations

1 Solve multi-step equations and inequalities
2 Matrix +/-
3 Solve compound inequalities
4 Solve absolute value equations
5 Solve absolute value inequalities

Unit 2 Polynomial Review/Add Depth

6 Factor trinomial a = 1
7 Factor trinomial a > 1
8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)
9 Factor out GCF first (factor completely)
10 Exponent rules
11 +/- polynomials
12 Multiply polynomials
13 Divide polynomials

Unit 3 Rational Expressions

14 Identify undefined values
15 Simplify rational expressions by factoring and canceling out common factors
16 Multiply and divide fractions
17 Multiply and divide rational expressions
18 Add and subtract fractions
19 Add and subtract rational expressions
20 Simplify complex fractions
21 Solve rational equations

Unit 4 Radicals, Radical Equations and Complex Numbers

22 Simplify numbers under radical
23 Simplify monomials under radical
24 Multiply and divide radicals
25 Add and subtract radicals
26 Nth roots to rational exponents and vice versa
27 Simplify expressions with nth roots and rational exponents
28 Solve radical equations
29 Simplify square roots with negative terms inside radical using i
30 Add and subtract complex numbers
31 Powers of i
32 Multiply complex numbers

Unit 5 Functions (intro)

33 Domain and range of relations (from ordered pairs, mapping, graph, table)
34 Identify relations that are functions and one-to-one
35 Given graph and a value k, find f(k)
36 Given graph, find zeros
37 Given graph and a value k, find where f(x)=k

Unit 6 Linear Functions

38 Slope from graph, equation, points
39 Graph from equation
40 Equation from graph
41 x- and y- intercepts
42 Determine whether lines are parallel, perpendicular, or neither from equation or graph
43 Write equations for parallel and perpendicular lines given line and point off the line
44 Graph linear inequalities

Unit 7 Systems

45 Solve systems of equations by graphing
46 Multiply Matrices using a graphing calculator
47 Inverse matrix method of systems
48 Systems of equations word problems
49 Graph systems of linear inequalities
50 Linear programming max/min problems

Unit 8 Functions (reprise)

51 Function math (addition, subtraction, multiplication, division)
52 Function composition, find a value i.e. f(g(3))
53 Function composition, find the function i.e. f(g(x))
54 Find an inverse function by switching variables

Unit 9 Quadratics

55 Graph from vertex form, identify max/min and zeros
56 Solve by factoring
57 Solve by Quadratic Formula (including complex solutions)
58 Determine roots using the discriminant
59 Write equation for quadratic given roots
60 Quadratic systems
61 Polynomials: relating x-intercept, zeroes and factors
62 End behavior for polynomials

Unit 10 Exponential/Logarithmic functions

63 Exponential growth or decay from function
64 Sketch base graph of exponential/log functions
65 Exponential to log and vice versa
66 Data analysis/curve of best fit for linear, quadratic, exponential and log

Unit 11 Transformations and Parent Functions

67 Graph absolute value functions
68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log
69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log
70 Combinations of transformations on parent functions
71 Identify parent graphs of parent functions
72 Identify equations of parent functions

Unit 12 Conics

73 Identify a conic from graph
74 Identify a conic from equation

Unit 13 Variations

75 Write equation for direct, inverse and joint variation problems
76 Find the constant of variation

Unit 14 Sequences/Series

77 Write n terms of an arithmetic sequence
78 Find the sum of a finite arithmetic series
79 Write n terms of geometric sequence
80 Find sum of geometric series
81 Use formulas to find nth term
82 Identify sequence/series as arithmetic, geometric or neither

Unit 15 Statistics

83 Determine probabilities associated with areas under the normal crve
84 Compute permutations and combinations

If you made it this far, here's my call for help: Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order? There is and will continue to be an emphasis on function families and transformations (as there should be). I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply. Any ideas?

...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit: I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

The Birth of an Assessment

2010-05-21T06:54:00.007-05:00

Sam recently blogged looking for feedback on an Algebra 2 assessment he gave, but mainly to start a conversation about assessment creation, etc. My classroom assessments have changed drastically in my short 2 years of experience.

Here's a chronology of my growth:

1st year teaching (Algebra 1 - full year course)

Classroom instruction followed the sequence (and pacing to some extent) of the textbook we were using (McDougall Littel Algebra 1).
Assessments were largely based on Chapter Tests from the end of whatever chapter we were in, re-typed/formatted but using the same problems with little thought to balance what was actually being tested.
Points were assigned to each problem to award partial credit for being on the right track (this often ended up meaning the more difficult problems were worth more points than the basic problems - more steps = more points)
Here's an example of one such test: Chapter 9 Test. Point distribution is as follows (side note: what was I thinking with these point distributions...they make no sense!)

#1 - #4 : 38 points total (one for coefficient and one for variable in each term of each problem)
#5 - #6: 6 points each (coefficient part, variable part for each term)
#7 - #8: 4 points each (2 for multiplying correctly, 2 for combining like terms correctly)
#9 - #10: 10 points total (coefficient part, variable part for each term)
#11 - #12: 9 points total (1 pt each - GCF number, x, y*for #12*, each term left inside parentheses)
#13 - #16: 4 points each
#17 - 20: 6 points each (4 for factoring, 2 for solving) *#19 was eliminated as unfactorable...oops*
Total out of 100 points (this was a rare occurrance...my tests rarely end up being "nice" numbers of points)

Looking back, getting ready for year two, I realized that the tests I gave in year one were nothing more than a random assortment of problems that may or may not have given me an idea into what level of understanding my students had. Mostly, it was a hoop they (and I) had to jump through at the end of a chapter that didn't tell either one of us anything relevant. If a student failed a test, I would work with them 1:1 to try and remediate some areas, but it was haphazard at best. If the whole class failed, then I would plan a retest.

2nd year of teaching (I'll stick to year-long Algebra 1 course for discussion purposes, despite having other classes as well)

- Fall Semester

Classroom instruction divided into more logical "units" instead of staying strict to the chapters in the text.

