Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Sunday, March 23, 2014

Upper Elementary in AMI

Upper Elementary in AMI

Every once in a while I hear that AMI does not "seem to have much for the 9-12 year old." I have to admit I am perplexed by that statement. As a mother of an almost 10 year old boy who is in the middle of upper elementary right now and "started" elementary a bit "early"... well, he's still pretty busy. On the one hand, I am entirely amazed at what we have accomplished, but we also started elementary at 5 1/2 (giving us more time) and he's an only child of a single mom who runs two businesses from her home and off/on has part-time work outside the home (read that as: lots of free time to avoid school work and play with Legos instead). On the other hand, now the DEEP work is part and parcel of our everyday lives, I can't imagine adding anything MORE to what we do ;)


Here is what I see when I look at AMI albums compared to other albums, in no particular order:

  • AMI albums have a general presumption that a child has done all or most of the work in the primary albums. 
    • A child not coming primary IS given remediation sections in mathematics and language to "bridge" into elementary without that previous background. These DO NOT repeat the primary albums, nor do they take as long. A normally developing 6 year old starting elementary Montessori can anticipate being less than a "year behind" his peers by the 3rd year of elementary, and likely not even that much. I say "behind" in quotes, because no child is truly behind - he is where he is and we work with the child in that place (this is what following the child means - following his NEEDS).
    • I personally strongly encourage use of the sensorial album with new elementary children; utilizing the presentations as "challenges" rather than presented work. It generally takes less than a month of daily sensorial activities to lay a strong foundation (while doing other subject areas of interest/need). But that is just my personal experience speaking.
  • In general, AMI has fewer materials, with more use of the same material in a variety of ways, going deeper with the one material rather than spreading out to more materials.
  • AMI lays the foundation and expectation for a child to go deeper with his work, ask his own questions, seek out answers and collaborate with others. There are cues along the way, begun in primary and continued throughout elementary - we do not provide all the child's math problems for example, but provide prompts of the sort of math problems to create on his own - we can monitor his work and prompt areas that need attention.
  • Upper elementary (ages 9-12) does not entirely repeat 6-9 - but all concepts are reviewed. Since personal research is encouraged from the get-go, by the time a child is in upper elementary, he should really be going much deeper with his work. Review concepts in history, for example, and most if not all upper elementary students should be delving into their own personal study of local national history, state/province history, and another area of choice (generally children have an area of history they flourish in - GO with it).
  • AMI does NOT bog a child down or remove his imagination, creativity, or passion for learning by dictating every single study he does. AMI provides keys - a foundation and a framework - then provides guides for following particular interests (Goings Outs, history question charts, reading great literature and delving into the language used, music experiences with the tone bars, economic geography, etc.). If a particular child or family has a particular interest or value, there is now time to follow that particular pursuit because you do not have 6 hours of schoolwork dictated to you for every day of upper elementary.
  • AMI does not utilize some materials in lower elementary that WERE used in primary, that some other albums say are still necessary at lower elementary (some of these items, such as the small bead frame, are not even used in AMI remedial mathematics at the elementary level - yet it is a "crucial" material in other elementary albums --- all those concepts can be covered with the large bead frame and NOT slow a child down) ---- thus beginning to go deeper, sooner and freeing up time/effort at the upper end of the age spectrum, when children in the well-run AMI schools DO get into algebra in 6th grade (not ALL children do! even at the best top-notch schools - again, we follow the child --- but here is another point: many children do NOT get to all the presentations in the math album and have more to do as they enter the adolescent plane of development.... so how can there not be enough in math?)
  • I can ALMOST see the concern in language - there is less "dictated" - there are less "direct lessons". This is a benefit to the child if they have done most or all of the official lessons in the language album before getting to upper elementary. Now they can explore IDEAS, delve into speech, debate, drama, writing papers in one style, then re-writing in another style for comparison ---- hitting on all those extensions of the early album pages that they weren't ready for in lower elementary or didn't have time for (because of all the personal research they were doing).
In summary, AMI is so RICH with the actual keys and with the individual paths of the children, that the only thing I can fathom in trying to understand "there's just not much there for an upper elementary child" is that "there is just not much there for an upper elementary child's parent to directly teach (if all the "lower elementary" work is done)". If all the lower elementary isn't done - well, there is what an upper elementary child can jump into, have fun and explore!



