Among historians today, is there an agreed upon historical method used to investigate a topic in the way that mathematics or science has?

One important point is that neither science nor mathematics has agreed-upon methods. While there is a commonly taught "scientific method", it is a poor representation of how science is done. Worse, some of the "steps" in the usual version:

1. Define a question

2. Observe/measure

3. Form a hypothesis

4. Experimentally test the hypothesis

5. Return to 3 if necessary

are not usefully reducible to steps in a method. For example, it's easy to say "form a hypothesis", but very difficult, if even possible, to say how to go about doing it. It is also very difficult to say when a hypothesis should be accepted (to the point that some philosophers of science say that the best that can be done is to falsify a hypothesis).

For more on the scientific method, or the lack thereof, see:

• Paul Feyerabend, Against Method - there are various editions; any will do for a start.

Mathematics is an entirely different beast from science. Theories and hypotheses in science are never certain - they are tentative conclusions subject to revision. Mathematics runs on proof - things can be known to be absolutely true (give or take some things that it has been proved cannot be proved).

And if so, why isn’t it taught in schools?

Historical method has a lot in common with scientific method, including the difficulty of reduction to a simple recipe. Science students are taught, in addition to the current body of science, some of the methods of science. This includes basic tools such as experimental methods, mathematical methods, and so on. Perhaps the things that they are taught that are most relevant to the practice of science include:

1. Evaluation of the quality of research papers.

2. Data analysis, including judgment of the quality of the data.

Still, even though these things are taught in school and to university undergraduates, science researchers typically begin gaining their real knowledge of how to do scientific research (i.e., apply the scientific method) when they start doing research (e.g., honours/masters research projects, and their PhD).

What are history students taught? Relevant to historical method are:

1. How to find sources.

2. How to evaluate sources.

3. How to construct a good argument from the sources.

None of these are simple. However, it can be reasonably argued that the common assessment task for history students - writing essays - is better training in historical method than typical assessment tasks for science students are for training them in scientific method. Despite this, I wouldn't be surprised if the typical beginning history PhD student gets the same rude shock that the typical beginning science PhD students gets about how poorly prepared they are to do research.

Research, whether historical or scientific, is difficult to teach in checklist/recipe manner. For good reason, both are traditionally taught via a long apprenticeship (centred on the PhD).

This seems like a particularly important question right now, given the massive amount of disinformation and conspiracy theories.

Evaluating potentially-disinformative claims can be usefully taught, both concerning science and history, more easily than scientific/historical method. Unfortunately, recognising and evaluating potential pseudo-science and pseudo-history doesn't easily fit into traditional curricula and courses.