Unit 1: Number Sense and Properties
Unit 2: Variables, Exponents and Substitution
Unit 3: Solving Equations and Inequalities
Unit 4: Proportional Reasoning
Unit 5: Graphing
Unit 6: Writing equations
Unit 7: Systems
Unit 8: Polynomials
Unit 9: Factoring
Unit 10: Quadratics
Unit 11: Statistics

Assessments were created with more thought given to the types of questions and what they were really asking/showing to give balance
Points were assigned for each problem for partial credit opportunities, but with consistency and balance in mind. (i.e., being careful not to weigh a really difficult problem too heavily or allow one specific skill to dominate the point distribution)
Here's an example of a unit test: Unit 2 Exam. Point distribution is as follows:

Simplify: 20 points total

first row - 1 pt each (basic exponent rules)
other problems in this section - 3 pts each

Evaluate: 2 pts each (1 for substituting, 1 for simplifying)
Let a = 3...: 3 pts each (2 for substituting, 1 for simplifying)
Order of operations: 3 pts each
Total out of 62 points

- Spring Semester

At the end of 1st semester, my colleague and I started talking much more about assessment. A lot had changed compared to my first year, but we still weren't satisfied with the information we were getting from students' test grades, nor were the students doing anything to study or improve their skills. We sat down during our "Snowpocalypse Week" and hashed out a standards based grading system.

Based on the needs of our students, we decided that assessments now would have two forms:

Individual skills assessments

focus is on progress towards mastery of one learning target
points are assigned with a 1 - 5 rating for each skill.

5 = A, mastery level: true mastery of high school level content
4 = B, mastery of the basic level content
3 = C, general understanding of basic level content, some mistakes
2 = D, several mistakes or holes in understanding
1 = F, many mistakes or solutions off point

Here's an example of a skills assessment used this term. (basic level, mastery level) The page has 4 skills, but each receive an individual grade

"Retention Tests"

focus is on whether or not a student is able to recognize solution strategies when there is more than one problem type being addressed
is the student is retaining the information from previous skills targeted?
points are assigned in a similar manner to the fall semester unit tests

Instruction is still in "units" and retention tests happen at the end of units.
Skills assessments happen on a more ongoing basis: teach, practice, skills assessment, reteach if necessary, re-assess as needed, etc.

In general, I like having at least one question on a retention test and/or on the mastery level of a skills assessment that isn't exactly like any other problem they have seen. These types of questions help students synthesize what they have learned and help me see if/how they can apply the strategies in new contexts instead of just regurgitating a procedure.

This year has certainly been one of growth! Some fruit of our labor in the field of standards based grading? Nine of twelve students in Algebra 1 passed the state End of Course Standards of Learning assessment on the first try. The other three qualified for an expedited retake. Two of them passed. This means we have a 90% pass rate for first time testers in Algebra 1 this year (9 out of 10...2 students that passed this year were re-taking the class)! Last year it was a mere 37.5% (3 out of 8). While I am aware that passing the state test is not a true picture of whether or not the students can *do* Algebra, I also know that they were more prepared for the test due to targeted remediation of their weak skills as shown on the skills assessments. That's an achievement.

ASL/English Vocabulary in the Math Classroom

2010-05-01T10:07:00.000-05:00

My last semester in college, while I was student teaching, I had a class that emphasized different key topics in the field of Deaf Education. One such topic was vocabulary development. We all already knew that students who are deaf/hard of hearing have a lower vocabulary than their same-age hearing peers for a variety of reasons not least of which being their limited access to "incidental learning" that comes from listening to other people's conversations/tv/radio, etc. In our class, we talked about ways to introduce new vocabulary in order to give students a more connected understanding of the new word in its five distinct forms.

Picture
Description/definition
ASL sign (if applicable)
English word (in print)
Fingerspelling of English word

I try to be conscious of this as I teach. It's very difficult sometimes, and many of the math terms to not have standard ASL signs, so it is more difficult for the students to attach meaning and use the new term through fingerspelling alone.

In Calc this week, I had my student doing practice AP Free Response questions. One day, after completing a no-calculator free response question requiring justification of responses, I read the justification and was reminded of vocabulary difficulties. The mathematical justification was great, but instead of saying the normal line is perpendicular to the tangent, therefore the slopes are opposite reciprocals, justification was that the slopes are "negatived and flipped." In ASL, it would be an appropriate explanation, because the sign for flip and the sign for reciprocal are the same. This is the class that I have been most conscious about vocabulary! We have had English lessons in the middle of calc class in order to recognize the different forms of words that have the same sign. i.e. differentiate (v.), derivative (n.), differentiable (adj.), derive (v.), etc. The majority of the calc vocabulary (inflection point, slope, tangent and many others) does not have ASL signs, so we do a lot of fingerspelling with the support of written English on the board. I am concerned that this might not be enough.

Any thoughts on how to make vocabulary a more essential part of the curriculum or to get students actively using appropriate terms in writing?

Trig Project Idea....suggestions?

2010-04-30T18:35:00.000-05:00

Inspired by @krisreid72 sharing this document with @Fouss, combined with the fact that I was looking for something that my trig students (who just finished a unit on solving triangles using Law of Sines/Law of Cosines) could wrestle with while I am out of the classroom Monday and Tuesday, I came up with an idea.

The Amazing Race!
random caveat: Season 14 had a deaf participant!

I will give students 2 options -

Option 1: No real trig involved, but still challenging thought processes and more stops to make

Find the shortest "round-the-world" trip visiting many of the tallest buildings in the world.

Assume (for the current purposes of this project) that you have a private jet/helicopter that can take off/land anywhere in the world.

Primary tool: Google maps

Go to http://brtva-math.wikispaces.com/
Click Trigonometry in the left navigation bar
Click Amazing Race
Follow the directions.

Option 2: (taken from @krisreid72's project) Significant amount of trig involved, along with challenging thought processes

Find the quickest and safest path from the Golden Triangle to the finish line at the Mabu-mabu tribe
Primary tools

Paper map of possible trails
Rules/directions/important information (see page 2 of this document)
Law of Sines/Law of Cosines/general trig knowledge

I'm really excited about this! I was so proud of my students after their Triangle test, because they struggled through some tough problems and tried to make sense of them. I think this will be a good opportunity to challenge their thinking skills even further and give them some freedom. I wish I could have more trig involved in Option 1, but I'm not sure how to do it naturally.

Thoughts?

Blogging hiatus

2010-04-26T18:41:00.000-05:00

I am still alive...I am still teaching...I am still moving, mostly forward.

I've really been struggling to keep up with things, mainly extra-curriculars (as a sponsor, or my own hobbies!) while at the same time being wholly present in my classroom as we're reviewing for end of course tests. I have a list of blog post ideas that haven't materialized...maybe some day soon.

Just wanted to say that I'm still here.

Must be doing something right?

2010-03-31T06:12:00.000-05:00

Highlight of the Day:

Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test.

Problem:

what is ;

Me (typical first question): So....what should we do?
Student: Substitute the 2 in for t to find the answer
Me: Why would we want to do that?
Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer.
Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo!

Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.