If a child has done ALL of the suggested work for the lower elementary child, here is a generic (not near as detailed as it could be) run-down of the work for an upper elementary child:
(please keep in mind that most children will not get to all suggested topics in lower elementary, because their interests and needs are elsewhere; some will delve into upper elementary topics earlier, but will need to get the other topics later)
(music is not included here - follow the child entirely on this one)

Geography


Chapter I: Creation of the Earth/Idea of the Universe
God with No Hands - experiments - follow-ups
Additional Creation stories
Composition of the Earth
Further Details of the Composition of the Earth (stages)
Formation of the Mountains

Chapter II: Nature of the Elements
Further States of Matter
Different Ways of Combining
Separation, Saturation, Super-saturation
Attraction and Gravity
Extensions of all of the above

Chapter III: The Sun and the Earth
Time Zone Chart
Tilt of the Axis: Solstice, etc
Seasons and the Two Tropics: terminology from tilt

Chapter IV: The Work of Air
Review entire chapter; cover anything missed; select follow-ups to research

Chapter V: The Work of Water
The River
The Rains - Erosion
Ocean Waves
Ice
Spread of Vegetation
People in Different Zones

Chapter VI: Human Geography
Human Geography (Economy)
Overview of Local Government
Follow-Ups
Study of Natural Resources - Introductions
What is Produced and Where
Study of Consumption
Study of Consumption - Follow-Up (extensive)
Comparison of Production and Consumption
Imports and Exports:
Volume of World Trade
World Commerce
FINAL NOTES: Children should be studying in areas of interest (astronomy, physics, geology, etc.) Topics of less interest will be covered in middle/high school.


Biology


Biology – Botany and Zoology
Botany Experiments and Exploration
Story Material
Dissection of Animals

Biology: Classification
Kingdom Vegetalia: Classification
Genera
Familes: Continuing Classification
Geneaology of the Plant
Tree of Classification:
Kingdom Animalia: Classification

Biology: Ecology
Ecosystems - variety



Language


Chapter I: History of Language
The Story of Communication in Signs
The History of Written Language
The History of Spoken Language

Chapter II: Grammar and Syntax
Compound Words - Conversations
Additional Grammar Symbols
Verbs - Simple Tense: Present
Verbs - Simple Tense: Past
Verbs - Auxiliary Verbs
Verbs - Simple Tense: Future
Verbs - The Perfect Tenses
Verbs - The Infinitive and Moods
Verbs - Negative Form of the Verb
LA: Simple Sent w Extensions - box 2
LA: Simple Sent w Extensions - on paper
LA: Verbal & Nominal Predicates (linking verbs)
Elliptical Sentences
Order of Sentences
Voice of the Verb
Voice of the Verb - Dictation
Transitive and Intransitive Verbs
Compound Sentences
Complex Sentences - Adjective Clauses
Complex Sentences - Adverbial Clauses
Complex Sentences - Noun Clauses - Direct
Complex Sentences - Noun Clauses - Indirect
Complex Sentences - Noun Clauses - Subject
Complex Sentences: Degrees of Dependence

Chapter III: Written Language
Written Language Part I & 2
Historical Investigation
Heraldry
Runes
Calligraphy
Decoration
Illustration
Illumination
Variety of paper
Exploration of grammar books
The Content of Children’s Work
Factual Writing - Various forms
Imaginative Writing - Various forms
Research and Note-Taking

Chapter IV: Spoken Language
Discussion
Reports
Speeches
Debates
Poetry Reading
Dialogue
Dialogue 2: Interviews

Chapter V: Literature
Introduction to Literature
Linguistic writing research
History of English Literature - research
Book of Kells
Chaucer
Etymology
Songs and Verse
Beowulf
Hymn of Caedman
Anglo-Saxon Chronicle
American Literature
include selections in the classroom
studies of authors and lives
Children’s Literature
older literature selections (pre 1900s)
1900s literature selections
Children’s Literature in the United States
Read and listen to books
Timelines
Biographies of authors
Goings Out related to literature
Other explorations

Chapter VI: Style
Style



Mathematics



Operations
Group Division
Group Division & Word Problems

Decimal Fractions
Relative Size of Terms/Numbers
Division of a Decimal Fraction by a Decimal Fraction
Leading to Abstraction of Multiplication of Decimal Fractions
Division of a Decimal Fraction on Paper

Squaring and Cubing
Squaring with a Hierarchical Value: stages
Pass From One Cube to Another
Cubing a Binomial
Cubing a Trinomial
Cubing a Quadrinomial
Cubing a Trinomial having Numerical Value
The Story of the Three Kings
Cubing a Number with Decimal Value
Square Roots
Square Roots - Abstraction stages
Special Cases - stages
Square Roots: review process and rules
Cube Roots
Cube Roots: Review concept and rule

