---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:17405
- loss:CachedMultipleNegativesRankingLoss
widget:
- source_sentence: 'Subject: Range and Interquartile Range from a List of Data
Construct: Calculate the range from a list of data
Question: What is the range of the following numbers?
\[
1,5,5,17,-6
\]
Incorrect Answer: \( 5 \)'
sentences:
- 'To find the range adds the biggest and smallest number rather than subtract
The passage is clarifying a common misunderstanding about how to calculate the
range of a set of numbers. The misconception here is that someone might think
the range is found by adding the largest number to the smallest number in the
dataset. However, this is incorrect. The correct method to find the range is to
subtract the smallest number from the largest number in the dataset. This subtraction
gives the difference, which represents how spread out the numbers are.'
- 'Finds the mode rather than the range
The passage is indicating a common mistake made in solving math problems, particularly
those involving statistics. The misconception lies in a confusion between two
statistical concepts: the mode and the range.
- **Mode**: This is the value that appears most frequently in a set of data. It
helps to identify the most typical or common value.
- **Range**: This is the difference between the highest and lowest values in a
set of data. It gives an idea about the spread or dispersion of the values.
The misconception described here suggests that a student might calculate the mode
when asked to find the range, or simply mix up these two concepts. The important
distinction is that while the mode tells you about the frequency of the most common
value, the range informs you about the span of the data.'
- "Believes a cubic expression should have three terms\nThe misconception described\
\ here is that someone might think a cubic expression, which is a polynomial of\
\ degree three, should consist of exactly three terms. This is a misunderstanding\
\ because a cubic expression can have any number of terms, but the highest power\
\ of the variable must be three. \n\nFor example, both \\( x^3 + 2x + 1 \\) and\
\ \\( 4x^3 - 3x^2 + x - 7 \\) are cubic expressions, even though they have different\
\ numbers of terms. The defining characteristic is that the highest power of the\
\ variable (x in these examples) is three. So, a cubic expression can have fewer\
\ or more than three terms, as long as the degree (the highest power) of the expression\
\ is three."
- source_sentence: 'Subject: Reflection
Construct: Reflect an object or a point in a diagonal line with the line of reflection
drawn, where the line of reflection lies on the edge or outside the object
Question: The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate
grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates:
(-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]()
Incorrect Answer: \( (-4,5) \)'
sentences:
- 'Reflects horizontally or vertically instead of across a diagonal line of symmetry
The passage is discussing a common mistake made in geometry, particularly when
dealing with reflections of shapes. The misconception is that students might incorrectly
think that the reflection is happening horizontally or vertically (i.e., across
a line that is either parallel to the x-axis or y-axis). In reality, the reflection
might be across a diagonal line of symmetry, which means the line that serves
as the mirror could be at an angle, such as a 45-degree line from one corner of
a square or rectangle to the opposite corner.
To correct this misconception, it''s important to emphasize the actual direction
and axis of reflection, understanding that a line of symmetry can be oriented
in any direction, not just horizontal or vertical. Visual aids and examples that
include diagonal lines of symmetry can help in grasping this concept better.'
- 'Fails to reflect across mirror line
The passage is discussing a common misconception in geometry, specifically in
relation to reflecting shapes or points across a line, often referred to as a
"mirror line." This reflection involves creating a mirror image of a given figure
on the other side of the mirror line, maintaining the same distance from the line
as the original figure.
The misconception "Fails to reflect across mirror line" means that someone might
not correctly understand or apply the rules of reflection in their work. They
might draw the reflected image incorrectly, perhaps by not maintaining the same
distance from the mirror line, or by not placing it directly opposite the original
shape with respect to the line.
In essence, the misconception stems from a misunderstanding of how reflection
works in geometry, leading to errors in the placement or orientation of the reflected
figure. Correcting this involves ensuring that each point of the original shape
is equidistant from the mirror line to its corresponding point on the reflected
side.'
- 'Believes that dividing by 100 gives 10%
The misconception described here is that someone might think dividing a number
by 100 results in getting 10% of that number. This is incorrect. Dividing a number
by 100 gives 1% of that number, not 10%. To get 10% of a number, you should divide
the number by 10. For example, if you have the number 200, dividing it by 100
gives 2, which is 1% of 200. To get 10%, you would divide 200 by 10, giving 20.'
- source_sentence: 'Subject: Time
Construct: Solve problems involving subtracting a period of time from a given
end time
Question: What time is \( 30 \) minutes before midnight?
Incorrect Answer: 11:30 am'
sentences:
- 'Thinks that times just before midnight are "am" times
The passage is discussing a common misconception about the timing just before
midnight. The misconception is that someone might incorrectly believe these times
are denoted as "am" (ante meridiem), when in fact, times just before midnight
are part of the "pm" (post meridiem) period. Midnight marks the transition from
"pm" to "am" — the period from midnight to noon is designated as "am", and from
noon to midnight, it is "pm". Therefore, the correct understanding is that the
times just before midnight are "pm" times, not "am".'