Help and Critique needed: GSP file

2010-03-14T15:30:00.002-05:00

Hello friends.

This is what I've been doing this afternoon. It's a Geometer's Sketchpad file that I hope to use with my calc class when we talk about volumes of revolution. I tried to upload it using Javasketch for those of you that don't have GSP, but found out that JavaSketch doesn't support function plots, or pretty much anything I used to create the sketch. Typical.

Anyway, I'm looking for feedback. Play with the sketch, press the buttons, see what you think. Ideally, I'd like this to be along the lines of a Dan Meyer "What Can You Do With This" type activity, but I don't think I'm there yet.

It's not finished, mainly because I don't quite know how to create functions for the last 1.5 pictures. Any help is appreciated! Thanks, friends.

**UPDATE**
A new version is posted here. Thanks to iTeach in the comments section (@PersidaB on twitter) for coming up with cubic regressions for the lasat 2 pictures. I didn't think to use my graphing calculator...wanted to do it all in GSP and couldn't figure it out. Thanks again! More feedback is always welcome, too. :-)

Budget Cuts and Future Plans

2010-03-13T11:00:00.005-06:00

Thursday we had a staff meeting led by our school Superintendent and the Human Resources director. The topic? Next year's budget cuts. As of the last governor's proposed budget, our school was scheduled to have $1.5 million cut from our budget for next year. The new governor has not approved a budget yet, so we're not sure if that number will remain, or increase.

Currently we have about 50 students in the deaf department high school. Twelve or thirteen will be graduating. Currently we have five 8th grade students. Our numbers in the high school are going to be dropping. Our numbers in general are dropping. Next year we will have 66 students in the deaf department. That is, 66 students from preschool through 12th grade. Not very many.

After telling us these numbers, HR discussed how the administration has been planning to deal with the budget cuts. They will be leaving vacant positions open, trimming utility and technology expenditures as much as possible, and decreasing hours for wage employees (teacher's assistants, bus aides, interpreters). They will also decrease some admin positions from 12 month positions to 10 or 11 months.

After all that, they still need to cut over $430,000. Layoffs are coming. It makes me sad to think of people that I have worked with for the past two years being laid off. At this point I feel some degree of security in my job because there are only 2 of us math teachers in the deaf department, teaching middle and high school. The administration has also informed me that I might be the person teaching the newly required Personal Finance and Economics class that all students will need to take (eek!). Looking around, though, I see people who have worked for more years than I, who have more education that I have, that are in jeopardy of losing their jobs because they are the most junior member of their "team." I don't know what will happen in the next few weeks, nor am I 100% certain that I won't be writing to say I'm out of a job for now. I am one of the most recent hires...low (wo)man on the totem pole, so to speak. I'll keep you posted.

One more thing...this information about the budget cuts and the future of our school further justifies my thought that I should broaden my scope for a master's program. Maybe Secondary Ed: Math? Or math in general? ...but I don't want to be proving deltas and epsilons and doing way far out math...I don't quite know yet. Any suggestions?

Graphing Sine and Cosine

2010-03-12T19:32:00.000-06:00

Recently in Trig, we've embarked on the task of graphing sine and cosine curves. Before this, we constructed the unit circle and students became familiar with the exact values of sin and cos at the special angles. To introduce the parent graphs, I used an activity that I found at Kate's blog last year (who I'm sure got it from somewhere else, but I don't know where).

To first see the "unwrapped" unit circle that is the sine (and later, cosine) function, students used yarn to mark intervals along the circumference of a unit circle, then used spaghetti to measure the y (later, x) value at each place. They then transfered these lengths of spaghetti to an x-y plane with x intervals of length matching the circumference intervals. This was a great picture for them of where the shape of the sine function comes from. One student even explained it (works much better in ASL), as though you've taken the bottom half of the unit circle and spun it around to make up the second half of the sine function. (my adaptation of worksheet)

Graphing sine and cosine with changes in period and amplitude came easily for my students, but when we started translating with horizontal and vertical shifts, the students were lost. The first day was a major failure on my part and I knew that I needed to have a new approach when I started the next day. I placed an open call for help on Twitter and was forwarded two GeoGebra applets (thanks Dave!). I quickly came up with a guided investigation to go along with the first applet.

We went to the computer lab, and had some success! Normally, when I've taken classes to the computer lab to use Geometer's Sketchpad or GeoGebra (or other programs), the students end up playing with the program, going through the motions, and they leave with little to no connection back to the paper and pencil world of the classroom. It's probably the way I present it, but they may understand the concept more indepth while using the computer program, without any transference back to the original idea or any application to the next topic.

This time, I required the students to answer the questions in a word doc, and I taught them how to use Print Screen to capture the image on screen and paste it into their document in order to later compare it to another graph. The next day, we continued by using the second applet (with some of the parameters changed) to walk us through the process of graphing sine functions with translations *and* changes to period/amplitude. We closed the day with an application of what the applet taught us about sine to help us graph cosine functions with translations. As a bonus, my boss happened to come and observe me explaining the second applet to the students. He just loves it when teachers use technology (and happens to observe me on days when I'm using it well...lucky me!)

Results: I know at least one of my (two) students benefitted from this process. We are still not at a point where they can graph the functions independently, but they have some strategies to help them, and a deeper understanding of what the numbers in the ugly looking equations mean and how changing them, changes the function. As their Algebra II teacher, I know I could have done a better job when we did function transformations. That probably adds to their confusion and weakness in this area. Something to think about for next time.

**update** I know I haven't even posted yet, so I feel like I shouldn't update, but I did see some good progress in my students today. Now we have a shared experience that I can link back to as they continue to develop their graphing/graph analysis skills.

Rewriting the Curriculum on Snow Days

2010-02-02T18:56:00.000-06:00

My school has had many more snow days this year than last year...we're already up to 4...and more are predicted. My colleague and I took advantage of the recent ones, since teachers are still required to work, and re-vamped our Algebra One curriculum and assessment scheme.

After a discussion prompted by Sean's blogpost about failure, and a discussion about homework and assessments in general, I gave her a list of required reading (basically, things I have read over the past year to give her the same background knowledge that I have coming into any conversation about these topics). After she read through the blogs (and did some exploring on her own, too, I think), we sat down and talked about Standards Based Grading. I also brought to the table these Algebra 1 concept lists (courtesy of Dan Greene).