Other Topics
Signed Numbers: Negative Snake Game
Signed Numbers: Operations (stages)
Powers of 2
Powers of 3: Full work
Powers of 2 and 3: Combined
Powers of 10
Operations Using Exponential Notation
Expanded Power Notation - Intro and Operations
Word Problems
Distance/Velocity/Time
Principal/Interest/Rate/Time
Non-Decimal Bases: Intro and Operations
Conversion of Number Bases
Balancing an Equation using operations
Solve for Unknown: Operations
Algebra Word Problems
Solve for Two Unknowns
All stages in upper elementary typically


Geometry


I. Introduction to Geometry
Various Geometry Stories from History
II. Congruency, Similarity, Equivalency I
Review all concepts in Upper Elementary
IX. Equivalency III
Equivalency with Iron Material: stages
Euclid’s Plate
X. Area
Concept of Area
Deriving Formulae with the Yellow Material: stages
Deriving Formulae with the Iron Material: stages
XI. Circle I
The Circle Nomenclature
Relationship Between Lines and Circumferences
Relationships Between Two Circumferences
XII. Circle II
Area of a Circle (stages)
Relationship Between the Apothem and Side of a Plane Figure
XIII. Solid Geometry
Concept of Volume
Equivalence as Related to Solid Figures
Three Important Dimensions
Equivalence Between Prisms with Various Bases
Derivation of the Formula
Solids of Rotation
Volume of the Pyramid
Volume of the Cylinder and Cone
Polyhedrons
Lateral and Total Surface Area of Solids

FINAL NOTES: Use 6th year to review and consolidate all concepts


History


The Coming of Life Story with Timeline
The Black Strip
Fundamental Needs of Human Beings – Charts --- some portions start in year 4
History Question Charts
Three Phases of History
Second Timeline of Human Beings
Migration Charts
Four River Civilizations
New World Civilizations
Timeline of Civilizations
Timelines for Memorization
American History (National History)
Clock
Personal Timeline
Calendar
BC-AD Timeline




Wednesday, March 19, 2014

Learning to Read - changing the words on the page

As my son was allegedly "learning" to read, he would make some of the following changes to words on the page:


"three angles" on the page, he says, "triangle"
"Holy Trinity" on the page, he says "God" (or vice versa)
"Mary" on the page, he says "Mother of God"

His mind was seeing the words and interpreting them - and the words coming out of his mouth were on the same topic, and appropriate, but NOT what was on the page.


Makes me wonder ---- all these years later.... is it possible my son was already reading at 2 and 3, but because he wasn't speaking, he wasn't sharing what he was reading (and Montessori does not require reading out loud from the youngest children - they should read and match labels with objects, follow commands, etc. - other ways of showing their comprehension ---- or practicing the words away from the adult and reading the words aloud when comfortable).


I wonder if some of our angst could have been spared if I had adjusted my in-the-moment expectations and just trusted that he COULD read (even when he was reading aloud, then afterward saying he couldn't read because some girl at school told him he couldn't).....


Friday, March 14, 2014

Album Tables of Contents

My Keys of the World website is in transition right now - I thought the sub-folders were working but they are not.... so no-one can purchase on that site! And that means that all the Montessori album tables of contents are NOT available....

So for the time being, I am posted them here:
http://montessoritrails.blogspot.com/p/keys-albums.html

--- a new page on this blog. Albums are available at Garden of Francis (all ages) and Keys of the Universe Elementary (elementary and adolescent; individual albums or complete set).

Saturday, March 1, 2014

REVIEW POST: Primary Grade Challenge Math - Zaccaro

(UPDATE 10/28/14: We have added Upper Elementary Challenge Math to our repertoire and couldn't be happier :) See the associated Montessori Trail post.)


Legoboy has another New Love:

Challenge Math by Zaccaro

We are starting with this one - covering grades 1-4 for "gifted children".



I ended up purchasing the entire of books in this series for several reasons:
  1. looking for a good set of word problems to review earlier concepts
  2. Montessori math and geometry do not align with any other available curriculum (I group the Montessori-inspired curricula options somewhere in the middle)
  3. Something just didn't sit right with me concerning the other options. They are useful; I will not say don't use them (especially if they are working great for you! Keep going with what works!) - but there was a mis-match for our family, my principles and my understanding of Montessori. 
  4. This set of books (there are several in the series) are designed for gifted children - children of younger ages who have particular gifts that correspond with typically older children. 
  5. I wanted to review them for the sake of other families looking for a resource to fill a similar need. 
  6. This series also includes some of those allegedly missing concepts, perfectly tying them into the included album pages (associating money with decimal fractions, converting into percents, etc. (NOTE: Please do not flame me in comments regarding missing concepts - I've covered this topic before, I am not saying Montessori is wrong, and I'm not saying the concepts aren't there - I am fully trained, I know where the concepts are and where they fit in. Comments of a flaming nature will be removed. I'm done with flaming when I speak peacefully. Thank you for speaking respectfully.)