- 'Answers as if there are 100 minutes in an hour
The passage is indicating a common mistake where individuals incorrectly assume
there are 100 minutes in an hour, rather than the correct 60 minutes. This misconception
could arise in problems that require calculations involving time, leading to inaccurate
results. It''s important to remember there are 60 minutes in an hour to perform
calculations correctly.'
- 'Thinks measures of area must end in squared
The misconception described here is that some people believe the units of measurement
for area must always end in "squared," such as square meters, square feet, etc.
While it is true that area measurements are often expressed using squared units
(like square meters, m²), this is a specific case when the measurements are taken
in units like meters, feet, etc.
However, depending on the context and the system of measurement, area can be expressed
in units that do not explicitly end in "squared." For example, when measuring
land, units like acres or hectares are used, which are not expressed as squared
units but represent a specific area. An acre, for instance, is a unit of area
commonly used in English-speaking countries, and it equals 43,560 square feet.
In summary, while squared units are a common way to express area, it is incorrect
to assume that all units measuring area must end in "squared."'
- source_sentence: 'Subject: Quadratic Equations
Construct: Solve quadratic equations using factorisation in the form x(x + b)
Question: Solve this equation, giving all solutions:
\[
k^{2}=4 k
\]
Incorrect Answer: \( k=4 \)'
sentences:
- 'Believes they can divide by a variable without checking whether it could equal
zero
The misconception described here pertains to the process of solving algebraic
equations, particularly when dividing both sides of an equation by a variable.
The misconception is that one can divide by a variable without considering whether
that variable could potentially be zero.
In algebra, dividing both sides of an equation by a variable (let''s say \(x\))
is generally valid only if \(x \neq 0\). If \(x\) could be zero, then dividing
by \(x\) is not allowed because division by zero is undefined in mathematics.
This oversight can lead to losing a solution (specifically, \(x = 0\)) or deriving
incorrect conclusions.
For example, consider the equation \(x^2 = 3x\). If one incorrectly divides both
sides by \(x\) without checking whether \(x\) can be zero, they might reduce it
to \(x = 3\), thereby missing the solution \(x = 0\).
The correct approach would be to rearrange the equation to \(x^2 - 3x = 0\), factor
it to \(x(x - 3) = 0\), and then conclude that \(x = 0\) or \(x = 3\), thus ensuring
no solutions are lost.'
- 'Thinks tables of values are symmetrical about (0,0)
The misconception described here pertains to the assumption that all tables of
values representing a mathematical function or a set of data points are symmetrical
about the origin, which is the point (0,0) on the coordinate plane. This means
someone might incorrectly believe that for every value of \(x\), the corresponding
\(y\) value would be mirrored on the opposite side of the origin, like in the
case of the function \(y = x^3\), which is symmetrical about the origin.
However, not all tables of values are symmetrical about (0,0). Symmetry about
the origin is a specific property that only applies to certain types of functions,
particularly odd functions, where \(f(-x) = -f(x)\) for all \(x\) in the domain
of \(f\). Many other functions and sets of data points do not exhibit this symmetry.
For example, a parabola \(y = x^2\) is symmetrical, but not about the origin;
it is symmetrical along the y-axis. A linear function \(y = mx + b\), unless it
passes through (0,0) with \(b=0\), would not be symmetrical about the origin either.
Thus, one should not assume symmetry about (0,0) for any given set of data or
function without proper analysis or evidence that confirms this symmetry.'
- "When solving an equation, multiplies instead of dividing\nThe passage is highlighting\
\ a common mistake made when solving mathematical equations, where a student might\
\ mistakenly multiply when they should be dividing. This can happen in various\
\ contexts, such as solving for a variable in an equation or converting units.\
\ For example, if a problem requires you to divide both sides of an equation by\
\ a number to isolate the variable, mistakenly multiplying instead would lead\
\ to an incorrect solution. \n\nThe key here is to carefully read the problem,\
\ understand the operations needed, and apply the correct mathematical operations\
\ to solve the equation accurately."
- source_sentence: 'Subject: Construct Triangle
Construct: Construct a triangle using Side-Side-Side
Question: Tom and Katie are arguing about constructing triangles.
Tom says you can construct a triangle with lengths \( 11 \mathrm{~cm}, 10 \mathrm{~cm}
\) and \( 2 \mathrm{~cm} \).
Katie says you can construct a triangle with lengths \( 8 \mathrm{~cm}, 5 \mathrm{~cm}
\) and \( 3 \mathrm{~cm} \).
Who is correct?
