Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

Friday, July 5, 2013

Teaching Well: Math

I was challenged on Twitter as I shared a host of tweets from a math conference. The statements were challenged and defined as platitudes.  "Platitudes," I wondered, "Why?, The last thing I want to do is tweet trite, meaningless statements."

I thought more about this challenge with the idea that there's usually some (or a lot) of truth in a naysayer's statements. I asked for further clarification and received some specifics, but not too much of a response. Then with further analysis, my thoughts led me back to a discussion I had a short while ago with a leader from a major United States company. He lamented that new engineering graduates he works with lack estimation and process skills. Then yesterday I queried a nuclear engineer who supported the first leader's comments, and further commented that new hires need to understand the math more--the relationships and the ability to estimate and design. As we conversed, I stated, "So you're telling me that good math teaching is about learning the math, and understanding it well?"

He responded that students need to build that foundation up step-by-step with a firm understanding and facility of one step before moving to the other, then he cited that early acquisition of facts and computation leads to confidence and efficiency when learning about and solving more complex problems. He felt that online models and real-world applications were good tools and approaches to learning the math too, and he supported actions which move students forward as they are ready rather than waiting until they advance to the next grade. Also, at a Googleplex conference in the winter, a leading venture capitalist in the science field affirmed this approach as he told the story of his son who passed an ap calculous exam in 5th grade. That child also had the good fortune of a small experienced teacher-student (1:2) ratio and responsive course of study.

So what does all of this conversation say to me as a fourth grade teacher who is interested in teaching children well?  First, these conversations point me in the direction of learning the math well--knowing as much as possible about math as a teacher of young children. Often courses for elementary school teachers focus more on the teaching process than the subject content itself. Yet we know that a solid, strong understanding of the content supports worthy teaching. Hence, I'll read a math text this summer--a book that reminds me, and synthesizes for me, the essential math concepts from early learning to calculus. What titles would you recommend in this regard?

Next, I'll look for structures and tools to solidify students' foundation skills and move students forward as they are ready. I'll work to utilize tech tools and other materials to individualize the math classroom as much as possible so that each child is growing with skill, concept, and knowledge in steady, worthwhile ways.  Finally, I'll focus on process and collaboration too as students work with each other to both learn the math and problem solve with meaningful, real-world math problems and projects. As you can imagine, I could spend the entire two months of the summer just focused on this topic and teaching focus.

This discussion brings me back to an earlier discussion about the role of generalist in the elementary school.  While I like the fact that as a generalist I am able to know each child well and teach in a targeted, personalized, and integrated way, I am also well aware of how much there is to learn and know in each subject area as information becomes more accessible and students more diverse and facile at the same time. At our fifth grade, teachers team. One teacher focuses on math and science, and the other teacher focuses on English language arts and social studies.  That model streamlines the teacher's needed area of expertise, but that model also doubles the teacher's responsibility to 50 students, rather than 25.

I'm not eager to adopt that model as I'd rather move to a menu approach of education where teachers' responsibilities are streamlined with new structures, routines, and models for education.  I don't think more of the same is the answer.  The engineer I spoke to yesterday agreed with this, and pointed to the many years, dollars and efforts spent on improving education--he recommended using engineer's "course correction" efforts to improve our craft and move schools forward.

Now this post is starting to jump all over the place, hence I'll summarize with yet another set of priorities for the new school year including the following:
  • Renewed efforts related to writer's workshop and teaching writing well.
  • Greater study and prep for the upcoming year of math teaching. 
  • Learning design research that results in a learning design template. 
Teaching children well is a job with limitless potential and paths, and as I've stated again and again, this task demands thoughtful collaboration, prioritization, and direction as we move towards serving every child with strength and purpose. With this in mind, the question remains: How will we structure school routines, roles, and responsibilities to maximize our impact with regard to teaching each child well? 



Tuesday, July 2, 2013

Wayland Math Institute: Final Notes

The Institute was a positive, informative event.  The final notes are below. Now it's time for summer break and "no school" for a while.


Kassia Omohundro Wedekind: Wayland Math Institute Keynote, Day Two

Kassia Omohundro Wedekind, author of Math Exchanges, delivered a wonderful keynote on day two at the Wayland Math Institute. Her presentation encouraged child-friendly, risk-taking, dynamic math workshops where students exchange ideas, engage in math learning, and publish what they learn. She further encouraged all of us to "live a rich mathematical life" and to share that life through storytelling, play, and problem solving. 

The notes below reflect Wedekind's links, strategies, and efforts.  I hope to synthesize these ideas with greater effort in the weeks to come as I look forward to school year 2013-2014.

Monday, July 1, 2013

Nicki Newton: Tips and Tricks for Teaching Fractions

Nicki Newton presented fraction teaching tips to third through fifth grade educators at the Wayland Math Institute today. These are a few of the links, strategies, and tools she shared.