By the end of two days, we decided to implement the concept/skill based assessment program, while still continuing cumulative testing. We will call the cumulative tests "Retention Tests," because we recognize that our students struggle with retention and with the preparation/focus needed for longer tests (which they must endure in May, so we might as well give them practice sitting for longer tests). Our rationale for wanting to add the skill/concept tests is threefold: 1) We will be more aware of what the students can and cannot do at any given time. 2) We will have numerical data for IEP time (ex. Suzy Q has achieved the basic level requirement of 80% of the concepts covered so far in Algebra 1. Furthermore, she has achieved mastery of the high school content for 10% of the concepts covered this year. Her areas of weakness lie in the 10% she has not yet reached mastery...). 3) Student grades will reflect their achievement and ability: old weaknesses can be recognized and remediated, and parents will be able to see their child's areas of strength and weakness.

My colleague is an over-achiever. She is implementing this strategy in not only Algebra 1 (which we both teach), but in Geometry, 7th grade and 8th grade math as well. She will be creating skills lists, assessments, and keeping track of it all for 4 classes! I'm just working on one. *smile* Here's what we have come up with for a skills list (note: concepts #1 - 44 were covered in the first semester of the course..we are starting at "systems of equations", student tracking graph (thanks to dy/dan reader Jacob Morrill for the template), and blank concept list for student record keeping. Here, too, is the letter that we're planning to send home to parents introducing the new system.

We decided on a "basic" and "mastery" level for each skill. The "basic" level shows a general idea of what they are expected to know. If the student can get to that level on each skill, they will earn a B in the course and will have the equivalent to a pre-algebraic understanding of the material. (Not bad, considering where they start the year...). If a student attains the mastery level, it shows that they are truly mastering the high school content and standards. As I mentioned before, our students are well aware that they are below grade level in reading/writing. This system will show them the areas where they truly are at grade level in math, and the areas they need to work on.

I'll keep you posted on how it goes, but I'm really excited to see where it's headed! I think the thing I'm most excited about is for students to take more ownership of their learning. I can't wait to see them with the tracking graphs, looking at where they are and wanting to improve. I think it will give them a realistic view of their strengths and needs in Algebra class, and a more obvious starting point for studying/remediation.

** Footnote: Special shout-outs to Kate, Sam, Dan Meyer, Dan Greene, Sean, and Riley for your awesome way of inviting us in on your process. Thanks for being great teachers and sharing what works with the rest of the world! Thanks to many, many other math teacher bloggers out there, too, and to my twitter pals for answering my questions.

We are not Intramural...

2010-01-30T16:36:00.000-06:00

Here's an analogy and the most recent joke going around my department:

Some of our kids get upset when they don't get all A's (understandable). My students are not all "on-level". In fact, most of them are not. In English class, they are accessing high school content at modified levels based on their independent and instruction reading levels as determined by the Qualitative Reading Inventory (QRI). These reading levels range from pre-Primer through High School, and the teachers adapt their materials accordingly. Students that read at the pre-Primer level can still get a grade of A in English by doing the work and improving their reading and writing skills.

Math is a different beast. Students are learning high school math content. You cannot change the Algebra 1, Algebra 2, or Geometry standards. You can modify the methods used to teach the content. You can create guided notes with picture support for vocabulary and explanations written in language they can access based on their independent reading level. You cannot, though, teach 5th grade content. Factoring trinomials is factoring trinomials.

To break the news to students used to getting straight A's, my colleague uses a sports analogy. She explains to them that math content is the same in public schools as it is in our school. Their grade and understanding reflects how they are doing in comparison to what they know and understand about the standards. The same standards being used in public schools. The sports analogy is this: If you were grading athletic ability, an A would mean you're an expert, the best in the field...like a professional athlete or a gold medalist. A "B" is like a college athlete, C - on a high school sports team. A D or F would be like an intramural/club player, someone not quite good enough to make the team. Students know that they are below level in English, and this analogy helps them understand better their progress in math. We are not trying to bring our students down, but give them a realistic perspective of their achievements. The downside of going to a school where everyone is deaf, is that the only people to compare yourself with are others who are fighting the same language battle as you are.

The joke stemming from this analogy has nothing to do with our students: my colleague and I regularly tell ourselves (especially on rough days...) "We are not Intramural!" We are continuing to look for ways to improve our methods of teaching and assessing. We are trying to make high school math content accessible for our students. We are looking for ways to improve their retention and make math more applicable to their lives. If I get to a point where I don't care about those things and am just going through the motions - I have become intramural. I hope that never happens, but if it starts trending that way, I hope I leave teaching. The kids deserve better than that.

Writing Across the Curriculum

2010-01-23T11:50:00.000-06:00

The Writing Committee at my school developed a task for this school year to help encourage writing across the curriculum in hopes of improving our students' writing abilities. (Students who are deaf, on average, are significantly below grade level in reading and writing. Some suggest it stems from lack of access to the phonology and patterns of spoken English, upon which the written form of English is based. Others suggest it is a symptom of language delay stemming from lack of access to a full language during the critical period for language development. Many oralists have cited ASL as the cause for low literacy rates among deaf people, but other research has shown that a strong foundation of ASL can actually support English reading and writing ability. It's all about language).**

Anyway, each class is required to submit 4 writing assignments for each student (one per quarter). Not too demanding, but there is an additional requirement that the writing assignments be of specific genre. I have, thus far, asked some students to provide a narrative "math autobiography", explain/describe the steps they took to solve a problem/how they would approach an unfamiliar problem, and (for my calculus student) compare and contrast optimization and related rates problems.

I see the benefit of writing in math class. I see how it can become an informal assessment of conceptual understanding. Some of my best math students, however, can explain to me the steps taken to solve a problem in a way that shows conceptual understanding, but cannot translate that into an English paragraph because they get so stuck on spelling and grammar. Their strength becomes a weakness because they cannot express themselves through writing. They get frustrated, write the absolute minimum required and/or refuse to do it.

I don't think the Writing Committee believes that this writing across the curriculum will be a "silver bullet" to solve the problems with our students' writing. I don't think that the way it's being implemented is helping at all, though. I don't know how to make it better in my classroom. I don't know how to have the students use writing to learn math when they aren't comfortable writing. Normally, teaching through writing is recommended for students who struggle with math and achieve in writing...letting them use their strength to support their weakness. I have students that are the exact opposite...They need so much assistance/instruction in their writing, that it no longer becomes about math, but about the writing.

Question for readers: Do you use writing in your math classroom? How? What strategies do you use to support your students with low literacy?

** Disclaimer: I am not trying to say that all deaf individuals have low literacy levels. Nor am I saying that all of my students are in this category. I am just seeking to provide some background information to give context for this conversation.