Incorrect Answer: Neither is correct'
sentences:
- "Does not realise that the sum of the two shorter sides must be greater than the\
\ third side for it to be a possible triangle\nThe passage is discussing a common\
\ misconception about the properties required to form a triangle. The misconception\
\ is that one might think any three given side lengths can form a triangle. However,\
\ for three lengths to actually form a triangle, they must satisfy the triangle\
\ inequality theorem. This theorem states that the sum of the lengths of any two\
\ sides of a triangle must be greater than the length of the remaining side. This\
\ rule must hold true for all three combinations of added side lengths. \n\nTo\
\ apply this to the misconception: one does not realize that the sum of the lengths\
\ of the two shorter sides must be greater than the length of the longest side\
\ to form a possible triangle. This ensures that the sides can actually meet to\
\ form a closed figure with three angles."
- 'Does not know that a single letter labels a vertex
The passage is indicating a common misconception in geometry or graph theory,
where students or individuals may not understand that a single letter can be used
to label or identify a vertex (a corner or a point where lines or edges meet)
in a geometric shape or a graph.
Explanation: In mathematics, particularly in geometry and graph theory, vertices
(plural of vertex) are often labeled with single letters (like A, B, C, etc.)
to easily identify and discuss them. This labeling helps in referring to specific
points when describing shapes, calculating angles, distances, or when analyzing
the structure of graphs. The misconception arises when someone does not recognize
or utilize this convention, potentially leading to difficulties in understanding
problems or communicating solutions effectively.'
- 'Draws both angles at the same end of the line when constructing a triangle
The misconception described refers to a common error in geometry when students
are constructing a triangle based on given angles and a line segment. The mistake
is to draw both given angles at the same end of the given line segment. This is
incorrect because in a triangle, each angle is located at a different vertex,
and each vertex connects two sides. To correctly construct the triangle, each
given angle should be drawn at different ends of the line segment (if constructing
based on one line segment and two angles) or at vertices defined by the construction
steps (if additional sides are given). This ensures that the three angles are
positioned to form the corners of the triangle, with each angle at a distinct
vertex, thereby creating a proper triangle.'
pipeline_tag: sentence-similarity
library_name: sentence-transformers
---
# SentenceTransformer
This is a [sentence-transformers](https://www.SBERT.net) model trained. It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.
## Model Details
### Model Description
- **Model Type:** Sentence Transformer
- **Maximum Sequence Length:** 256 tokens
- **Output Dimensionality:** 384 dimensions
- **Similarity Function:** Cosine Similarity
### Model Sources
- **Documentation:** [Sentence Transformers Documentation](https://sbert.net)
- **Repository:** [Sentence Transformers on GitHub](https://github.com/UKPLab/sentence-transformers)
- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers)
### Full Model Architecture
```
SentenceTransformer(
(0): Transformer({'max_seq_length': 256, 'do_lower_case': False}) with Transformer model: BertModel
(1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
(2): Normalize()
)
```
## Usage
### Direct Usage (Sentence Transformers)
First install the Sentence Transformers library:
```bash
pip install -U sentence-transformers
```
Then you can load this model and run inference.
```python
from sentence_transformers import SentenceTransformer
# Download from the 🤗 Hub
model = SentenceTransformer("minsuas/Misconceptions_1")
# Run inference
sentences = [
'Subject: Construct Triangle\nConstruct: Construct a triangle using Side-Side-Side\nQuestion: Tom and Katie are arguing about constructing triangles.\n\nTom says you can construct a triangle with lengths \\( 11 \\mathrm{~cm}, 10 \\mathrm{~cm} \\) and \\( 2 \\mathrm{~cm} \\).\n\nKatie says you can construct a triangle with lengths \\( 8 \\mathrm{~cm}, 5 \\mathrm{~cm} \\) and \\( 3 \\mathrm{~cm} \\).\n\nWho is correct?\nIncorrect Answer: Neither is correct',
'Does not realise that the sum of the two shorter sides must be greater than the third side for it to be a possible triangle\nThe passage is discussing a common misconception about the properties required to form a triangle. The misconception is that one might think any three given side lengths can form a triangle. However, for three lengths to actually form a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This rule must hold true for all three combinations of added side lengths. \n\nTo apply this to the misconception: one does not realize that the sum of the lengths of the two shorter sides must be greater than the length of the longest side to form a possible triangle. This ensures that the sides can actually meet to form a closed figure with three angles.',
'Draws both angles at the same end of the line when constructing a triangle\nThe misconception described refers to a common error in geometry when students are constructing a triangle based on given angles and a line segment. The mistake is to draw both given angles at the same end of the given line segment. This is incorrect because in a triangle, each angle is located at a different vertex, and each vertex connects two sides. To correctly construct the triangle, each given angle should be drawn at different ends of the line segment (if constructing based on one line segment and two angles) or at vertices defined by the construction steps (if additional sides are given). This ensures that the three angles are positioned to form the corners of the triangle, with each angle at a distinct vertex, thereby creating a proper triangle.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]
# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
```
## Training Details
### Training Dataset
#### Unnamed Dataset
* Size: 17,405 training samples
* Columns: anchor
, positive
, and negative
* Approximate statistics based on the first 1000 samples:
| | anchor | positive | negative |
|:--------|:------------------------------------------------------------------------------------|:-------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|
| type | string | string | string |
| details |
Subject: Cubics and Reciprocals
Construct: Given a positive x value, find the corresponding y value for reciprocal graphs
Question: This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.1 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?