Math Conversations and SMPs: Wayland Math Institute

More wonderful take aways from The Wayland Math Institute:

Nicki Newton Keynote: Day One Wayland Math Institute

Nicki Newton gave us numerous ideas to think about and implement as we continue to hone our math craft and teach children well. I made a storify of the main notes, links, and tools mentioned that will impact my teaching next year. Feel free to read, use, and comment.

Math Workshop Presentation: Wayland Math Institute

Wayland's two-day Math Institute begins today. The institute sets the stage for educators from Wayland and nearby districts to share math knowledge, strategies, and questions with experts and each other.

I will share knowledge and strategy related to math workshop with the presentation below:



I look forward to the workshop participants' questions, suggestions, and further ideas with regard to promoting active math learning within a workshop format.

New standards, structures, and tools are enhancing math teaching and share in wonderful, invigorating ways.  I'm sure that I'll leave the two-day Institute with many new ideas for teaching math well year next year and in the years to come.

Does your math teaching and practice look similar to mine?  What would resources, connections, mentors, strategies, and efforts would you add?  What strategies would you replace or delete? I look forward to your thoughts, questions, and expertise.

Tuesday, June 4, 2013

STEAM Share

Today I'm getting the chance to learn with students.  The teacher next door has invited my class to a STEAM (science, teach, engineering, art, math) share.  She and her students will share the many innovative projects they've embarked on over the year. They will also demonstrate the ways that they learn in hands-on, student-directed, investigative ways.

All year I've watched this class create with enthusiasm.  Hence, I'm looking forward to this collective way to learn. While in the room I plan to do a lot of observation and take lots of notes since I plan to replicate this learning event in my own classroom soon.  Then I plan to think more deeply about the tools and strategies I see over the summer so that I can employ similar strategies next year.

My grade level colleagues and I have started thinking about new ways to share our strengths and teaching strategies; we hope to get into each other's rooms more often next year to observe and share.  We've built a strong level of collegial trust and common vision which makes this possible. I'm excited about the learning to come as I know this will help us to teach children well.

Wednesday, May 29, 2013

Fourth Grade Math Scope and Sequence Notes

Math Scope and Sequence

Yesterday the team met about the math scope and sequence for next year's fourth grade. Essentially we made room for all the main grade-level concepts. The meeting gave us a positive launching pad for next year's math program. I hope to add more detail to the chart over the summer and next year to guide the classroom efforts.

My math goal next year will be to use an SMP planning chart and the standards to guide the roll-out of each unit in differentiated ways providing room for all on the continuum from remediation and review to enrichment in engaging ways.

In addition to the scope and sequence, I will also employ a number of “Mental Push-ups” (a term coined by my colleague, Mike O'Connor) and math routines to develop facility and fluency with math concepts. The routines will include the following:

  • oral routines
  • fact practice
  • math message
  • computation practice
  • online home study (self grading/reporting) i.e. Xtra Math, That Quiz, SumDog
Over the summer months, I'll revise the class math website to reflect this scope and sequence as well as the many activities we employed this year to develop students' understanding. If you have any additions, revisions, or deletions for me, please let me know. There's so much potential when it comes to math education today, and I believe that yesterday's meeting was one step in the right direction with next year's students in mind.


Date
Assessments
Concept Thread
Computation/Problem Solving  Thread
September


GMADE
CBM?
Symphony Benchmark?
Facts Assessment



Concept
Measurement /Line plots**
Roll-Out
Use multiple tools to introduce measurement equivalencies, standards.


Include patterns
Tools
Youtube videos, songs, problem solving sheets.


rulers, meter sticks, yard sticks, tape measures, images of landmark measurements.
Homework



*Note that measurement is a nice introductory unit as it is new for many and you can use it help introduce classroom information. Here is a link to many measurement activities.



Concept
Addition / Subtraction with regrouping / Place Value and Problem Solving - September - EDM Unit 2
Roll-Out
*Individual fact menus set for each child.
*Math Routines and Systems - week 1 (SMPs intro)
Add/Subtract Facts
*Place value  and Rounding - how does our base 10 system work? - week 2
*Addition with regrouping - week 3
(including adding three or more numbers, adding money, numbers w/decimal points)
*Subtraction with regrouping - week 4
(subtracting large numbers, numbers w/0, money- check with addition)

Tools
  • Tech Connect: Symphony, That Quiz, Xtra Math, Sum Dog
  • EDM book
Homework
Online/offline computation work.
Strategies
Grow at your own rate computation work, practice efforts that last throughout the year.