Class Sessions, Instructional Days, and a Conversation I Never Thought I'd Have at my School

2010-01-20T06:08:00.000-06:00

Last week was the tail end of SOL (Standards of Learning) testing for 1st semester. We're on a 4-block set-up, so some classes are finished after 1 semester, and the students take their state End of Course multiple choice assessment. If you follow me on twitter, you might have noticed that my Algebra 2 class was one of these semester-long courses, and that the kids took their SOL test last week. None of them passed on the first go-round, but 3 were in what the state calls the "bubble". A score of 400 is required for passing, but the students who score between 375 and 399 are permitted an expedited retake...they are the "bubble". Those three students took the test (different form) again on Friday morning and scores came yesterday. One student improved by 52 points! Well into the passing range. The other two both improved, but not enough to cross over that 400 benchmark. I was pleased with their scores because with many students in the retake bubble, their 2nd score is lower than their first...the tests are often much more difficult than the first test.

Anyway, enough background/babble about test scores. That's not the whole purpose of this post. Last week my principal sent a request to the high school teachers. He said that he was looking at lesson plans recently and noticed that some teachers had noted class cancelled for a variety of reasons (IEP meetings, early dismissals for sports away games, clubs, etc). He was curious to know how widespread the class cancellations have been this term, so he asked us to total (for each class): class sessions, instructional days (with the teacher present...not a sub), instructional homegoing days (we have 1/2 days with students on homegoing days...they get on buses at noon on Fridays/Thursdays), and then write a narrative about whether or not we feel there was enough time in the schedule to cover the pace of the class.

The semester is supposed to have 90 days. Eighteen of those are "homegoing" days. We had 3 snow days, and I was out for a few days for various reasons. When the calculations were finished,* one class had only met 44 times due to student illness/absences. Another class had only met 68 times, with 64 instructional days! To top it all off, the class with 64 instructional days is one of the fastest paced math classes we offer: Algebra 2. The students struggle in that class without missing 1/3 of instructional days because there is so much information to cover and a strong reliance on what you remember from Algebra 1. When I saw the numbers, I didn't feel so bad about the students not passing the state test, but I was still sad that they missed out. Think of how much better it might have been...

Well, Friday afternoon we had a meeting to clarify the intentions behind the principal's request, and to talk about some data. I was one of the few that had already turned their stats in, so my data was brought up. The conversation that I never expected to have was about test scores. I know public schools have dialogue all the time about needing to raise test scores and some teachers are worried for their job if the students don't perform well. I also know that most public schools expect 90% of their students to pass the Alg1 SOL (or any...) on the first try. We don't have those expectations. First of all, I don't even have 10 kids in my class...so it's impossible for me to have a 90% pass rate. Secondly, they don't all have the foundation in reading or math to do well. I expect them to work hard and try their best, but I know that some kids just won't pass the first time. That's okay.

What I didn't expect was to be told the data about our pass rates...We then discussed the time data...powers that be are putting two and two together, thinking that one is the direct result of another and are now looking for solutions. What can we do so that kids don't miss so much class? Move clubs to after school? What about day students? Cancel away games? Students will leave. Cancel sports/clubs entirely? Students will leave. We were not being accused of not teaching, but we were being asked for solutions. No one has any. Administration is afraid that if kids are not passing tests they, their parents, or their local districts won't want to send them to our school anymore.

There's more to our school than getting kids to pass tests.

*Secretly I loved doing this...I was even doing it before he asked, because I knew one of my classes had lost a lot of time...I guess I like data

Further Discussions on Higher Education

2010-01-15T19:30:00.000-06:00

Sarah got me thinking about different kinds of graduate level programs after she commented on my last post. I also posted a tweet when I found out the program I had been eyeing has been closed. Our dialog (and some other tweets that have gone back and forth since then, has prompted me to want to do more research to see what's actually out there.

I have come to a couple conclusions:

I do not entirely know what I want to study
I am afraid of making the wrong decision and finding out in 15 years that I am not marketable for what I actually want to do
There might not be a program out there that fits my ideal

The options I am looking at (so far) are either a M.A. in Deaf Education (with a focus in secondary math education), or a M.A/S in Mathematics Education (as long as there is a program that doesn't require me to a. have a BS in Math or b. student teach in order to get math certification...I already teach math...kthx).

Pros for the Deaf Education program would be that I would be learning more specific methods that would help me teach my students right now. Classes would be offered in ASL, thus further expanding my vocabulary and experience learning in the language I teach through. I would be with other deaf educators, or prospective deaf educators, having people to bounce ideas off.

Cons for Deaf Education include pidgeon-holing myself into only being marketable to residential schools for the deaf. I love residential schools, and I do see myself teaching at one for a long time (if not my entire career). I am concerned, though, about the future of such schools. State funding, standardized testing, and IDEA are causing more deaf students to be mainstreamed into public schools. Residential schools are decreasing in numbers, and some schools are becoming more specialized in serving students with disabilities. A specialized master's degree with a focus in Deaf Education might cost me a job teaching in a public school some day if that ever needed to be the case.

Pros for general math/math ed include expanding my math knowledge and knowledge of general math teaching strategies (that may be useful in hearing and deaf classrooms). It would also almost certainly ensure my Highly Qualified status should I ever decide/need to teach hearing students in a public school (middle or high school math).

Cons for general math/math ed are that the people in the program will most likely have no clue what kind of students I work with every day. There won't be the shared experience or language. It would require more investigating on my part to discover and decide how to apply the general theories and strategies to my specific context.

So that's the basic idea of what's been tossing around in my head the past week. I know that there are many factors to consider and most likely no "wrong" path, but I want to make an intelligent, informed decision before I go dedicate a lot of time and money to a master's degree.

Professional Goals

2009-12-09T19:00:00.000-06:00

On my way to an evaluation team meeting today (I want to write more about that...but don't feel I can confidentially...one bad thing about being myself online and not having a blog pseudonym), I had a bit of a heart to heart with my boss (principal).

You might think, "on the way" isn't very long...but picture 100+ outdoor stairs from the school building to the admin building where the meeting was being held...lol.

Anyway, he was asking me how things were going, if I could believe that the year is already almost halfway over, and how time has flown in the 1.5ish years I've been in VA. He also mentioned that I have 30 more years to go before retiring. After that comment, he asked about my professional goals: When you're getting ready to retire, what do you hope to have accomplished/done?

At first, I didn't know how to respond. I'm not much for long-term planning. I'm lucky to know and have decided that I indeed will be staying in VA for at least one more year...to think 30 years down the road and wonder about what I hope to have achieved/accomplished?! That's way out of my comfort zone. Not on the horizon, even. I did answer him, however. I said that I want to get my Master's. The program I want might be closing, so I need to do more research, but I would *love* to do something along the lines of math/science instructional design/curriculum or, like the program I originally wanted, Deaf Education with a focus on math and science instruction.