Incorrect Answer: \( 0.3 \)
| Multiplies instead of divides when division is written as a fraction
The passage is highlighting a common mistake students sometimes make when dealing with fractions in mathematics. This misconception occurs when a student encounters a fraction (which inherently involves a division operation, i.e., the numerator divided by the denominator) but instead of performing division, the student multiplies the numerator by the denominator. This misunderstanding can lead to incorrect solutions in problems where the correct interpretation and handling of fractions are crucial. For example, if presented with the fraction 8/2, the correct operation is to divide 8 by 2, resulting in 4, not to multiply 8 by 2, which would incorrectly yield 16.
| Forgets that a number divided by itself is 1
The passage is highlighting a common mistake made in mathematics where a student forgets the fundamental fact that any non-zero number divided by itself equals 1. For example, 5 divided by 5 is 1, or more generally, for any non-zero number n, n/n = 1. This principle is crucial for simplifying fractions, solving equations, and understanding basic arithmetic properties. Forgetting this can lead to errors in calculations and problem-solving scenarios.
|
| Subject: Angle Facts with Parallel Lines
Construct: Identify a transversal
Question: What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]()
Incorrect Answer: Parallel
| Does not know the meaning of the word parallel
The passage is indicating a misconception related to a math problem, specifically one that involves the concept of "parallel." In mathematics, particularly in geometry, "parallel" refers to lines or planes that are equidistant from each other at every point and never intersect, no matter how far they are extended. A misunderstanding or lack of knowledge about this definition can lead to errors when solving problems that involve parallel lines or planes, such as determining angles or distances. Thus, to correctly interpret and solve problems involving parallel lines or planes, one must understand that they maintain a constant distance from each other and never meet.
| Does not know the term transversal
The passage is indicating a common pitfall in geometry where a student may not be familiar with the term "transversal." A transversal is a line that passes through two or more other lines, often creating several angles with them. When discussing parallel lines and the angles formed when a transversal intersects them, understanding the term and its implications is crucial. The misconception here is likely that without knowing what a transversal is, a student might struggle to identify the relationships between the angles formed (such as alternate interior angles, corresponding angles, etc.), which are fundamental concepts in solving geometry problems involving parallel lines.
|
| Subject: Sharing in a Ratio
Construct: Divide a quantity into two parts for a given a ratio, where each part is an integer
Question: Share \( £360 \) in the ratio \( 2: 7 \)
Incorrect Answer: \( £ 180: £ 51 \)
| Divides total amount by each side of the ratio instead of dividing by the sum of the parts
The misconception described refers to a mistake made when dividing a total amount according to a given ratio. For instance, if someone has to divide $100 in the ratio 2:3, a correct approach would be to first add the parts of the ratio (2+3=5) to find the total number of parts. Then, divide the total amount by this sum ($100 ÷ 5 = $20) to determine the value of one part. This $20 can then be multiplied by each number in the ratio (2 and 3) to correctly distribute the $100.
The misconception occurs when someone divides the total amount ($100) by each individual number in the ratio (2 and 3) rather than by the sum of the parts (5). This method would incorrectly distribute the $100, as it does not account for the proportional relationship that the ratio is meant to establish.
| Estimates shares of a ratio instead of calculating
The passage is discussing a common mistake made in mathematics, particularly when dealing with ratio problems. The misconception lies in estimating the shares or parts of a ratio rather than calculating them accurately. For example, if a problem involves dividing a quantity in the ratio of 2:3, the misconception would be to guess or estimate what parts of the quantity correspond to 2 and 3, instead of using the correct method to find the exact shares. The correct approach involves first adding the parts of the ratio (in this case, 2 + 3 = 5) and then using this sum to calculate each part's exact share of the total quantity. Thus, it's important to calculate each part of the ratio precisely rather than estimating.
|
* Loss: [CachedMultipleNegativesRankingLoss
](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#cachedmultiplenegativesrankingloss) with these parameters:
```json
{
"scale": 20.0,
"similarity_fct": "cos_sim"
}
```
### Training Hyperparameters
#### Non-Default Hyperparameters
- `per_device_train_batch_size`: 512
- `num_train_epochs`: 1
- `lr_scheduler_type`: cosine
- `warmup_ratio`: 0.1
- `fp16`: True
#### All Hyperparameters