October


Concept
Basics of Multiplication - second half of October - EDM Unit 3
Roll-out
*Understand factors and find all factor pairs for a given whole number  / multiples
*Commutative property
*Fact strategies
*Variables to represent unknowns
*Prime and composite
Tools
Factor Game (online/Off)
That Quiz has good algebra practice.
Tynker project
Homework
Fact Practice online/off


That Quiz Factors/Multiple Tests





Concept
Multiplication Facts
Roll-out

Tools
Tech Connect: Symphony, That Quiz, Xtra Math, Sum Dog, FastMath
Homework
Multiplication fact practice


November


Concept
Area and Perimeter**
Roll-out

Tools
video song
manipulatives
graph paper
lots of practice w/open response problems from the past
That Quiz has great online practice tests for this.


Sketch-Up
Chrome Room Design App
Ikea Room Design

Homework
That Quiz has great area/perimeter practice tests.




Concept
Multi-Digit Multiplication  - EDM Unit 5
Roll-out
*2 by 1, 3 by 1 (distributive property)
*Partial products
*2 by 2
*Distances on a map (scale) (option?)
*Introduction of standard algorithm
Tools
lots of paper/pencil practice
lots of practice with word problems and model making
review videos
related open response problems.
Homework
practice sets


December-
mid January


Concept
Patterns and algebra. Geometry**
Roll-out

Tools
online balance activity
students create and analyze patterns.
Possible measurement review with patterns.
Homework
Utilize past concepts of factors, multiples, and measurement in patterns/algebra.


Use algebra when solving simple math problems that review facts, addition and multiplication.




Concept
Long Division - Unit 6

Roll-out
*use equal groups (base ten blocks)
*partial quotients
*area model (using base ten blocks)
*standard algorithm

Tools
related open response problems
conceptual lessons/models
Homework
practice sets


Video review


Mid January- March


GMADE
Symphony Mid-Year Benchmark?


CBM?


Concept
Fractions/Decimals -  Unit 7
Roll-out
*Fraction of a whole – using circles (360 into really helps), number line, rectangles and discrete sets (use manipulatives)
*Mixed numbers and improper fractions (supplement)
*Converting mixed to improper fractions and back  (worksheets)
*Changing the whole changes the value of the fraction
*Comparing and ordering fractions with different numerators and different denominators by comparing to a benchmark fraction – use PROBE 2
*Simple equivalent fractions
*Adding and subtracting fractions (up to mixed numbers with like denominators) –
lesson 7.5
*Fraction addition and subtraction with estimating
*Compose and decompose fractions into unit fractions
*Multiplying fractions by whole numbers – see the “Cloud Model” for multiplying fractions
-lesson 7.12a
*Use decimal notation for fractions with denominators of 10 or 100
*Locate decimals on a number line
*Compare and order decimals to the hundredths place


Tools
Multiple resources available online/offline including project base endeavor and problem solving.
Homework
Lots of practice




Concept
Computation/Facts Practice, Review and Related Problem Solving
Roll-out
Regular practice with problem solving, problem solving with fractions.
Tools

Homework



April


Concept
Geometry Part 2
Roll-out
*Identify and draw points, line segments, lines and rays (1.2)
*Naming angles (1.3) and parallel / perpendicular lines
*Identifying 2D figures (rest of 1.3, 1.4 and 1.5)
*Line of symmetry (10.4)
*Recognizing 360 degrees in a circle (6.5)
*Measuring angles with a half circle and full circle protractor (6.6 and 6.7)
*Recognizing angle measure as additive - Angle Add Up (unit 7 p 619 in manual - MM 507-509, which include directions)
*Constructing angles (6.6 and 6.7)
*Review 3D
Believe there’s a considerable emphasis on quadrilaterals--I’ll check on that.
Tools
That Quiz has a great online protractor/angle measurement activity


360 packet helps w/fractions and angles.


Pattern block exploration


Open response problem solving.
Homework
That Quiz has great fraction test practice.


Use Line Plot to practice work w/fractions.





Students seem to grasp these concepts with ease.


Concept
Open Response Problem Solving Close Review /Computation Review


MCAS Review of all concepts
Roll-out
Teach /Review Strategies:
  • underline key words
  • circle question
  • show work, label, use structure
  • write Answer: and answer with complete sentence
  • check work.
Tools
Old MCAS problems that match problem.


New Parcc/CC problems.
Homework



May



Symphony end year benchmark


CBM end year?


MCAS


Concept
MCAS Review
Roll-out
At-home give student practice packets for homework.


In-class use practice packets for collaborative work, practice test.


Review packets together, reteach concepts that are not mastered, but close.
Tools
Former MCAS packets
Homework
MCAS practice test and problems


That Quiz 10-problem quick review sets at home and in-school, independent and collaborative.




Concept
Open Response Problem Solving Close Review /Computation Review
Roll-out

Tools

Homework



June


Concept
Math/Science Project Base Learning - Applying math concepts to science information (endangered species) possible link with data and stats, i.e. infographics
Roll-out

Tools

Homework





Concept
Continued fact, computation review and problem solving.  Perhaps a focus on “math talk” and lively math discussion.
Roll-out

Tools

Homework




**Units that can be moved to different times of the year without too much trouble.

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