I guess as a long range goal after that, it would be neat to be a tech facilitator (like @msgregson is studying to become), or a math specialist. I think I would like to be a consult or resource for the elemetary teachers (at least in my current school) with ideas and maybe even push-in math-specific services. There currently is no such position at my school, but I think it would be neat.

Just thought I'd share what my current thoughts are about long-term goals...any thoughts?

Thanksgiving Observations

2009-12-06T15:19:00.000-06:00

Over my week-long Thanksgiving Break, I spent 1 1/2 days doing observations of other math classrooms. A bit of background: my major in college was Special Education - Deaf Education with minors in math and english. Basically, though, I was treated as an Elementary Education major, with the addition of some ASL classes. All of my observations and practicums, as well as my internship placements, were in elementary classrooms. I *did* observe in a public middle school program for d/hh students at one point, but other than that, all of my exposure was to elementary teaching methods.

Tune into now, my 2nd year as a high school math teacher. I realized that the only high school math teachers I have ever observed were my own, and that was long enough ago that I don't remember specifics about what they did (let alone, while I was in high school I didn't really think I would ever be a high school math teacher...I started college majoring in music education with a minor in math thinking I could maybe teach middle school math if the band directing thing didn't work out).

Needless to say, I thought it might be a good idea to observe some other teachers at work with my "teacher goggles" on, looking at things like classroom management and structure, lesson organization, how to handle notes/homework, and just generally what other people's classrooms look like.

I went to Wisconsin School for the Deaf to look at Bilingual/Bicultural teaching philosophy, as well. I was able to observe a HS geometry, HS simulated budgeting, middle school, and several elementary classrooms. I was a little disappointed that my schedule wasn't exactly as it had been planned, but it was good to see what was happening at another school for the deaf. One of the major things I took away from those observations are ideas that I hope to bring to a personal finance class in the future. The simulated budgeting program that they have is very detailed and organized, and gives students real experience! I'd love to see something like that at my school. Something that surprised me, though, is that I only saw one student all day write anything on paper (as in, notetaking) other than their homework assignment. I spend a lot of time making guided notes and "worksheets" to allow the students to work through problems and then keep them as a reference in the future. The classes I observed did not do that. Problems were "through the air" or students worked them out on the board.

I also went to see @JackieB for a day! It was really fun to meet her in person, as I've been learning from her blog and tweets for about a year now. I got to see her integrated classes of freshmen and seniors, and her Algebra 2 class, as well as an AP Calc AB class. We also had the opportunity to go out to lunch and talk math. If only we could change the world...and the system...and kids' motivation to learn math. Something that I learned from Jackie is to highlight *every* opportunity to connect equations, graphs, tables and situations. In certain types of problems, I just forget to look at one of those 4, I now realize that the connections that can be made across the board might make at least a little easier for students to build connections and understanding of concepts. She asks really good questions, and makes her students squirm sometimes by refusing to tell them if their answer is right or wrong, but continuing to ask them questions like, "why?" and "how did you get there?" Keep it up, Jackie, and thanks again!

Contrary to popular belief (my friends and grandparents in the Chicago area), I am not looking for a job for next year. I'm just looking to get ideas of how I can improve my teaching, what I can do differently, and affirmation of some of the things I am already doing well. I wish I could take more time to go observe at different schools for the deaf across the country. There *has* to be someone out there that is having success teaching math to students who are d/hh. I want to steal every bit of wisdom I can!

Humbling

2009-11-19T05:47:00.000-06:00

I'd forgotten how humbling it is to make something and then send it to another person for feedback. As I was making my derivatives test yesterday, Sam mentioned that he would like to see it to compare with his. As I was writing the test, I was adding specific questions to target certain skills, but I also became highly aware that someone whose teaching I highly respect would be looking at this test very soon. It made me nervous! I'm in the very early stage of my career so I feel like I don't have anything to offer these teachers who have been at it for years. I become self-conscious. But I sent it anyway, despite my insecurities, and hopefully he'll have some feedback on how it could be better. *smile*

Thanks for making me strive to be a better teacher.

Running headfirst into a brick wall...

2009-11-15T19:11:00.000-06:00

...is what it felt like in my Algebra 1 class on Thursday. We had been making major progress Monday and Tuesday looking at function machines, finding outputs when given inputs and a rule, finding a rule and predicting outputs when given several input-output pairs. Then Wednesday we didn't have class because of standardized testing being done at school (Stanford Achievement Test-10...it has Deaf/Hard of Hearing norms so we use it every year to see how our students are improving with respect to their same aged d/hh peers). Thursday it was as if Monday and Tuesday had never happened.

While one student was trying to figure out the rule (2-step) for the table he had completed, two other students were struggling trying to complete the table. I had felt confident after Monday and Tuesday because this year I was actually talking about the functions and talking about the rates of change of the input and output, how they were related to the equation, how they related to each other, etc. (side note: last year I don't think I even talked about rate of change at all...I know that's terrible...but I didn't think the students had the grasp of the language *or* the concept, so we were in major survival mode when it came to slope, functions and graphing). Granted, the problem we were tackling on Thursday wasn't simple, but I was bamboozled when 2 students, half of my class, couldn't fill out a table given inputs and a rate of change!

The hardest thing to do in this class is differentiate. I have one very high student that needs to be challenged, and two fairly low students that need my support and guidance/hand-holding for much longer than other students need. Problem is, when I challenge the one student that is ahead, he needs my assistance to get going and to guide him along the way, then the other two are either lost or they go ahead and try their best to work independently and end up making errors along the way.

Catapults and Algebra 2

2009-10-30T19:06:00.000-05:00

In a previous post, I talked about how I used Sean Sweeney's catapult lesson in Calculus. I also used it in Algebra 2, as an enrichment project for two students while the rest of the class was gone for a sports event. I also talked here about how I introduced the project without actually being there.

Unfortunately, time for the actual project was cut short by an assembly that ran long. From what I could gather from sub notes and the notes that the students left, they enjoyed it. Unfortunately, with the short amount of time that Algebra 2 gets (and it keeps getting cut shorter when the kids leave early for sports games!!), they never finished it. It might be something I resurrect once the pressure of the SOL test is finished. There is just so much material to cover and I want to be able to take the time to actually *teach* the material instead of just showing it to them last minute.

Maybe it'll work better next year...?

p.s. this post was started on October 13th...it's now October 30th. Where does the time go?