Word Problems: 
     A few people have shared a few solutions to the dearth of word problems - and the lack of time to create their own (and my lack of time to create my own!) for each and every concept. Especially in a sporadic co-op/tutoring, mostly homeschooled by himself situation, there just aren't classmates around to pull up the caliber - and I am one person unable to cover everything (stop laughing!). ;) 

Montessori Mathematics and Geometry Studies: 
     Montessori math and geometry use hands-on materials to bring the children to the point of abstraction. In some areas, it seems that the children hold on to the materials longer than their public school counterparts, but once they release the materials, they are almost always ahead in conceptual understanding. Where we have children not able to apply the concepts, we have a situation where the adult likely didn't assure the child was working with appropriately challenging work and likely didn't ensure there were appropriate real life word problems and experiences available. 

Not sitting right: 
     What is about the other options that didn't sit right? I think because they are geared towards public school curriculum, several of the options have already been re-written to correspond to Common Core (the dumbing down of our country's children), and I just don't want to participate. 

     In addition, I really wanted something that more closely resembled Montessori. Life of Fred is a great complement to Montessori elementary mathematics but there are few word problems. 
     I think this is my main thing - I don't want to dig into 4th grade books to find word problems to give to a 1st grader, just to find math skills that fit.  

Young Age - Older Work: 
     Isn't that the mis-match of Montessori to other expectations again? 

Perhaps my reason are the same thing over and over - with different words: I wanted something that better corresponds what we are doing as compared to constantly tweaking, reading, adjusting, pulling "7th grade" materials for a 2nd grader who isn't "special" in that way, but simply has been given the tools to go deep with his understanding.... I was (and am!) tired of tweaking already!!!!

What we are using: 
     Legoboy is 1st year upper elementary, or 4th year elementary - and I would NOT say he is gifted in this way. However, he has received the keys provided through Montessori throughout his life. As a "4th grader", we started with the primary level book to review past concepts - kind of catch up in the word problem category. We did great for 1st-3rd grade, but I'm done tweaking (have I said that yet!?) and I have to be done looking too. 

Legoboy loves it! He is actually working out the math in his head or on paper as needed, then he challenges me with it. Even with Life of Fred, I have to "encourage" him to record any work, or answer out loud. He just wants to read the story (although he can do the math in the books). 


How it is set up: 

Each chapter contains some background/how-to-solve information on a particular topic - most is review for Legoboy, some is new or said in a new way. Then there are 4 pages of problems - 1-2 page(s) for each "level". The chapters can be done in any order, but easier concepts are towards the beginning. Chapters can cover a variety of topics but are generally somewhat grouped together.


The four core books we will be using are the following: 
  1. Primary Challenge Math - grades 1-4: Includes chapters on Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. This book includes topics that Montessori has in upper elementary. Guess what? That tells me it is likely to trust a child's abilities and correspond well. I am NOT disappointed. 
  2. Upper Elementary Challenge Math - grades 3-5 (this is available for pre-order, shipping in April)
  3. Challenge Math - grades 4-9: Includes chapters on Astronomy, Algebra, Problem Solving, Percents, Fractions, Decimals, Ratio & Proportions, Physics, Statistics, Probability, Metric System, Perimeters, Area, Volumes, Trigonometry, Calculus
  4. Real World Algebra - grades 4-9: Includes chapters on Language of Algebra, Geometry and Algebra, Proportions and Algebra, Physics, Levers, Pythagorean Theorem, Percents and Algebra, Simultaneous Equations, Algebra and Money
We also have the following that at first skim have been great: 
  • Becoming a Problem Solving Genius: A Handbook of Math Strategies
  • 10 Things All Future Mathematicians and Scientists Must Know (but are rarely taught)
  • 25 Real Life Math Investigations That Will Astound Teachers and Students
  • Scammed by Statistics: How we are lied to, cheated and manipulated by statistics and why you should care


I am working on something of a correlation between the AMI mathematics album and these books - slowly creating a correlation. I will share this on the Keys of the Universe Discussion Community in Excel format and will likely post it on this blog at some point in pdf format (this will happen faster if those who are interested, let me know - I'll prioritize it ;) ). 

Sample - Chapter 4 - On Money