On Catapults and Calculus

2009-10-22T17:00:00.000-05:00

I stole Mr. Sweeney's catapult project and tweaked it (more like, added to it) for Calculus class.

It was fun! We not only calculated the equation of the parabolic motion of the projectile, but at the end we talked about how fast it was going using the limit definition of the derivative at different points during its flight. It was a really great discovery point of how the velocity is zero at the maximum height. We were also able to then talk about why that "makes sense".

The next goal was for my calculus student to help my Algebra 2 students with the project while I was at a conference...stay tuned to hear how that went!

(I started writing this post 1 1/2 weeks ago...and the other one has been started, too...just waiting for some TIME to finish up!)

Discouraged

2009-10-13T16:49:00.001-05:00

Last week was a definite high. Things were going great! My observation went well, I was excited for the projects that I was leaving for while I was going to be out, and the substitute teacher that was scheduled to cover for me knew the language *and* the math! It was all looking good!

I arrived back at school to find my plans weren't completely followed. I know this is not unusual, but in preparing I thought I was ready for everything that could happen and that I had thought of everything...organized, etc. I guess not.

My Algebra 1 class that was solving 2-step equations like crazy on Wednesday bombed a quiz that they took on Friday (which they were supposed to take Thursday...but that's another story entirely). I felt like I needed to start from scratch again, and that everything from the week before was lost.

I had no Algebra 1 class today, so no chance to redeem. Tomorrow is a new day, though. We're going to correct the quizzes and then move on. We can't be solving 2-step equations forever, but we need it as a foundation!

Encouraged, Again

2009-10-08T15:20:00.000-05:00

Last Monday I was feeling overwhelmed. I go through these phases when I plan ahead, get a few days worth of lessons/notes put together, and then I get through one day and realize I'm not really ready for the next day at all because things didn't go the way I planned. These phases often leave me frustrated and irritated that I spent time up front that seems to be wasted. In the long run the time spent is not wasted, but it's still frustrating to *think* you're ahead and then *realize* that you're just as far behind as you normally are, despite the extra time you put in.

Anyway, that's how I was feeling Monday. And Tuesday I was supposed to get observed for the first time this school year. "Great," I was thinking, "just great." I had a less-than-stellar lesson planned, introducing graphing one-variable inequalities and solving one-step inqualities. Not something normally covered in Alg1 (it's a middle school concept), but that's what my kids need. I sent my lesson overview to my principal the day Monday and continued brain-storming ideas on how to make it more interesting.

I arrived Tuesday morning, less frantic than Monday (did I metion that I slept through my alarm on Monday morning, too...talk about a rough start to the week), and prepared myself mentally for the lesson and observation. Class started and I knew it was going to be a good day. I picked my best class for this observation. To provide some sort of closure from the day before and transition to the new topic, I had 2 students present problems from earlier (one- and two-step equations).

I was blown away as they were presenting. Without my prompting, they were explaining why the balance method for solving equations worked.

ex. 4x-7=9. I first added 7 to both sides because it's the opposite of the negative 7 that you have right now. I can cancel out the -7 and +7 because they equal zero. Then 9+7 is 16. I pull down the 4x = 16. Next I need to divide because it's the opposite of the multiplication that's happening now. I end up with x = 4

This type of reasoning and explanation never happened voluntarily in my classes last year. It's something I really have been working on with the students by asking a lot of "Why?" and conceptual questions. While the student was presenting, I kept thinking, "He's answering every question that I would have asked him!"

Later in the class, I found a way to make a boring part interesting by having the kids move around a bit. They needed to decide whether or not to flip the inequality. If it needed to be flipped, they stood up. If it could stay, they stayed sitting. One student made a mistake and stood up when the rest were still sitting. He felt silly at first, but his neighbor looked at him and explained why it didn't need to be flipped. He even gave an example of a situation (using the same numbers) where it would need to be flipped.

I was astounded. I love my job because I get to see things like that happen. I get to see kids grow and learn and teach each other. And I get to sit back and just watch sometimes! LOVE it. *smile*

Really excited for this week!

2009-10-04T15:41:00.000-05:00

I'm getting really excited for this week. Plans include catapults with Calculus and Algebra 2, complete with video instructions (really hoping that technology is my friend this week) and peer mentoring.

The goal for catapults is to work through the project in Calculus on Monday and Tuesday. We'll be taking it a bit more in depth than Mr. Sweeney's Algebra 2 project, talking about velocity and position relating to the initial discussions of derivatives. Then, on Thursday, Algebra 2 student will make a catapult from my model, and begin his investigation. Friday, Calculus student will join Algebra 2 student to help with the "math" of the project. All this will happen without me being there, which is why we need video directions!

I'm really excited for this, and the excitement easily turns into anxiety and thinking of all the ways it could completely bomb and blow up in my face when I return. But, it's worth a shot, right? Two-thirds of my Alg2 class is going to be gone Thursday and Friday anyway at a volleyball tournament, so here's my time to throw in a project for one of the more advanced students in my class.

Any words of wisdom?

GSP meets Algebra 1

2009-10-03T13:25:00.000-05:00

I was pleasantly surprised when my ITRT (read: tech person) at school emailed and said she found out we had a lab license for Geometer's Sketchpad (GSP). Last summer I took an online course from KeyPress to learn how to use GSP and more specifically, how it can be used in Algebra classes. I was very excited to learn more about this software and to be given examples of how it can apply to the concepts we teach in Algebra classes.

Earlier in the year, I used GSP to demonstrate adding and subtracting integers. I was using it as a demonstration tool at first, projected on my SMARTBoard. One problem I found using it that way, was that the sketch itself was too small for the students to see, and I ended up having one student sit at my computer and do the manipulating. I tried to make it work, and to let students take turns doing the manipulating, but it just didn't work the way I wanted it to. It was good, however, introducing the basic concept of what I was trying to develop: adding and subtracting integers on the number line. We then took that concept/idea and went back to paper and pencil methods.

This time, I took the students to the lab. We are solving equations, starting with the basics and moving forward to multi-step. I started the unit asking them to find the missing number in some simple equations, to see what methods they intuitively used. Next, we talked about working backwards, doing the opposite of what is currently being done to the variable, in order to get the variable alone. Finally, I wanted them to be able to explore the balance method of solving equations. I found a sketch with a balance, using positive and negatives. Gave the students a guided worksheet to explore what happens when you do different things to the balance. Was looking for the students to discover some properties about balancing equations (i.e. adding/subtracting the same number from both sides keeps the equation balanced, a positive and negative "cancel" each other, whatever you do to one side you must do to the other).

The students (as could be expected) struggled with the software. It was the first time they used it and the sketch had too many other things they could explore. They were curious and excited to play with it. I was able to ask some higher level questions, and the students responded well because they could support their ideas with the sketch. Their reading level caused them to struggle, even with the simple worksheet I created. I spent a lot of time going from student to student explaining what to do next.

Hopefully I'll be able to use this program again with this class, because I think they will be more comfortable with it and it'll probably be more successful the more they use it. Just thought I'd share my experience. Any suggestions are welcome.

**Note: I can't figure out how to upload the GSP files, so if you want a copy, leave a comment or email me**

Becoming more Human

2009-10-03T11:17:00.000-05:00

Wednesday I gave a test in Calculus. It was covering limits at a point, at infinity, one-sided limits, continuity, etc., even some free fall questions leading into our next unit on differentiation. The day before the test, I was nervous that the test was not going to go well. Review, things that should have been easy, was like pulling teeth. I was starting to doubt myself and my teaching.

During the test, I was looking through some stuff in my classroom and I happened upon my limits test from when I was in high school. I got a B+, and there was a calculator and no-calculator portion. I instantly thought, "Arg! I should've made a no-calculator portion!" Instead of dwelling on that, though, I just looked it over and found my mistakes...very interesting ones. Since the class finished the test with time to spare, I decided to show my test, and look at my mistakes. Looking at the problems I answered incorrectly, I asked the student to decide where I went wrong and what the answer should be. We went through the whole test like this, and even on some of the questions I answered correctly, I asked why that is the right answer.

This little exercise was a time-filler, yes. I think it made my student view me as a co-learner and as someone who has gone through what he is going through. I'm not just a teacher, I'm a student and learner too. I make mistakes in the classroom all the time, so it's not that my students view me as perfect and error free, but I think showing my old test and what was expected made a stronger bond between us. While I don't have all of my tests from calc, so I won't be able to do this frequently, I do plan to share from my experiences in calc during high school, and I hope to bring in some of the activities that we used (and some others!)

Encouraged

2009-09-28T21:10:00.000-05:00

Calc class today:

Limits review...he was actually on it! Material that I thought was going way over his head last week was processed and we had some really good conversations about different types of problems. Great questions were asked, showing that he's actually thinking about what he's doing and why, too. (There are, of course, still some trouble areas like knowing when to factor/rationalize and what numbers will "help" in the simplification process, but it's a process, right?).

Then, we did some free fall problems, applying limits and previewing derivatives. It was so great to actually apply what we've been talking about to a real situation and make it mean something. Here's the problem we spent time looking at, and some of the humor that came out of it...

A construction worker is working on a building that is 1000 feet tall. (side note, we took a tangent to see how many stories that would be, because 1000 ft is just an strange number to envision). Suppose the construction worker accidentally drops his wrench. If he immediately yells "Look out below!" (or something similar), how long will the person standing on the ground below him have to get out of the way before the wrench hits the ground? What will the speed of the wrench be at that time?

We took a tangent to talk about finding speed (using the limit definition of derivative, but he doesn't know that yet) at 5 seconds, and then at the time the wrench would hit the ground. We also had a good conversation about why the velocity is negative. When we found the velocity (-160ish ft/sec at 5 seconds, -252ish ft/sec at impact), we talked about how fast that really is, relating it to a football field. He couldn't believe the wrench could fall that fast.

When we had spent a lot of time talking about speed. He asked, "Wait, we didn't answer our question yet, can the person get out of the way in time?" *GRIN*

ASL is so visual with these kinds of problems...I love it.

Panic Mode

2009-09-27T19:33:00.000-05:00

Last week was the official Mid-Quarter marker for my school. This meant that mid-quarter grades were due, as well as updates on all IEP goal progress. It made for a busy week for all at school, learning a new grading program (I <3 PowerTeacher) and keeping up with *all* of the IEPs. (For those of you that don't know, every student I teach has an IEP...though not all have math-specific goals).

At the mention of Mid-Quarter, my heart started fluttering a little. It means that the school year is 1/8 finished. It also means that my semester-long Algebra 2 class is 1/4 finished. When I was looking at the state Standards of Learning for that class (there are 20) and thinking about what my students know and are able to do at this point, I entered what we will call "Panic Mode".

Algebra 2 is a tough course. There is so much to cover that is built upon Algebra 1 skills, more indepth and some entirely new concepts. I'm trying to remediate skills from Algebra 1, and cover new skills from Algebra 2, but they aren't getting it! The days that I have had great success and the students "got it", are the concepts that on a quiz 2-3 days later, the students missed the boat completely.

This is my fault for assuming that because they "got it" the first day, it didn't need to be revisited the next day. The "one and done" approach is not effective, but it is so difficult for me to think that it can be different in such a packed course.

Questions for the PLN:

How do you handle the pressure of time and breadth of courses while still covering concepts rather than procedures?
How much of your class time is spent allowing students to practice new skills/concepts on their own or with a partner as opposed to watching you demonstrate examples, group problem solving, or the like?

Planning and Time Management

2009-09-20T20:08:00.000-05:00

I've been a bit frazzled lately. I feel like I'm constantly running around at school and I don't have time to get my head on straight. When I sit down to work on planning the next day's lessons, or creating materials, I get sidetracked by other things that I *know* must be done while I am at school. I then leave the rest of the planning and creating for time over the weekend or at home. I'm not really liking that strategy.

I know that, as a teacher, it is almost innate within me to bring work home and to think about work when I am not actually working. I seriously think it's in our genes or something. What I don't like, though, is that I feel ineffective in the time I do have at school. Does anyone have any suggestions for how to manage planning time more effectively? How to use resources available online and from textbooks to develop lessons without feeling like you're recreating the wheel every time you make notes for a new topic?

I'm at the beginning of year number 2, and of the 4 classes that I teach, 2 are new to me (one is new to the school). I'm trying not to rely on the textbook so heavily, and trying to develop more activities and less worksheets to teach concepts, but it's a process. I'm also trying to go from primarily guided notes in Algebra 1 to a mix in Algebra 2, and teaching my calculus student how to take notes himself (this whole process is made much more difficult in a signing environment, because students cannot listen and write at the same time).

Hello!

2009-09-19T17:22:00.000-05:00

Well, I've entered the math 'blog-o-sphere." Don't set your expectations too high ("the best math teacher blog EVER"? not quite). My goal is to post at least once/week...but I'm not exactly sure how it's all going to work out. Be patient with me and if I get quiet, feel free to bug me on twitter or in comments. *smile*